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Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber
Jupiter Images
Photo Credits Cover, i Jupiter Images; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 1 2 3 4 6 7 8 9 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo; vii CORBIS; viii Mitchell Funk/Getty Images; ix S. Alden/PhotoLink/Getty Images; x Peter Barritt/Alamy; 2–3 Getty Images; 3 (t)Getty Images, (b)The McGraw-Hill Companies, Inc./Bob Coyle, photographer; 16 Bettmann/CORBIS; 30 Mark Ransom/RansomStudios; 32 Masterfile; 37 Getty Images; 45 CORBIS; 51 Jupiter Images; 54–55 Arnulf Husmo/Getty Images; 55 CORBIS; 56 Keith Ovregaard/Cole Group/Getty Images; 57 (l)Photodisc/Getty Images, (r)CORBIS; 58 Mark Ransom/ RansomStudios; 59 John A. Rizzo/Getty Images; 60 (t)Jules Frazier/Getty Images, (b)Mark Ransom/RansomStudios; 67 CORBIS; 76 Gary Cralle/Getty Images; 82 (t)Getty Images, (b)Lawrence Manning/CORBIS; 83 GK & Vikki Hart/Getty Images; 89 (frame)Getty Images, (insert)Mark Ransom/RansomStudios
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-878213-8 MHID: 0-07-878213-9 Printed in the United States of America. 1 2 3 4 5 6 7 8 9 10 055/027 16 15 14 13 12 11 10 09 08 07
California Math Triumphs Volume 6A
California Math Triumphs Volume 1 Place Value and Basic Number Skills 1A Chapter 1 Counting 1A Chapter 2 Place Value 1A Chapter 3 Addition and Subtraction 1B Chapter 4 Multiplication 1B Chapter 5 Division 1B Chapter 6 Integers Volume 2 Fractions and Decimals 2A Chapter 1 Parts of a Whole 2A Chapter 2 Equivalence of Fractions 2B Chapter 3 Operations with Fractions 2B Chapter 4 Positive and Negative Fractions and Decimals
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Volume 3 Ratios, Rates, and Percents 3A Chapter 1 Ratios and Rates 3A Chapter 2 Percents, Fractions, and Decimals 3B Chapter 3 Using Percents 3B Chapter 4 Rates and Proportional Reasoning Volume 4 The Core Processes of Mathematics 4A Chapter 1 Operations and Equality 4A Chapter 2 Math Fundamentals 4B Chapter 3 Math Expressions 4B Chapter 4 Linear Equations 4B Chapter 5 Inequalities Volume 5 Functions and Equations 5A Chapter 1 Patterns and Relationships 5A Chapter 2 Graphing 5B Chapter 3 Proportional Relationships 5B Chapter 4 The Relationship Between Graphs and Functions Volume 6 Measurement 6A Chapter 1 How Measurements Are Made 6A Chapter 2 Length and Area in the Real World 6B Chapter 3 Exact Measures in Geometry 6B Chapter 4 Angles and Circles iii
Authors and Consultants AUTHORS
Frances Basich Whitney
Kathleen M. Brown
Dixie Dawson
Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California
Math Curriculum Staff Developer Washington Middle School Long Beach, California
Math Curriculum Leader Long Beach Unified Long Beach, California
Philip Gonsalves
Robyn Silbey
Kathy Vielhaber
Mathematics Coordinator Alameda County Office of Education Hayward, California
Math Specialist Montgomery County Public Schools Gaithersburg, Maryland
Mathematics Consultant St. Louis, Missouri
Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California
Dinah Zike Educational Consultant, Dinah-Might Activities, Inc. San Antonio, Texas
CONSULTANTS Assessment Donna M. Kopenski, Ed.D. Math Coordinator K–5 City Heights Educational Collaborative San Diego, California
Instructional Planning and Support
ELL Support and Vocabulary
Beatrice Luchin
ReLeah Cossett Lent
Mathematics Consultant League City, Texas
Author/Educational Consultant Alford, Florida
iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
CONTRIBUTING AUTHORS
California Advisory Board CALIFORNIA ADVISORY BOARD
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program. They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan.
Linda Anderson
Cheryl L. Avalos
Bonnie Awes
Kathleen M. Brown
4th/5th Grade Teacher Oliveira Elementary School, Fremont, California
Mathematics Consultant Retired Teacher Hacienda Heights, California
Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California
Math Curriculum Staff Developer Washington Middle School Long Beach, California
Carol Cronk
Audrey M. Day
Jill Fetters
Grant A. Fraser, Ph.D.
Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California
Classroom Teacher Rosa Parks Elementary School San Diego, California
Math Teacher Tevis Jr. High School Bakersfield, California
Professor of Mathematics California State University, Los Angeles Los Angeles, California
Eric Kimmel
Donna M. Kopenski, Ed.D.
Michael A. Pease
Chuck Podhorsky, Ph.D.
Mathematics Department Chair Frontier High School Bakersfield, California
Math Coordinator K–5 City Heights Educational Collaborative San Diego, California
Instructional Math Coach Aspire Public Schools Oakland, California
Math Director City Heights Educational Collaborative San Diego, California
Arthur K. Wayman, Ph.D.
Frances Basich Whitney
Mario Borrayo
Melissa Bray
Professor Emeritus California State University, Long Beach Long Beach, California
Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA
Teacher Rosa Parks Elementary San Diego, California
K–8 Math Resource Teacher Modesto City Schools Modesto, California
v (L to R 1 2 3 4 6 7 8 9 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo
California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction. Melody McGuire
Math Teacher California College Preparatory Academy Oakland, California
6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California
Eppie Leamy Chung
Monica S. Patterson
Teacher Modesto City Schools Modesto, California
Educator Aspire Public Schools Modesto, California
Judy Descoteaux
Rechelle Pearlman
Mathematics Teacher Thornton Junior High School Fremont, California
4th Grade Teacher Wanda Hirsch Elementary School Tracy, California
Paul J. Fogarty
Armida Picon
Mathematics Lead Aspire Public Schools Modesto, California
5th Grade Teacher Mineral King School Visalia, California
Lisa Majarian
Anthony J. Solina
Classroom Teacher Cottonwood Creek Elementary Visalia, California
Lead Educator Aspire Public Schools Stockton, California
vi
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Bobbi Anne Barnowsky
Volume 6A Measurement Chapter
How Measurements Are Made
1
1-1 Unit Conversions: Metric Length ...................................4. 3AF1.4, 3MG1.4, 6AF2.1
1-2 Unit Conversions: Customary Length .........................11 3AF1.4, 3MG1.4, 6AF2.1
Progress Check 1 .............................................................18 1-3 Unit Conversions: Metric Capacity and Mass ............19 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1
1-4 Unit Conversions: Customary Capacity and Weight… ...................................................................25 3AF1.4, 3MG1.4, 6AF2.1
Progress Check 2 .............................................................32 1-5 Time and Temperature ...................................................33 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1
1-6 Analyze Units of Measure .............................................39
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6AF2.1, 7MG1.1, 7MG1.3
Progress Check 3 .............................................................46 Assessment Study Guide .....................................................................47
Chapters 1 and 2 are contained in Volume 6A. Chapters 3 and 4 are contained in Volume 6B.
Standards Addressed in This Chapter 3AF1.4 Express simple unit conversions in symbolic form (e.g., ___ inches = ___ feet × 12). 3MG1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes). 6AF2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems. (e.g., miles per hour and feet per second, cubic inches to cubic centimeters) 7MG1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
Chapter Test .....................................................................50 Standards Practice ...................................................52
Lake Tahoe
vii CORBIS
Contents Chapter
Length and Area in the Real World
2
Standards Addressed in This Chapter 2-1 Length ..............................................................................56 2MG1.3, 4MG2.2, 4MG2.3
2-2 Perimeter ..........................................................................63 3MG1.3
Progress Check 1 .............................................................70 2-3 Introduction to Area .......................................................71 3MG1.2
2-4 Introduction to Volume ................................................. 77 3MG1.2
Progress Check 2 .............................................................83 Assessment
2MG1.3 Measure the length of an object to the nearest inch and/or centimeter. 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 3MG1.3 Find the perimeter of a polygon with integer sides. 4MG2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates. 4MG2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates.
Study Guide .....................................................................84 Chapter Test .....................................................................88 Standards Practice ...................................................90
Mitchell Funk/Getty Images
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
viii
Alamo Square, San Francisco
Contents Chapter
Exact Measures in Geometry
3
3-1 Area of a Rectangle ..........................................................4 3MG1.2, 4MG1.1
3-2 Area of a Parallelogram..................................................11 4MG1.1, 5MG1.1
Progress Check 1 .............................................................18 3-3 Area of a Triangle ............................................................19 3MG1.2, 5MG1.1
3-4 Surface Area of Rectangular Solids ............................. 27 3MG1.2, 4MG1.1, 5MG1.2
Progress Check 2 .............................................................36 3-5 Volume of Rectangular Solids .......................................37 3MG1.2, 5MG1.3
Assessment
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Study Guide .....................................................................43 Chapter Test .....................................................................48 Standards Practice ...................................................50 Santa Cruz
Chapters 1 and 2 are contained in Volume 6A. Chapters 3 and 4 are contained in Volume 6B.
Standards Addressed in This Chapter 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them. 4MG1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in.2), square yard (yd.2), or square mile (mi.2). 5MG1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing each with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by pasting and cutting a right triangle on the parallelogram). 5MG1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to complete the surface area for these objects. 5MG1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in.3], cubic yard [yd.3]) to compute the volume of rectangular solids.
ix S. Alden/PhotoLink/Getty Images
Contents Chapter
Angles and Circles
4
Standards Addressed in This Chapter 4-1 Lines 5MG2.1 ....................................................................54 4-2 Angles 5MG2.1 .................................................................63 Progress Check 1.............................................................72 4-3 Triangles and Quadrilaterals 5MG2.1 ...........................73 4-4 Add Angles 5MG2.1, 5MG2.2, 6MG2.2 ............................. 81 Progress Check 2.............................................................90 4-5 Congruent Figures 7MG3.4 ............................................91 4-6 Pythagorean Theorem 5MG2.1, 7MG3.3 ........................ 99 Progress Check 3...........................................................108 4-7 Circles 6MG1.2 ...............................................................109 4-8 Volume of Triangular Prisms and Cylinders ........... 117 6MG1.3
Progress Check 4...........................................................127
Study Guide ..................................................................128 Chapter Test ..................................................................134 Standards Practice.................................................136 Mono Lake Tufa State Reserve
5MG2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems. 6MG1.2 Know common estimates 22 of π (3.14, ___) and use these values to 7 estimate and calculate the circumference and the area of circles; compare with actual measurements. 6MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. 7MG3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 7MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures.
x Peter Barritt/Alamy
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Assessment
5MG2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straight edge, ruler, compass, protractor, drawing software).
R E G N E V A SC HUNT Let’s Get Started Use the Scavenger Hunt below to learn where things are located in each chapter.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1 What is the title of Chapter 2?
2
What is the Key Concept of Lesson 2-2?
3
On which pages are the Chapter 1 Test?
4
What are the vocabulary words for Lesson 1-4?
5
How many Examples are presented in Lesson 1-6?
6
Which California Standards are covered in Lesson 2-4?
7
Look at the table on page 11. What is a real-world benchmark for one inch?
8
What do you think is the purpose of the Standards Practice on p. 52?
9
On what pages will you find the Study Guide for Chapter 2?
10
In Chapter 2, find the Internet address that tells you where you can take the Online Readiness Quiz. 1
Chapter
1
How Measurements Are Made How tall are you? How much does your dog weigh? How far do you travel to school? These questions ask for measurements of weight and length. Other measurements include capacity, time, and temperature.
Copyright © by The McGraw-Hill Companies, Inc.
2
Chapter 1 How Measurements Are Made
Getty Images
STEP
STEP
1 Quiz
2 Preview
Are you ready for Chapter 1? Take the Online Readiness Quiz at ca.mathtriumphs.com to find out. Get ready for Chapter 1. Review these skills and compare them with what you’ll learn in this chapter.
What You Know
What You Will Learn
You know how to multiply and divide by powers of ten.
Lessons 1-1 and 1-3
Examples:
4 × 1,000 = 4,000 300 ÷ 100 = 3
The metric system is a measurement system in which units differ from the base unit by a power of ten.
Copyright © by The McGraw-Hill Companies, Inc.
TRY IT! 1
5 × 100 =
2
7 × 10,000 =
3
12 × 100,000 =
4
90,000 ÷ 10 =
5
24 ÷ 100 =
6
15 ÷ 10,000 =
You know how to multiply and divide. Examples:
3 × 12 = 36 20 ÷ 4 = 5
TRY IT! 7
4 × 12 =
8
36 × 3 =
9
32 × 14 =
10
64 ÷ 16 =
11
288 ÷ 16 =
12
768 ÷ 128 =
1l
1,000 ml
1 liter of juice = 1,000 milliliters of juice So, 4 liters of juice = 4 × 1,000, or 4,000 milliliters of juice.
Lessons 1-2 and 1-4 The customary system of measurement uses units such as foot and quart. You multiply or divide to change units.
1 foot = 12 inches So, 3 feet = 3 × 12, or 36 inches. 4 quarts = 1 gallon So, 20 quarts = 20 ÷ 4, or 5 gallons.
3 (bkgd t)Getty Images, (b)The McGraw-Hill Companies, Inc./Bob Coyle, photographer
Lesson
1-1 Unit Conversions:
3AF1.4 Express simple unit conversions in symbolic form. 3MG1.4 Carry out simple unit conversions within a system of measurement. 6AF2.1 Convert one unit of measurement to another.
Metric Length KEY Concept Prefixes used for units of metric measurement always have the same meaning. The meter is the basic unit of length in the metric system . Each prefix shows the size of a unit compared to a meter. Prefix milli centi deci
kilo
Meaning
Metric Unit
Symbol
onemillimeter thousandth onecentimeter hundredth
mm cm
one-tenth
decimeter
dm
one
meter
m
one thousand
kilometer
km
VOCABULARY metric system a measurement system that includes units such as meter, kilogram, and liter
Real-World Benchmark thickness of a dime width of a paper clip length of a crayon length of a baseball bat length of 10 football fields
meter the standard unit of measurement for length in the metric system benchmark an object or number used as a guide to estimate or reference convert to switch or exchange for something equal in value
Use a ruler to help you understand how the units of length compare. 1 dm
1 mm
0 dm
1
4
Chapter 1 How Measurements Are Made
1
0.1
ones
tenths
0.01 0.001 thousandths
10
hundredths
100
tens
To convert a smaller unit to a larger unit, you should divide.
1000
hundreds
To convert a larger unit to a smaller unit, you should multiply.
thousands
Sometimes it is necessary to convert from one unit of measurement to another. Prefixes can help you understand the relationship between the two units. A metric place-value chart can also be useful.
Copyright © by The McGraw-Hill Companies, Inc.
1 cm
Example 1
YOUR TURN!
Convert 6 centimeters to meters.
Convert 3 millimeters to meters.
1. Use a chart. Place 6 in the cm column.
1. Use a chart. Place mm column.
2. Place zeros in the m and dm columns.
tenths
hundredths
deci (dm)
centi (cm)
0.01 0.001 thousandths
ones meters (m)
0.1
milli (mm)
1
thousands
centi (cm)
The chart is set up this way because a centimeter 1 1 is ____ of a meter. A decimeter is ___ of a meter. 100 10
1000
kilo (km)
6
thousandths
hundredths
0
milli (mm)
tenths
0
deci (dm)
0.01 0.001
ones
kilo (km)
0.1
meters (m)
1
thousands
1000
in the
2. Place zeros in the m, dm, and cm columns. 3. Read the number from the chart for the conversion. 3 cm = m
2. Place zeros in the columns between 5 and the decimal point. 3. Read the number from the chart for the conversion. 4.5 km = 4,500 m
hundredths
1. Use a chart. Place column and
0.01 0.001
milli (mm)
thousandths
0.1
centi (cm)
0
1
meters (m)
thousandths milli (mm)
0.01 0.001
1000
kilo (km)
hundredths centi (cm)
0
tenths
5
0.1
deci (dm)
4
1
meters (m)
thousands
1000
ones
1. Use a chart. Place 4 in the km column and 5 in the next column to the right.
tenths
Convert 8.2 decimeters to meters.
deci (dm)
Convert 4.5 kilometers to meters.
ones
YOUR TURN!
thousands
Example 2
kilo (km)
Copyright © by The McGraw-Hill Companies, Inc.
3. Read the number from the chart for the conversion. 6 cm = 0.06 m
in the dm in the cm column.
2. Place a zero in the
column.
3. Read the number from the chart for the conversion. 8.2 dm =
m
GO ON
Lesson 1-1 Unit Conversions: Metric Length
5
Example 3 Complete the conversions using the Metric Equivalents table below. kilometers (km)
meters (m) decimeters (dm) centimeters (cm) millimeters (mm)
1 km =
1,000 m =
10,000 dm =
100,000 cm =
1,000,000 mm
0.001 km =
1m=
10 dm =
100 cm =
1,000 mm
0.00001 km =
0.01 m =
0.1 dm =
1 cm =
10 mm
0.000001 km =
0.001 m =
0.01 dm =
0.1 cm =
1 mm
Convert from 8 meters to kilometers using division. You are converting from a smaller unit to a larger unit, so you divide. 8m=
km
YOUR TURN! Convert from 8 meters to centimeters using multiplication. You are converting from a 8m=
unit to a
unit, so you
.
cm
Who is Correct? Convert 7.3 meters to millimeters.
7.3 × 10,000 = 73,000 mm
Marcus
Silo
7.3 ÷ 1,000 = 0.0073 mm
7.3 × 1,000 = 7,300 mm
tenths
hundredths
thousandths
centi (cm)
milli (mm)
m
deci (dm)
4 km =
0.1
kilo (km)
1
1
ones
Convert using a place-value chart.
1000
meters (m)
Guided Practice
thousands
Circle correct answer(s). Cross out incorrect answer(s).
6
Chapter 1 How Measurements Are Made
0.01 0.001
Copyright © by The McGraw-Hill Companies, Inc.
Lana
0.1
tenths
hundredths
thousandths
centi (cm)
milli (mm)
kilo (km)
1
deci (dm)
1000
ones
m
meters (m)
3 dm =
thousands
2
0.01 0.001
Step by Step Practice Convert. 3
9m=
mm millimeters is equal to 1 meter.
Step 1
Step 2 You are converting from a unit, so you
unit to a .
Step 3 Convert. 1,000 =
9
Copyright © by The McGraw-Hill Companies, Inc.
9m=
mm
Convert. 4
5m=
cm
1m=
cm
5
Multiply or divide? 5 5m=
8m=
km
1 km =
m
Multiply or divide?
100 =
1,000 =
8 8m=
cm
km
6
6.5 cm =
m
7
0.4 m =
8
0.7 cm =
m
9
5.1 mm =
10
15 mm =
11
4m=
km
12
34 dm =
13
2 km =
m
cm m
dm cm
GO ON
Lesson 1-1 Unit Conversions: Metric Length
7
Step by Step Problem-Solving Practice
Problem-Solving Strategies Draw a diagram.
Solve. 14
SPORTS A soccer field is 120 meters long. How many decimeters long is a soccer field?
✓ Look for a pattern.
Understand
Read the question. Write what you know. A soccer field is meters long.
Plan
Pick a strategy. One strategy is to look for a pattern.
Act it out. Solve a simpler problem. Work backward.
decimeters is equal to 1 meter. Find a rule. One rule is to add . The pattern begins with the numbers 10, 20, and 30. Continue the pattern until the final term is 120.
Solve
10, 20, 30, The number 120 is the The soccer field is
Plan Solve Check
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
SEWING Frances bought 1,850 millimeters of ribbon to make a pillow. The pillow required 170 centimeters of ribbon. In centimeters, how much extra ribbon is left? Check off each step. Understand
8
decimeters long.
Think: Decimeters are a smaller unit of measure than meters, so the number of decimeters of a soccer field is greater than the number of meters. The answer makes sense.
Check
15
term.
16
SHOES The sales clerk measured Wayne’s foot to be 2.4 decimeters long. How many millimeters long is Wayne’s foot?
17
Is 600 millimeters equal to 6 meters? Explain.
Skills, Concepts, and Problem Solving Convert using a place-value chart.
thousandths milli (mm)
hundredths
tenths deci (dm)
centi (cm)
ones meters (m)
6 dm =
0.01 0.001
1
0.1
hundredths centi (cm)
0.01 0.001
milli (mm)
thousandths
1000
tenths
m
deci (dm)
thousandths milli (mm)
0.1
ones
hundredths centi (cm)
1
meters (m)
tenths deci (dm)
1000
kilo (km)
ones
0.01 0.001
m
thousands
thousandths milli (mm)
0.1
meters (m)
thousands
21
1
6 km =
kilo (km)
hundredths centi (cm)
cm
1000
19
0.01 0.001
tenths
ones
7m=
kilo (km)
Copyright © by The McGraw-Hill Companies, Inc.
20
0.1
deci (dm)
1
meters (m)
1000 thousands
m
thousands
7 cm =
kilo (km)
18
Convert. 70 m =
22
dm 23
94.5 cm =
m 24
46.4 mm =
cm
25
360 m =
GO ON
Lesson 1-1 Unit Conversions: Metric Length
9
km Convert. 26
0.2 cm =
28
4.3 m =
30
2.9 dm =
32
9,100 mm =
dm
27
530 mm =
cm
mm
29
0.035 km =
m
cm
31
6.4 cm =
m
33
14 cm =
mm
m
Solve. TRAVEL It is 49 kilometers from Jesse’s house to his grandmother’s house. How many meters is it to Jesse’s grandmother’s house?
35
AIRPLANES Hernando’s paper airplane traveled 3,400 centimeters. How many meters did it travel?
36
PETS Ginny’s cat was found wandering around a park that was 2,200 meters from her home. How many kilometers away was Ginny’s cat?
37
TRAVEL Ataro passed a sign that said “Albany 192 km.” How many meters did he have left to drive?
Vocabulary Check sentence.
Write the vocabulary word that completes each
38
The system is a measurement system that includes units such as meter, gram, and liter.
39
A is the standard unit of measurement for length in the metric system.
40
Writing in Math
10
Chapter 1 How Measurements Are Made
Explain how to convert 5.2 meters to centimeters.
Copyright © by The McGraw-Hill Companies, Inc.
34
Lesson
1-2 Unit Conversions:
3AF1.4 Express simple unit conversions in symbolic form. 3MG1.4 Carry out simple unit conversions within a system of measurement. 6AF2.1 Convert one unit of measurement to another.
Customary Length KEY Concept Unit for Length inch
Abbreviation
Equivalents
in.
foot
ft
yard
yd
mile
mi
1 ft = 12 in. 1 yd = 3 ft 1 yd = 36 in. 1 mi = 1,760 yd 1 mi = 5,280 ft
Real-World Benchmark small paper clip
VOCABULARY customary system a measurement system that includes units such as foot, pound, and quart
standard ruler baseball bat
benchmark an object or number used as a guide to estimate or reference
about 8 city blocks
Use the last column of the table to help you understand the relative size of a unit by comparing it to everyday objects.
convert to switch or exchange for something equal in value
Use a ruler to see how the units of length compare.
(Lesson 1-1, p. 4)
Copyright © by The McGraw-Hill Companies, Inc.
0 in.
1
2
3
Sometimes it is necessary to convert from one unit of measure to another. Knowing customary conversions can help you understand the relationship between two units.
Example 1
YOUR TURN!
Convert 60 inches to feet using a table.
Convert 15 feet to yards using a table.
feet
1
2
3
4
5
yards
inches
12
24
36
48
60
feet
1. There are 12 inches in 1 foot. 2. Fill in the table. 2 feet = 2 × 12 inches 3 feet = 3 × 12 inches 4 feet = 4 × 12 inches 5 feet = 5 × 12 inches 60 inches is equal to 5 feet.
3
6
9
12
15
1. There are 3 feet in 1 yard. Enter the number of feet in the chart by using multiples of three. 2. Fill in the table. feet is equal to 5 yards. GO ON Lesson 1-2 Unit Conversions: Customary Length
11
To convert a larger unit to a smaller unit, multiply. To convert a smaller to a larger unit, divide.
Example 2
YOUR TURN! Convert 156 inches to feet.
Convert 7 yards to feet.
1. You are converting from inches to feet, which is a smaller unit to a larger unit. You should .
1. You are converting from yards to feet, which is a larger unit to a smaller unit. You should multiply.
2.
2. 1 yard is equal to 3 feet. So, 7 yards is equal to 3 × 7, or 21 feet.
inches are equal to foot.
So, 156 inches is equal to ÷ or
, feet.
Who is Correct? Convert 48 inches to feet.
Lucita
12 inches is equal to 1 foot. 48 × 12 = 576 feet
Graham
12 inches is equal to 1 foot. 48 ÷ 12 = 4 feet
3 feet is equal to 1 yard and 12 inches is equal to 1 foot. 48 ÷ 3 = 16 feet
Circle correct answer(s). Cross out incorrect answer(s).
Guided Practice Convert using a table. 1
6 yd =
in.
yards
1
2
3
4
5
inches
2
4 mi =
yd
miles yards
12
Chapter 1 How Measurements Are Made
1
2
3
4
6
Copyright © by The McGraw-Hill Companies, Inc.
Ohin
Step by Step Practice Convert. 3
9 yd =
ft
Step 1 You are converting from a unit, so you should Step 2 1 yard is equal to Step 3 So, 9 yards are 9
unit to a .
feet. 3, or
feet.
Convert. 4
2 mi =
ft
1 mi =
ft
5
1 ft =
Multiply or divide? 2
Copyright © by The McGraw-Hill Companies, Inc.
2 mi =
72 in. =
ft in.
Multiply or divide?
5,280 =
72
12 =
72 in. =
ft
7
3 mi =
yd
ft
6
8,800 yd =
8
5 yd =
ft
9
4.5 mi =
10
9 yd =
ft
11
1 mi =
in.
12
72 in. =
ft
13
15 ft =
in.
14
1.5 ft =
in.
15
0.5 ft =
in.
16
90 in. =
yd
17
112 ft =
yd
mi
ft
GO ON Lesson 1-2 Unit Conversions: Customary Length
13
Step by Step Problem-Solving Practice
Problem-Solving Strategies Draw a diagram. Look for a pattern. Guess and check. Solve a simpler problem. ✓ Work backward.
Solve. 18
HOMES The bedroom in Teri’s apartment is 144 inches long. How many yards long is the room? Understand
Read the question. Write what you know. A bedroom is inches long.
Plan
Pick a strategy. One strategy is to work backward. You know the total number of inches. Subtract repeatedly until the answer is 0. Count the number of times you subtracted 36. 144
Solve
- 36 =
yard
- 36 =
yards
- 36 =
yards
- 36 =
yards
The room is
SCHOOL Ina’s desk is 42 inches wide. How many feet wide is her desk? Check off each step. Understand Plan Solve Check
20
21
14
SPORTS During Saturday’s football game, James set the school record by running 96 yards to score a touchdown. How many feet did James run for the touchdown? Is 108 inches equal to 9 feet? Explain.
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
Think: An inch is a smaller unit of measure than a yard. So the number of inches should be greater than the number of yards. The answer makes sense.
Check
19
yards long.
Skills, Concepts, and Problem Solving Convert using a table. 22
8 ft =
in.
feet
1
2
3
4
5
6
7
8
inches
23
4 yd =
in.
yards
1
2
3
4
inches
Copyright © by The McGraw-Hill Companies, Inc.
Convert. 24
2 mi =
26
26,400 ft =
28
360 in. =
yd
30
1,821 ft =
yd
32
45 ft =
34
What are the dimensions of the toy chest in inches?
in. mi
yd
1 ft =
TOYS 2 ft
1 ft
1.5 ft = 2 ft =
25
39 ft =
yd
27
10 mi =
ft
29
17,600 yd =
31
17 yd =
in.
33
2.5 yd =
in.
mi
in. in. in.
1.5 ft
GO ON Lesson 1-2 Unit Conversions: Customary Length
15
Solve. 35
RACES Carla measured a bicycle course in her neighborhood. It was 7,040 yards. How many miles was the bicycle course?
36
HISTORY One of the largest balls of string is in Branson, Missouri. How many inches is the circumference of the ball of string? 41.5 ft
37
DECORATING Olivia is redecorating her bedroom. She measured the length as 138 inches. She measured the width as 114 inches. What are the dimensions of Olivia’s room in feet?
38
SCHOOL At Wakefield Junior High School during a fire drill, students have to go to the football field and stand single-file in lines. One line was 12 feet long. Another line was 15 feet long. A third line was 24 feet long. How many yards were the lines formed by the students?
Write the vocabulary word that completes each
39
The system is a measurement system that includes units such as foot, pound, and quart.
40
To means to switch or exchange for something equal in value.
41
A(n) to estimate or reference.
42
Writing in Math
16
Chapter 1 How Measurements Are Made
Bettmann/CORBIS
is an object or number used as a guide
Explain how to convert 288 inches to yards.
Copyright © by The McGraw-Hill Companies, Inc.
Vocabulary Check sentence.
Spiral Review
Copyright © by The McGraw-Hill Companies, Inc.
Convert.
14 mm =
thousandths
tenths deci (dm)
0.01 0.001
milli (mm)
0.1
hundredths
1
centi (cm)
1000
ones
m
meters (m)
thousandths milli (mm)
tenths deci (dm)
0.01 0.001 hundredths
0.1
44
centi (cm)
1
ones
kilo (km)
thousands
1000
m
kilo (km)
8 dm =
meters (m)
43
(Lesson 1-1, pp. 4–10)
thousands
Convert using a place-value chart.
(Lesson 1-1, pp. 4–10)
45
980 km =
m
46
85.2 cm =
47
0.32 m =
cm
48
600 m =
49
0.05 dm =
cm
50
0.306 cm =
mm
51
9.07 mm =
cm
52
1,405 dm =
km
53
120 mm =
cm
54
0.05 m =
55
1,540 m =
km
56
0.75 km =
57
What are the dimensions of the book in centimeters?
258 mm 30 mm 206 mm
Solve. 58
258 mm =
cm
206 mm =
cm
30 mm =
m km
cm m
cm
(Lesson 1-1, pp. 4–10)
ADVERTISING Keeley placed an ad in the newspaper. The ad could be no longer than 75 millimeters long. How many centimeters long could the ad be?
Lesson 1-2 Unit Conversions: Customary Length
17
Chapter
Progress Check 1
1
(Lessons 1-1 and 1-2)
Convert using a place-value chart. 45 mm =
thousandths milli (mm)
tenths deci (dm)
0.01 0.001 hundredths
0.1
centi (cm)
1
ones
thousands kilo (km)
thousandths milli (mm)
tenths
m
1000
0.01 0.001 hundredths
0.1
centi (cm)
1
deci (dm)
2
ones
thousands kilo (km)
ten thousands
10,000 1000
m
meters (m)
15 km =
meters (m)
1
Convert using a table. 3
3 mi =
in.
miles
1
2
3
inches
4
15 ft =
yd
yards feet
3
6
9
12
15
5
0.68 cm =
dm
6
155 mm =
m
7
301 dm =
mm
8
1,800 m =
km
9
12 yd =
in.
10
2 mi =
yd
11
96 in. =
ft
12
42 ft =
yd
Solve. 13
LAND The road on Rachel’s farm is 5,960 meters long. How many kilometers long is the road?
14
NUMBER SENSE The community pool measures 25 yards long. How many inches long is the pool?
18
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
Convert.
Lesson
1-3 Unit Conversions: Metric Capacity and Mass KEY Concept Prefixes used for standard units of measurement in the metric system always have the same meaning. The base unit of capacity in the metric system is the liter . Metric Units for Capacity Unit for Abbreviation Capacity milliliter mL liter
L
kiloliter
kL
Equivalents 1 mL = 0.001 L
1 kL = 1,000 L
Real-World Benchmark drop of water sports water bottle bathtub filled with water
The base unit of mass is the gram . Metric Units for Mass
Copyright © by The McGraw-Hill Companies, Inc.
Unit for Abbreviation Capacity milligram mg gram
g
kilogram
kg
Equivalents 1 mg = 0.001 g
Real-World Benchmark grain of salt paper clip
1 kg = 1,000 g
3AF1.4 Express simple unit conversions in symbolic form. 3MG1.4 Carry out simple unit conversions within a system of measurement. 6AF2.1 Convert one unit of measurement to another. 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems.
VOCABULARY metric system a measurement system that includes units such as meter, gram, and liter (Lesson 1-1, p. 4)
capacity the amount of dry or liquid material a container can hold liter a metric unit for measuring volume or capacity mass the amount of matter in an object gram a metric unit for measuring mass
watermelon
Sometimes it is necessary to convert from one unit of measure to another. Prefixes can help you understand the relationship between two units. A metric place-value chart can also be useful.
GO ON Lesson 1-3 Unit Conversions: Metric Capacity and Mass
19
2. Read the number from the chart for the conversion.
1
0.001
liter (L)
milli (mL)
1000
1
0.001
1. Use a chart. Place in the chart so that the zero that is farthest right is in the mL column.
ones
2. Read the number from the chart for the conversion. 270 mL = L
liter (L)
0
kilo (kL)
0
thousands
5
kilo (kL)
5
thousandths
1. Use a chart. Place 5,500 in the chart so that the zero that is farthest right is in the mL column.
1000
ones
Convert 5,500 milliliters to liters.
thousands
Example 1
5,500 mL = 5.5 L
milli (mL)
Convert 270 milliliters to liters.
thousandths
YOUR TURN!
To convert a larger unit to a smaller unit, multiply. To convert a smaller to a larger unit, divide.
YOUR TURN! Convert.
Convert. 0.0027 kg =
mg
1. 1,000 milligrams = 1 gram. 1,000 grams = 1 kilogram. So, 1,000 × 1,000 milligrams = 1 kilogram. 2. You are converting from a larger to a smaller unit. You need to multiply.
0.0027 × (1,000 × 1,000) =
20
kg
1. 1 gram = 1 kilogram =
milligrams grams
2. You are converting from a to a unit. You need to . 3. Convert.
3. Convert.
0.0027 ×
4,600,000 mg =
1,000,000
= 2,700 mg
Chapter 1 How Measurements Are Made
4,600,000 ÷ =
kg
Copyright © by The McGraw-Hill Companies, Inc.
Example 2
Who is Correct? Convert 650 liters to kiloliters.
Sema
Tom
650 × 1,000 = 650,000
Selby
650 ÷ 10 = 65
650 ÷ 1,000 = 0.65
Circle correct answer(s). Cross out incorrect answer(s).
Guided Practice Convert using a place-value chart.
Copyright © by The McGraw-Hill Companies, Inc.
6 mg = 1000
1
0.001
ones
thousandths
gram (g)
milli (mg)
g
thousands
ones liter (L)
0.001 thousandths
1
2
milli (mL)
1000 thousands
L
kilo (kg)
3 kL =
kilo (kL)
1
Step by Step Practice Convert. 3
28 g =
kg grams is equal to 1 kilogram.
Step 1
Step 2 You are converting from a unit. You need to
unit to a .
Step 3 Convert. 28 28 g =
1,000 = kg GO ON Lesson 1-3 Unit Conversions: Metric Capacity and Mass
21
Convert. 4
1.2 L = 1L= 1.2 1.2 L =
6
1,050 mL =
8
246 mg =
10
936 mL =
12
404 g =
5
900 mg = 1 kg = 900 900 mg =
7
0.25 g =
g
9
2,010 L =
L
11
880 g =
mg
mg
13
31 kL =
L
mL mL 1,000 = mL kL
Step by Step Problem-Solving Practice
mg kL
Problem-Solving Strategies
Solve. 14
kg mg 1,000,000 = kg
NUTRITION Hershel bought a giant turkey sandwich for a party. The giant sandwich has 200 grams of protein. How many milligrams of protein are in the giant turkey sandwich?
Draw a diagram. Look for a pattern. Guess and check. ✓ Solve a simpler problem. Work backward.
Read the problem. Write what you know. The giant sandwich has grams of protein.
Plan
Pick a strategy. One strategy is to solve a simpler problem. Work with 100, and then multiply your answer by 2 to find the total milligrams in the sandwich. milligrams is equal to 1 gram.
Solve
You are converting from , so you need to 100 grams × 1,000 = milligrams × 2 =
to . milligrams total milligrams
Hershel’s giant sandwich has milligrams of protein. Check
22
A milligram is a smaller unit of measure than a gram, so the number of milligrams of protein should be greater than the number of grams.
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
Understand
15
HEALTH Wendy weighs 45 kilograms. How many grams does she weigh? Check off each step. Understand Plan Solve Check
16
NUTRITION Elijah drank all of the water in the bottle shown. How many milliliters of water did he drink? Are 65 liters equal to 0.065 kiloliters? Explain.
17
Skills, Concepts, and Problem Solving Convert using a place-value chart. 752 mL =
ones
0.001 thousandths
1
milli (mL)
1000
liter (L)
L
thousands
ones gram (g)
0.001 thousandths
1
19
milli (mg)
1000 thousands
g
kilo (kL)
7 kg =
kilo (kg)
Copyright © by The McGraw-Hill Companies, Inc.
18
Convert. 20
0.0036 kL =
22
0.01 kg =
24
0.2 mg =
26
9.4 mL =
21
1.09 g =
g
23
15 L =
kL
g
25
65 kL =
L
27
4.8 g =
kg
mL
kL
mg
GO ON
Lesson 1-3 Unit Conversions: Metric Capacity and Mass
23
Solve. 28
COOKING Norma needed 1,500 milliliters of vegetable oil to cook a chicken for the family reunion. She bought a 2-liter bottle of oil. How many liters of oil did Norma have left over?
29
TRAVEL At the airport, you can only have 32 kilograms of mass per bag. How many grams are you able to carry in each bag?
Vocabulary Check sentence.
Write the vocabulary word that completes each
30
is the amount of matter in an object.
31
is the amount of dry or liquid material a container can hold.
32
A(n)
is a metric unit for measuring volume or capacity.
33
A(n)
is a metric unit for measuring mass.
34
Writing in Math
Explain how to convert 6.07 grams to kilograms.
Spiral Review Convert using a table. 84 in. =
ft
feet
1
2
3
4
5
6
Copyright © by The McGraw-Hill Companies, Inc.
35
(Lesson 1-2, p. 11)
7
inches 36
5 mi =
yd
miles
1
2
3
4
5
yards
Solve. 37
(Lesson 1-2, p. 11)
TRAVEL It is 2.5 miles from Kiki’s house to Laurie’s house. How many feet is this?
Convert.
(Lesson 1-1, p. 4)
38
1.4 m =
40
7.01 m =
24
Chapter 1 How Measurements Are Made
km dm
39
9.5 cm =
dm
41
546 m =
km
Lesson
1-4 Unit Conversions: Customary Capacity and Weight KEY Concept The customary system of measurement is not based on powers of ten. It is based on numbers like 12 and 16, which have many factors. Customary Units for Capacity Unit for Abbreviation Capacity fluid ounce fl oz cup
c
pint
pt
quart
qt
gallon
gal
Real-World Benchmark eye dropper
Equivalents
1 c = 8 fl oz 1 pt = 2 c 1 pt = 16 fl oz 1 qt = 2 pt 1 qt = 4 c 1 qt = 32 fl oz 1 gal = 4 qt 1 gal = 8 pt 1 gal = 16 c 1 gal = 128 fl oz
coffee mug cereal bowl pitcher
milk carton
3AF1.4 Express simple unit conversions in symbolic form. 3MG1.4 Carry out simple unit conversions within a system of measurement. 6AF2.1 Convert one unit of measurement to another.
VOCABULARY customary system a measurement system that includes units such as foot, pound, and quart (Lesson 1-2, p. 11)
capacity the amount of dry or liquid material a container can hold (Lesson 1-3, p. 19) weight a measurement that tells how heavy or light an object is benchmark an object or number used as a guide to estimate or reference
Copyright © by The McGraw-Hill Companies, Inc.
Customary Units for Weight Customary Units for Weight Unit for Abbreviation Capacity ounce oz
Equivalents
Real-World Benchmark a strawberry
pound
lb
1 lb = 16 oz
bunch of grapes
ton
T
1 T = 2,000 lb
car
Sometimes it is necessary to convert from one unit of measure to another. Knowing customary conversions can help you understand the relationship between two units.
GO ON Lesson 1-4 Unit Conversions: Customary Capacity and Weight
25
Example 1
YOUR TURN!
Convert 32 pints to gallons using a table. gallons
1
2
3
4
pints
8
16
24
32
1. 8 pints is equal to 1 gallon. 2. Fill in the table. 1 gallon = 1 × 8 pints 2 gallons = 2 × 8 pints 3 gallons = 3 × 8 pints 4 gallons = 4 × 8 pints
Convert 3 quarts to pints using a table. quarts
1
2
3
4
pints 1.
pints is equal to 1 quart.
2. Fill in the table. pints is equal to 3 quarts.
32 pints is equal to 4 gallons.
To convert a larger unit to a smaller unit, multiply. To convert a smaller to a larger unit, divide.
Example 2 Convert 9 tons to pounds.
2. 1 ton is equal to 2,000 pounds. So, 9 tons are 9 × 2,000 pounds, or 18,000 pounds.
26
Chapter 1 How Measurements Are Made
Convert 48 ounces to pounds. 1. You are converting from , which is a to a unit. You need to . 2. 1 pound is equal to So, 48 ounces are 48 ÷ pounds, or pounds.
to unit
ounces.
Copyright © by The McGraw-Hill Companies, Inc.
1. You are converting from tons to pounds, which is a larger unit to a smaller unit. You need to multiply.
YOUR TURN!
Example 3
YOUR TURN! Convert 22 pints to gallons.
Convert 56 fluid ounces to pints. 1. You are converting from fluid ounces to pints, which is a smaller unit to a larger unit. You need to divide. 2. 1 cup is equal to 8 fluid ounces. 1 pint is equal to 2 cups. So, 1 pint is equal to 16 fluid ounces. 56 ÷ 16 = 3.5
=
So, 22 pints equals
Example 4
to unit
2. 1 gallon is equal to . 1 quart is equal to . So, 1 gallon is equal to . 22
So, 56 fluid ounces equals 3.5 pints.
.
YOUR TURN! Convert 3.2 tons to ounces.
Convert 2 tons to ounces.
Copyright © by The McGraw-Hill Companies, Inc.
1. You are converting from , which is a to a unit. You need to .
1. You are converting from tons to ounces, which is a larger unit to a smaller unit. You need to multiply.
1. You are converting from , which is a a unit. You need to .
2. 1 ton is equal to 2,000 pounds. 1 pound is equal to 16 ounces. So, 1 ton is equal to 32,000 ounces.
2. 1 ton is equal to 1 pound is equal to 3.2
2 × 32,000 = 64,000 ounces
to unit to
. .
=
So, 3.2 tons equals
So, 2 tons equals 64,000 ounces.
.
Who is Correct? Convert 64 fluid ounces to quarts.
Erin 64 ÷ 16 = 4 quarts
Miquel
Gretchen
64 ÷ 32 = 2 quarts
64 ounces ÷ 8 = 8 cups 8 cups ÷ 2 = 4 pints 4 pints ÷ 2 = 2 quarts
Circle correct answer(s). Cross out incorrect answer(s).
GO ON
Lesson 1-4 Unit Conversions: Customary Capacity and Weight
27
Guided Practice Convert using a table. 1
320 fl oz =
qt
quarts fluid ounces 32 64 96 128 160
2
3T=
oz
tons
1
2
3
ounces
Step by Step Practice Convert. 3
16 pt =
c unit to a .
Step 1 You are converting from a unit. You need to Step 2 1 pint is equal to Step 3 So, 16 pints are 16
cups. 2, or
cups.
4
6 pt =
qt
1 qt =
pt
6
5
144 oz = 1 lb =
2=
144
lb oz 16 =
144 oz =
6 pt =
qt
6
7 lb =
oz
8
800 fl oz =
10
6c=
12
3,000 lb =
14
3T=
28
Chapter 1 How Measurements Are Made
qt fl oz T lb
lb
7
2 gal =
qt
9
10 pt =
c
11
8 pt =
13
16 pt =
gal
15
3 gal =
qt
c
Copyright © by The McGraw-Hill Companies, Inc.
Convert.
Step by Step Problem-Solving Practice
Problem-Solving Strategies Draw a diagram.
Solve. 16
MEASUREMENT A bathtub for a baby can hold 7 gallons of water. How many quarts of water can the bathtub hold? Understand
Read the question. Write what you know. A baby bathtub holds gallons of water.
Plan
Pick a strategy. One strategy is to look for a pattern.
✓ Look for a pattern. Write an equation. Solve a simpler problem. Work backward.
How many quarts are in 1 gallon? quarts =
gallon
Find a rule. One rule is to add
The pattern begins with the numbers 4, 8, and 12. Continue the pattern until you find the seventh term.
Solve
4, 8, 12,
,
,
,
The seventh term is quarts =
. gal
Copyright © by The McGraw-Hill Companies, Inc.
The baby bathtub can hold
quarts of water.
Think: A quart is a smaller unit of measurement than a gallon. So the number of quarts of water is greater than the number of gallons of water. The answer makes sense.
Check
17
.
ZOO ANIMALS An animal at the city zoo weighs 7,000 pounds. How many tons does the animal weigh? Check off each step. Understand Plan Solve Check GO ON Lesson 1-4 Unit Conversions: Customary Capacity and Weight
29
18
COOKING For the baking contest this year, each baker will be given 48 ounces of flour. Diedra needs more flour than that for her recipes. She is bringing 32 ounces of flour. How many pounds of flour will Diedra have altogether? Are there 64 cups in 2 gallons? Explain.
19
Skills, Concepts, and Problem Solving Convert using a table. 20
6c=
fl oz
cups
1
2
3
4
2
3
4
5
5
6
fluid ounces 21
5 lb =
oz
pounds
1
ounces
Convert. 9,000 lb =
23
12 c =
24
7 gal =
qt
25
256 oz =
26
20 qt =
pt
27
8 pt =
28
1.5 T =
oz
29
4 gal =
T
qt lb
Copyright © by The McGraw-Hill Companies, Inc.
22
fl oz c
Solve. 30
ART Claus mixed the paint shown to make a shade of gray. How many gallons of gray paint did Claus make?
31
PETS Vincent feeds his dog one cup of dog food in the morning and one cup of dog food in the evening. How many ounces of food will Vincent’s dog eat in 14 days?
30
Chapter 1 How Measurements Are Made
Mark Ransom/RansomStudios
16 pints
8 pints
Vocabulary Check sentence. 32
Write the vocabulary word that completes each
A(n) to estimate or reference.
is an object or number used as a guide
is a measurement that tells how heavy or
33
light an object is. is the amount of dry or liquid material a
34
container can hold. 35
Writing in Math
Explain how to convert 12 fluid ounces to cups.
Spiral Review Solve.
NUTRITION If a person consumes 71,700 grams of sugar in a year, how many kilograms of sugar was consumed?
(Lesson 1-2, p. 11)
yd
ones
tenths
hundredths
thousandths
deci (dm)
centi (cm)
milli (mm)
0.01 0.001
m
1000
1
0.1
thousandths
0.1
5 km =
(Lesson 1-1, p. 4)
milli (mm)
1
42
yd
hundredths
1000
meters (m)
m
234 in. =
centi (cm)
9 cm =
thousands
41
40
mi
tenths
Convert using a place-value chart.
36,960 ft =
deci (dm)
1.5 mi =
38
ones
39
in.
meters (m)
11 ft =
thousands
37
kilo (km)
Convert.
kilo (km)
Copyright © by The McGraw-Hill Companies, Inc.
36
(Lesson 1-3, p. 19)
0.01 0.001
Lesson 1-4 Unit Conversions: Customary Capacity and Weight
31
Chapter
1
Progress Check 2
(Lessons 1-3 and 1-4)
Convert. 1
3,400 mL =
3
332 mg =
5
6,050 L =
2
0.56 g =
g
4
22 L =
kL
6
775 mL =
kL
mg mL L
Convert using a table. 7
8
4 gal =
4 qt =
c
gallons
1
cups
16
fl oz
2
quarts
1
fluid ounces
32
3
4
2
3
4
5
Convert. 9
400 lb =
10
16 c =
11
5 gal =
qt
12
160 oz =
13
15 qt =
pt
14
1 pt =
15
1T=
16
1 gal =
oz
Solve. 17
BABIES Suzie’s little brother weighs 128 ounces. How many pounds does he weigh?
18
CONSTRUCTION Edgar needs 5.3 liters of paint for his garage. How many milliliters of paint does he need?
32
Chapter 1 How Measurements Are Made
Masterfile
qt lb fl oz c
Copyright © by The McGraw-Hill Companies, Inc.
T
Lesson
3AF1.4 Express simple unit conversions in symbolic form. 3MG1.4 Carry out simple unit conversions within a system of measurement. 6AF2.1 Convert one unit of measurement to another. 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems.
1-5 Time and Temperature KEY Concept Unit for Time second
Abbreviation
min
hour
h
Copyright © by The McGraw-Hill Companies, Inc.
week
VOCABULARY
s
minute
day
Equivalents
1 min = 60 s 1 h = 60 min 1 h = 3,600 s 1 d = 24 h 1 d = 1,440 min 1 d = 86,400 s 1 wk = 7 d 1 wk = 168 h 1 wk = 10,080 min 1 wk = 604,800 s
d
wk
Unit for Temperature
Abbreviation
Formula
Fahrenheit
°F
9 F = __C + 32 5
Celsius
°C
5 C = __(F - 32) 9
time the measure of how long or short an event is temperature the measure of how hot or cold something is degree a unit of measure for temperature Celsius a temperature scale in which water freezes at 0°C and boils at 100°C Fahrenheit a temperature scale in which water freezes at 32°C and boils at 212°F
Use the formulas given to convert from Celsius to Fahrenheit and from Fahrenheit to Celsius.
Example 1 Convert 4 minutes to seconds using a table. 1. 60 seconds is equal to 1 minute.
minutes
1
2
3
4
2. Fill in the table.
seconds
60
120
180
240
1 minute = 1 × 60 seconds 2 minutes = 2 × 60 seconds 3 minutes = 3 × 60 seconds 4 minutes = 4 × 60 seconds 240 seconds is equal to 4 minutes.
GO ON Lesson 1-5 Time and Temperature
33
YOUR TURN! Convert 3 days to hours using a table. 1.
hours is equal to 1 day.
days
1
2
3
4
hours
2. Fill in the table. hours is equal to 3 days.
To convert a larger unit to a smaller unit, multiply. To convert a smaller to a larger unit, divide.
Example 2
YOUR TURN!
Convert 50°F to degrees Celsius. 5 C = __(F - 32) 9 5 C = __(50 - 32) 9 5 C = __(18) 9 18 C = 5 × ___ 9 C = 10
Write the formula. Substitute 50 for F. Simplify.
Convert 20°C to degrees Fahrenheit. 9 Use the formula F = __C + 32 5 9 Substitute for C. F = __ ( 5 32. +
F=
)+
Simplify.
F= So, 20°C =
°F.
So, 50°F = 10°C.
Convert 45°C to degrees Fahrenheit.
Rudy
Adela
James
5 __ C = 9(F - 32) 5 __ C = 9(45 - 32) 5 __ C = 9(13) 65 ___ C= 9 C = 7.2°F
9 __ F = 5C + 32 9 __ F = 5(45) + 32 F = 81 + 32 F = 113°
9 __ F = 5C + 32 9 __ F = 5(45) + 32 F = 9 + 32 F = 41°
Circle correct answer(s). Cross out incorrect answer(s). 34
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
Who is Correct?
Guided Practice Convert using a table. 1
6h=
min
hours
1
2
3
4
5
6
minutes 2
35 d =
wk
weeks days
7
14
Step by Step Practice Convert. 3
100°C =
°F .
Step 1 The formula to use is for C.
Step 2 Substitute 9 F = __( 5
) + 32
Copyright © by The McGraw-Hill Companies, Inc.
Step 3 Simplify. 9 F = __( 5 F= F= 100°C =
) + 32 + 32 °F
Convert. 4
3h=
s
1h=
s
3 3h=
5
3,600 =
672 h =
wk
1 wk =
h 168 =
672 672 h =
wk
7
480 s =
min °C
s
6
2 wk =
8
30°C =
°F
9
104°F =
10
10 d =
h
11
1,800 s =
12
41°F =
°C
13
25°C =
min
min °F
GO ON
Lesson 1-5 Time and Temperature
35
Step by Step Problem-Solving Practice Solve. 14
HISTORY It took Elizabeth 240 minutes to complete her history project. How many hours did it take Elizabeth to complete her history project?
Problem-Solving Strategies Draw a diagram. Look for a pattern. Act it out. Solve a simpler problem. ✓ Work backward.
Understand
Read the problem. Write what you know. It took Elizabeth minutes to complete her history project.
Plan
Pick a strategy. One strategy is to work backward. minutes is equal to 1 hour. You know the total minutes. Subtract 60 minutes repeatedly until you get 0. Count the number of times you subtracted 60. 240 - 60 = - 60 = - 60 = - 60 =
Solve
Elizabeth took project.
hours to complete her
FOOD SERVICE It took Darcy 420 seconds to order, pay, and pick up her food at the drive-thru at Biggie Burger. How many minutes did it take Darcy to get her food? Check off each step. Understand Plan Solve Check
16
36
SCIENCE The boiling point of water in degrees Fahrenheit is shown at the right. What is the boiling point of water in degrees Celsius?
Chapter 1 How Measurements Are Made
Copyright © by The McGraw-Hill Companies, Inc.
Think: A minute is a smaller unit of measurement than an hour. So the number of hours it took Elizabeth to complete her history project should be less than the number of minutes. The answer makes sense.
Check
15
hour hour hour hour
Are there 72 hours in 3 days? Explain.
17
Skills, Concepts, and Problem Solving Convert using a table. 18
4d=
h
days
1
2
3
4
hours 19
4,320 min =
d
days
1
2
3
4
minutes
Copyright © by The McGraw-Hill Companies, Inc.
Convert. 20
6 wk =
22
210 min =
24
3 wk =
26
14,400 min =
d h h d
21
9,000 min =
23
32°F =
°C
25
37°C =
°F
27
288 h =
d
d
Solve. 28
TRAVEL William traveled around the world. He spent 96 hours on an airplane, a car, or a bus. How many days was William on an airplane, a car, or a bus?
29
TEMPERATURE The hottest temperature recorded in the United States was in Death Valley, California, at 134°F. What was the temperature in degrees Celsius? (Round to the nearest tenth degree.)
Death Valley
GO ON Lesson 1-5 Time and Temperature
Getty Images
37
Vocabulary Check sentence.
Write the vocabulary word that completes each is the measure of how long or short
30
an event is. is the measure of how hot or cold
31
something is. 32
temperature can be found using the
9 formula __C + 32. 5
33
34
temperature can be found using the
9 formula __(F - 32). 5 Writing in Math
Explain how to convert 5 days to seconds.
Spiral Review Solve.
PACKAGING Joseph bought a 2-pound box of chocolates. How many ounces of chocolate did he buy?
Convert.
(Lesson 1-3, p. 19)
36
0.49 L =
38
0.0025 kL =
Convert using a table. 40
5 yd =
mL mL
37
78,000 mg =
39
5.3 g =
yards
1
2
3
4
inches 41
3 mi =
ft
miles feet
38
kg
(Lesson 1-2, p. 11)
in.
Chapter 1 How Measurements Are Made
1
2
3
kg
5
Copyright © by The McGraw-Hill Companies, Inc.
35
(Lesson 1-4, p. 25)
Lesson
1-6 Analyze Units of Measure KEY Concept Use the table to convert between customary and metric units of measure. Customary Unit 1 inch
1 yard
Approximate Metric Equivalent 2.54 centimeters 30.48 centimeters or 0.3048 meters 0.914 meter
1 mile
1.609 kilometer
1 ounce
1 fluid ounce
28.35 grams 454 grams or 0.454 kilogram 29.574 milliliters
1 quart
0.946 liter
1 gallon
3.785 liters
1 foot
Copyright © by The McGraw-Hill Companies, Inc.
1 pound
6AF2.1 Convert one unit of measure to another. 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems. 7MG1.3 Use measures expressed as rates and measures expressed as products to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
VOCABULARY unit rate a rate simplified so that it has a denominator of 1
To convert customary units to their metric equivalents, multiply by the numbers in the chart. To convert metric equivalents to their customary equivalents, divide by the numbers in the chart.
Example 1
YOUR TURN!
Convert from yards to meters. Round to the nearest thousandth. 18 yd ≈
m
≈ 18 yd × 0.914 m/yd Use the equivalent chart. ≈ 16.452 m Convert from customary units to metric units. Multiply. 18 yards is approximately equal to 16.452 meters.
Convert from kilograms to pounds. Round to the nearest thousandth. 3.178 kg ≈
lb
≈ 3.178 kg ÷
kg/lb
Use the equivalent chart. ≈
lb
Convert from metric units to customary units. Divide. 3.178 kilograms is approximately equal to pounds.
GO ON
Lesson 1-6 Analyze Units of Measure
39
A rate is a fraction that compares two different units of measure, such as 123 miles _________ . Unit rates have a denominator of 1, such as 41 miles per hour. 3 hours
Example 2 Eva ran 5 kilometers in 15 minutes. If she continued running at the same speed, how far would she run in 1 hour? 1. Find the equivalent measurements. 60 minutes = 1 hour 2. Write a rate using the information given. 5 km n km _______ = _______ 15 min 60 min 4 to find the unit rate. 3. Use __ 4 4 5 n ___ × __ = ___ 15
4
Barry read a 420-page book in 1 week. On average, how many pages did he read each day? 1. Find the equivalent measurements. 7 days = 1 week 2. Write a rate using the information given. 420 pages _______ n pages _________ = 7 days 1 day 3. Use ______ to find the unit rate.
60
20 ___ ___ = n 60
YOUR TURN!
60
20 = n
420 pages n pages _________ ÷ ______ = _______ 7 days
4. Eva would run 20 kilometers in 60 minutes, or 1 hour.
1 day
n ______ = __ 1
1
5 km 60 min 5 × 60 300 _______ × _______ = ______ = ____ = 20 15 min 1h 15 15
=n 4. Barry read about
pages in 1 day.
5. Check your answer. 420 pages __________ 1 week _________ × = 1 week
________ =
40
Chapter 1 How Measurements Are Made
days
Copyright © by The McGraw-Hill Companies, Inc.
5. Check your answer.
Example 3 Mateo’s family drank 6 quarts of milk in 2 weeks. Camille’s family drank 10 quarts of milk in 3 weeks. Whose family drank more milk on average per week? 1. Find the unit rate for each family.
1 quarts 3__ 10 quarts 3 3 = _________ Camille’s family: _________ ÷ 3 3 weeks 1 week
_
_
3 quarts 6 quarts 2 = ________ Mateo’s family: ________ ÷ 2 2 weeks 1 week
2. Compare the unit rates. 1 quarts per week is more than 3 quarts per week. 3__ 2 3. Camille’s family drank more milk on average per week. YOUR TURN! The table shows practice times for three runners on the track team. Who is the fastest runner? 1. Find the unit rate for each runner. Consider that 60 minutes is equal to 1 hour. Convert all rates to laps per hour.
Jake
Number of Laps 10
Number of Minutes 15
Ginny
22
60
Siva
5
10
Runner
_
Jake: 15 minutes × 4 = 60 minutes 10 laps × 4 = laps per hour
_
Copyright © by The McGraw-Hill Companies, Inc.
Ginny: 60 minutes = 1 hour 22 laps per hour
Siva: 10 minutes × 6 = 60 minutes 5 laps × 6 = laps per hour
2. Compare the unit rates. 3. The fastest runner is
.
Who is Correct? Riqui finished 45 math problems in 60 minutes. What was his unit rate?
Stan
60 ÷ 45 = 1.3ˉ Riqui’s unit rate is 1.33 problems/minute
Kim 45 ÷ 60 = 0.75 Riqui’s unit rate is 0.75 problems/minute
Circle correct answer(s). Cross out incorrect answer(s).
Neka
__ _
60 min = 45 problems 1 min n problems
Riqui’s unit rate is 1.33 problems/minute
GO ON
Lesson 1-6 Analyze Units of Measure
41
Guided Practice Convert. Round to the nearest thousandth. 1
20 in. ≈
3
18.925 L ≈
5
31.5 mi ≈
cm gal km
2
283.5 g ≈
4
198.45 oz ≈
g
6
609.6 cm ≈
ft
lb
Step by Step Practice Find the equivalent rate. 7
150 miles in 3 hours =
miles in 1 day
Step 1: Find the equivalent measurements. 24 hours = 1 day Step 2: Write a rate using the information given.
n mi _______ = _____ 24 h
Step 3: Use ______ to find the unit rate. 150 n ________ = ___ 24 3
n ___________ = ___ 24
Step 4: 150 miles in 3 hours =
n=
miles in 1 day
150 mi ____ 150 × 24 3,600 _______ × 24 h = ________ = _____ = 3h
1d
3
3
Find each equivalent rate. 8
$336 for 7 pounds = $
9
48 gallons per minute =
10
57 tiles in 10 decimeters =
11
25 kilometers in 10 minutes =
12
54 yards in 5 minutes ≈
13
1,362 grams per box ≈
42
Chapter 1 How Measurements Are Made
for 1 ounce pints per minute tiles in 1 meter kilometers in 1 hour meters in 5 minutes pounds per box
Copyright © by The McGraw-Hill Companies, Inc.
Step 5: Check your answer.
14
ENTERTAINMENT Four friends paid a total of $32 for movie tickets. What was the price per ticket?
15
ANIMALS Vince’s pet rabbit can run 96 miles in 3 hours. At this rate, how far can his rabbit run in 1 hour?
Step by Step Problem-Solving Practice
Problem-Solving Strategies Draw a diagram. Look for a pattern. Act it out. ✓ Solve a simpler problem. Work backward.
Solve.
Copyright © by The McGraw-Hill Companies, Inc.
16
WORK At a warehouse, Team 101 can unload 18 trucks in 6 hours. Team 105 can unload 14 trucks in 4 hours. Which team unloads more trucks each day? Understand
Read the question. Write what you know. Team 101 unloads trucks in hours. Team 105 unloads trucks in hours.
Plan
Solve a simpler problem. Treat each team as a separate problem and find the unit rate. Then compare those unit rates.
Solve
Team 101: 6 hours × 4 = 24 hours (1 day) 18 ×4= trucks per day Team 105: 4 hours × 6 = 24 hours (1 day) 14 ×6= trucks per day
Team Check
trucks per day is the fastest unit rate. unloads more trucks per day.
Check your answer. 18 trucks ____ _________ × 24 h = 18 × 4 = 6h
1d
14 trucks ____ _________ × 24 h = 4h
1d
×
=
GO ON Lesson 1-6 Analyze Units of Measure
43
17
RECIPES Laquita’s lemonade recipe calls for 8 teaspoons of sugar for every 4 cups of water. How many teaspoons of sugar will she need to make one quart of lemonade? Check off each step. Understand Plan Solve Check
18
IRRIGATION A water pump for an irrigation system will pump 72 gallons per minute. How many liters of water per minute can be pumped?
19
Scientists from the United States are working on a project with scientists from England. The U.S. scientists have completed all the measurements in customary units. The English scientists have completed all the measurements in metric units. Should the scientists convert to using the same system? Explain.
Convert. Round to the nearest thousandth. 20
6.096 m ≈
22
63 in ≈
ft cm
21
147.87 mL ≈
23
12 lb ≈
Find each equivalent rate. 24
$17 for 100 centimeters = $
25
12 tablespoons for 16 cups =
26
8 inches in 8 hours =
27
180 pages in 24 hours =
28
50 miles per hour ≈
44
Chapter 1 How Measurements Are Made
for 4 meters tablespoons for 4 gallons inches in 1 day pages in 1 week km per hour
fl oz kg
Copyright © by The McGraw-Hill Companies, Inc.
Skills, Concepts, and Problem Solving
Circle the higher or faster rate in each situation. 29
3 books in 4 months
30
10 books in 1 year
10 inches in 2 hours
31
6 inches in 60 minutes
24 degrees in 30 hours 18 degrees in 1 day
Solve. 32
ADVERTISING A candidate bought 5 commercial spots for a total of $4,500. What was the price per commercial?
33
PHOTOGRAPHY Yancy took 112 photos of La Purisima Mission shown at right in 4 hours. At this rate, how many photos could he take in 2 hours?
Vocabulary Check Write the vocabulary word that completes each sentence.
Copyright © by The McGraw-Hill Companies, Inc.
La Purisima Mission 34
A rate simplified to have a denominator of 1 is a(n)
.
35
Writing in Math Explain how to find the cost of 12 bottles of water if two bottles of water cost $1.50.
Spiral Review Convert.
(Lesson 1-4, p. 25, Lesson 1-2, p. 11)
36
8 lb =
39
96 in. =
Solve. 42
43
oz ft
37
5 qt =
pt
40
18 ft =
yd
38
9c=
41
3 mi =
fl oz yd
(Lesson 1-2, p. 11)
TRAVEL It is 150 yards from Keenan’s house to the library. How many feet is it from Keenan’s house to the library? NATURE Yolanda found a snake in her backyard that was 24 inches long. How long, in feet, was the snake?
Library 150 yd
Keenan’s house
Lesson 1-6 Analyze Units of Measure CORBIS
45
Chapter
1
Progress Check 3
(Lessons 1-5 and 1-6)
Convert. 1
2 wk =
d
2
259,200 s =
3
50°F =
°C
4
59°F =
°C
5
212°F =
6
32°F =
°C
7
45°C =
8
55°C =
°F
°C °F
d
Convert. Round to the nearest thousandth. 9
10 gallons ≈
10
10 miles per hour ≈
11
1,300 kilometers ≈
12
32 ounces per package ≈
liters kilometers per hour miles grams per package
Circle the higher or faster rate in each situation. 13
115 cm in 1 hour
$18 per pound $1 per ounce
Solve. 15
GROCERIES Look at the receipt shown at the right. How much does one loaf of bread cost at the Thrifty Bakery?
16
CONSTRUCTION Craig needs 3 gallons of water to clean the deck. It will take him 2 hours to clean the deck. How much water will he use in one hour?
46
Chapter 1 How Measurements Are Made
Thrifty Bakery 12 loaves @ $6.72
Thank you for shopping with us!
Copyright © by The McGraw-Hill Companies, Inc.
25 cm in 10 minutes
14
Chapter
1
Study Guide
Vocabulary and Concept Check capacity, p. 19
Write the vocabulary word that completes each sentence.
Celsius, p. 33
A(n) measuring mass.
1
convert, p. 4 customary system, p. 11
is the measure of the length of an
2
Fahrenheit, p. 33
event.
gram, p. 19 kiloliter, p. 19
9 The formula __C + 32 is used to find 5 temperatures.
3
liter, p. 19 mass, p. 19
4
The is a measurement system that includes units such as meter, gram, and liter.
5
The amount of dry or liquid material a container can hold is its .
6
is the amount of matter in an
metric system, p. 4 meter, p. 4 milliliter, p. 19 millimeter, p. 4 time, p. 3
is a metric unit for
object.
temperature, p. 33
Copyright © by The McGraw-Hill Companies, Inc.
weight, p. 25
7
The is the basic unit of measurement for length in the metric system.
8
The pound, and quart.
9
A measurement that tells how heavy or light an object is .
10
The is the metric unit for measuring volume or capacity.
includes units such as foot,
Label each diagram below by writing the word for the abbreviation. 11
12
1 m = 1,000 mm 13
14
1 kL = 1,000 L Chapter 1 Study Guide
47
Lesson Review
1-1
Unit Conversions: Metric Length
Convert using a place-value chart. 15
4.5 mm =
16
3 km =
17
57 mm =
18
7m=
19
500 m =
20
2,570 m =
(pp. 4–10)
Example 1
dm
Convert 28.7 kilometers to meters.
1-2
dm
You are converting from kilometers to meters, which is a larger unit to a smaller unit. You need to multiply.
cm cm
There are 1,000 meters in 1 kilometer. Multiply. 28.7 × 1000 = 28,700 28.7 km = 28,700 m
km km
Unit Conversions: Customary Length
Convert using a table. 21
18 ft =
(pp. 11–17)
Example 2
yd Convert 12 feet to yards using a table.
yards
1
2
3
4
5
6
7
feet in. = 5 ft
22
1
2
3
4
inches
1-3
2
3
4
feet
3
6
9
12
There are 3 feet in 1 yard. Fill in the table. There are 12 feet in 4 yards.
Unit Conversions: Metric Capacity and Mass
Convert. 23
5
1
30 L =
(pp. 19–24)
Example 3 mL Convert 19 kilograms to grams.
24
2g=
25
15 kg =
g
26
45 g =
kg
27
12,400 mL =
kg
L
You are converting from kilograms to grams, which is a larger unit to a smaller unit. You need to multiply. There are 1,000 grams in 1 kilogram. Multiply. 19 × 1,000 = 19,000 19 kg = 19,000 g
48
Chapter 1 Study Guide
Copyright © by The McGraw-Hill Companies, Inc.
feet
yards
1-4
Unit Conversions: Customary Capacity and Weight (pp. 25–31)
Convert.
Example 4
28
20 qt =
29
3T=
lb
30
2c=
fl oz
31
16,000 lb =
gal Convert 5 pounds to ounces. You are converting from a larger unit to a smaller unit. You need to multiply. There are 16 ounces in 1 pound. 5 × 16 = 80
T
5 lb = 80 oz
1-5
Time and Temperature
(pp. 33–38)
Convert using a table. 32
4 wk = weeks
Convert 4 hours to minutes using a table.
d 1
2
3
There are 60 minutes in 1 hour. Fill in the table.
4
days 33
Convert 15°C to degrees Fahrenheit.
Copyright © by The McGraw-Hill Companies, Inc.
15°C =
1-6
Analyze Units of Measure
34
90 feet in 3 minutes
35
$5.00 for 4 cards
36
180 m for 40 ribbons
hours
1
2
3
4
minutes
60
120
180
240
There are 240 minutes in 4 hours.
°F
Find each unit rate.
Example 5
(pp. 39–45)
Example 6 An airplane flew 2,000 miles in 8 hours. On average, how far did the airplane fly in 1 hour? Write a rate using the information 2,000 mi t mi given. ________ = ____ 8h 1h 8 Use __ to find the unit rate. 8 2,000 mi ÷ __ 8 3 t mi _____________ = ____ 8h÷ 4 8 1h
37
27 pages in 3 hours
2,000 ÷ 8 = 250 The plane flew 250 miles in 1 hour.
Chapter 1 Study Guide
49
Chapter
1
Chapter Test
Convert. 1
0.28 km =
3
3 mi =
5
400 g =
m ft kg
2
5 cm =
dm
4
48 in =
ft
6
2.2 L =
mL
8
5 yd =
in.
Convert using a place-value chart or table. 9 cm =
m
thousandths
g
2
3
4
5
inches
10
7 gal =
0.001
gallons
thousandths
ones gram (g)
1
quarts
1
qt 2
3
4
5
6
7
milli (mg)
thousands kilo (kg)
1
yard
Convert. 11
5T=
13
16 pt =
15
104°F =
50
Chapter 1 Test
12
19 gal =
qt
14
25°C =
°F
°C
16
2 lb ≈
g
oz
fl oz
GO ON
Copyright © by The McGraw-Hill Companies, Inc.
1000
milli (mm)
tenths deci (dm)
6,300 mg =
0.01 0.001 hundredths
ones
kilo (km)
9
0.1
meters (m)
1
thousands
1000
centi (cm)
7
Convert. 17
120 miles per hour =
miles per minute
18
21 gallons per week ≈
liters per week
Copyright © by The McGraw-Hill Companies, Inc.
Solve. 19
TRAVEL It is 12 kilometers from Joey’s house to the community swimming pool. How many meters is it to the pool?
20
SPORTS A football field is 100 meters long. How many inches long is the football field?
21
COOKING Mitchell needs 500 milliliters of water for a recipe. How many liters of water does Mitchell need?
22
CHEMISTRY The freezing point of zinc is approximately 420°C. What is the freezing point of zinc in degrees Fahrenheit? Use the 9 formula: F = __C + 32. 5
Football stadium near Petaluma, California
8 gallons needed × 2 quarts per gallon = 16 quarts needed
Correct the mistakes. 23
Mr. Hopkins went to a farm store to buy liquid fertilizer. He needed at least 8 gallons. The gallon-size liquid fertilizer was sold out, so he purchased 16 quarts instead. What was wrong with the purchase Mr. Hopkins made?
24
Show how you would correct Mr. Hopkins’ mistake.
25
The clocks to the right show when Guillermo started and stopped doing his homework. How many total minutes did he spend on homework?
11
12
1
10
11 2
9
3 8
4 7
6
5
Started
12
1
10
2
8
4
9
3 7
6
5
Stopped
Chapter 1 Test Jupiter Images
51
Chapter
1
Standards Practice
Choose the best answer and fill in the corresponding circle on the sheet at right. 1
A tree grew 50 feet in 4 years. How much did it grow per year?
5
Which has a mass of about 1 kilogram?
A 200 feet
C 12.5 feet
A a grain of salt
B 46 feet
D 10 feet
B six medium apples C a small paper clip D a granola bar
2
246 centimeters =
meters
F 0.00246
H 24.6
G 2.46
J 2,460
6
Which is a unit rate? F 40 grams for 10 packages G 300 miles in 6 hours H 55 books in 1 year
3
J $350 for 2 cameras
Which symbol makes this sentence true? 3 yards □ 9 feet C +
B >
D =
7
The pitcher can hold 16 cups. How many quarts can the pitcher hold? A 2
4
F 5 × 5,280 = 26,400
C 6 D 8
G 5 × 12 = 60
Which symbol makes this sentence true?
H 2+3=5
2 pounds □ 40 ounces
J 5 × 100 = 500
52
B 4
Dandre rode his bike 2 miles to Kameron’s house. Together they rode another 3 miles to the park. Which sentence shows how many feet Dandre traveled to get to the park?
Chapter 1 Standards Practice
8
F
J =
GO ON
Copyright © by The McGraw-Hill Companies, Inc.
A
