4th Grade | Unit 8
MATH Student Book
4th Grade | Unit 8
Unit 8 | WHOLE NUMBERS AND FRACTIONS
MATH 408 WHOLE NUMBERS AND FRACTIONS
1. Signs and Fractions....................................3 Operation Signs |5 Fractions |6
Self Test 1 |9
2. Division of Two-Digit Numbers............ 11 Fractions with Unlike Denominators |13 Missing Number Problems |15 Self Test 2 |18
3. Multiply a Four-Digit Number............. 20 Division |22 Polygons |25
Self Test 3 |27
4. Metric Measurements............................ 29 _1_ Add and Subtract Fractions |34
Digital Clock |36 Self Test 4 |38
4
5. Application and Review......................... 40 Circle Graphs |45 Self Test 5 |47 LIFEPAC Test |Pull-out
_3_ 4 |1
WHOLE NUMBERS AND FRACTIONS | Unit 8
Author: Carol Bauler, B.A. Editor: Alan Christopherson, M.S. Media Credits: Page 3: © Magdalenawd, iStock, Thinkstock; 11: © RTsubin, iStock, Thinkstock; 20: © sumkinn, iStock, Thinkstock; 29: © valeo5, iStock, Thinkstock; 40: © scyther5, iStock, Thinkstock; 43: © KakigoriStudio, iStock, Thinkstock; 46: © Marvid, iStock, Thinkstock.
804 N. 2nd Ave. E. Rock Rapids, IA 51246-1759 © MCMXCVII by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc. All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
2|
Unit 8 | WHOLE NUMBERS AND FRACTIONS
1. SIGNS AND FRACTIONS Objectives Read these objectives. When you have completed this section, you should be able to: Multiply by a 2-digit number. Recognize operation signs. Simplify fractions.
Complete these activities. 1.1 1.2
A prime number can be divided only by 1 and itself. Circle the prime numbers. 6
11
17
20
27
29
32
A composite number can be divided by 1, itself, and other numbers. Circle the composite numbers. 7
19
21
24
31
35
36
1.3
Factors are numbers that when multiplied together produce a given number. Write all of the factors of these numbers.
6 _____________________________ 12 _______________________________
1.4
Multiples are the multiplication facts for a given number. Write five multiples of each number.
3 _____________________________
7 _______________________________
Section 1 | 3
WHOLE NUMBERS AND FRACTIONS | Unit 8 1.5
Follow the steps to multiply to tens’ place by two-digits. Solve.
48 × 63 144 2,880 3,024
1. Multiply 48 by 3 ones. 2. Put a 0 place holder in the ones’ place below the 4. 3. Multiply 48 by 6 tens. 4. Total the products.
1.6
Follow the steps to multiply to tens’ place by two-digits. Solve.
68 × 24
752 × 45 3,760 30,080 33,840
32 × 38
19 × 67
58 × 26
1. Multiply 752 by 5 ones. 2. Put a 0 place holder in the ones’ place below the 0. 3. Multiply 752 by 4 tens. 4. Total the products. 630
189 × 36
× 85
782 × 24
936 × 12
1.7
Write the largest number possible using the digits 3, 2, 5, 9, 1, 0.
_________________________
1.8
Write the numbers in order from smallest to largest.
352,649
__________ __________ __________ __________ __________ __________
1.9
Write the number in number words. Remember hyphens and commas.
a. 325,462 _________________________________________________________
b. 405,650 _________________________________________________________
4 | Section 1
325,649
25,469
525,694
52,699
365,649
Unit 8 | WHOLE NUMBERS AND FRACTIONS 1.10
Write the number words in digits.
three hundred thousand, fifty-six
_________________
seventeen thousand, two hundred three
_________________
Operation Signs 1.11
Perform the operations and circle the correct operation sign. (not all of these signs are equality / inequality signs some are > , < ) 7 × 5
16 – 3 ( > , < ) 4 + 8
d. 5 + 7 ( > , < ) 5 × 3
66 ÷ 11 ( > , < ) 6 × 2
1.12
Write the answer to the number sentence.
a. 3 + 8 – 6 = _____________
5 + 9 + 6 + 2 = _____________
b. 22 + 5 – 3 = _____________
63 – 2 + 8 = _____________
c. 9 + 3 + 8 + 4 = _____________
12 – 3 + 6 – 2 = _____________
d. 18 + 5 – 4 + 2 = _____________
4 + 4 + 2 + 10 = _____________
1.13
Circle the number ...
a. in the hundreds’ place.
638,742
b. in the ten thousands’ place.
890,361
c. in the ones’ place.
256,183
d. in the hundred thousands’ place.
745,102
1.14
What is the value of the underlined number?
a. 362,491 ______________
b. 462,108 ______________
c. 775,036 ______________
d. 963,482 ______________
1.15
Find the product.
a. 7 × 3 × 0 = _____________
c. 4 × 4 × 2 × 0 = _____________ d. 3 × 6 × 0 × 8 = _____________
b. 5 × 0 × 2 = _____________
Section 1 | 5
WHOLE NUMBERS AND FRACTIONS | Unit 8
Fractions Proper fractions have smaller numerators than denominators. They are less than a 2 __ whole number. 1 3
Mixed numbers are written with a whole number and a fraction. They are greater than 1 a whole number. >1 1__ 3
Complete this activity. 1.16
Describe each one of the following as: a) a proper fraction, b) an improper fraction, or c) a mixed number.
_______________ _______________ _______________
3 1 __ 5
_______________ _______________ _______________
6 | Section 1
15 ___ 8
5 __ 9
7 __ 4
1 1 __ 2__ 8 3
Unit 8 | WHOLE NUMBERS AND FRACTIONS Fractions can be simplified by:
• changing improper fractions to whole numbers or mixed numbers. (Divide denominator into numerator.)
• changing proper fractions to the smallest equivalent fraction. (Divide numerator and denominator by same factor.)
9 __ 4
=
2 R1 4 ) 9 8 1
=
1 2__ 4
3 ÷ 3 __ 9 ÷ 3
1 = __ 3
Complete these activities. 1.17
Simplify or reduce these fractions to lowest terms. Show your work.
a.
4 ___ = 12
10 ___ = 20
12 ___ = 18
b.
13 ___ = 8
11 ___ = 6
9 __ 7
=
Section 1 | 7
WHOLE NUMBERS AND FRACTIONS | Unit 8 We add or subtract fractions by drawing the fraction bar, writing the denominator, adding or subtracting the numerators, and simplifying the answers. 1.18
Add or subtract.
a. +
b. +
c. –
d. –
7 __ 9 1 __ 9
3 __ 8 2 __ 8
10 ___ 12 5 ___ 12
10 ___ 12 6 ___ 12
+
+
–
–
3 __ 4 2 __ 4
6 ___ 12 4 ___ 12
14 ___ 15 6 ___ 15
8 __ 9 6 __ 9
+
+
–
–
4 __ 5 3 __ 5
5 __ 8 4 __ 8
5 __ 9 2 __ 9
7 __ 9 2 __ 9
+
+
–
–
7 ___ 10 2 ___ 10
3 __ 7 2 __ 7
6 __ 8 4 __ 8
6 ___ 10 4 ___ 10
Review the material in this section to prepare for the Self Test. The Self Test will check your understanding of this section. Any items you miss on this test will show you what areas you will need to restudy in order to prepare for the unit test. 8 | Section 1
Unit 8 | WHOLE NUMBERS AND FRACTIONS
SELF TEST 1 Complete these activities (each question, 1 point). 1.01
Circle the prime numbers.
1.02
Circle the composite numbers.
3
6
8
14
14
19
17
25
21
31
25
29
35
33
Fill in the blanks (each question, 2 points). 1.03
Write all of the factors of these numbers.
1.04
Write five multiples of each number.
9 ________________________
14 ________________________
6 ________________________
8 ________________________
Solve these problems (each answer, 2 points). 1.05
Find the product a. b. 67 18 × 35 × 28
c.
d. 372 × 63
515 × 76
Write the answer for these questions (each question, 1 point). 1.06
Write the number in number words. Remember hyphens and commas.
402,391
1.07
Write the number word in digits.
three hundred thousand, fifty-six _________________
_________________________________________________________
Section 1 | 9
WHOLE NUMBERS AND FRACTIONS | Unit 8 Complete these activities (each answer, 1 point unless otherwise noted). 1.08
Circle the correct operation sign.
a. 18 ÷ 3 ( = , ≠ ) 2 × 3
8 × 3 ( = , ≠ ) 29 – 6
b. 48 – 3 ( > , < ) 39 + 5
15 ÷ 5 ( > , < ) 12 ÷ 3
1.09
Write the answer to the number sentence.
a. 3 + 6 – 5 = _____________
13 – 5 + 6 = _____________
b. 83 + 5 – 4 + 2 = _____________
76 – 3 – 3 + 7 = _____________
1.010 Circle the number ...
a. in the one thousands’ place.
546,728
b. in the hundred thousands’ place.
172,934
1.011 What is the value of the underlined number?
a. 831,492 ______________
b. 648,081 ______________
1.012 Describe each one of the following as: a) a proper fraction, b) an improper fraction, or c) a mixed number. 13 ___ 6
7 2 __ 1__ 4 3
4 __ 5
_____________ _____________ _____________ _____________
1.013 Add or subtract. Simplify answers. (each problem, 2 points)
+
10 | Section 1
2 __ 6 1 __ 6
+
4 __ 7 3 __ 7
–
8 __ 12 4 __ 12
–
4 __ 9 1 __ 9
Teacher check:
Initials ____________
Score ______________________
Date
____________
32 40
MAT_Gr3-5
MAT0408 – Jan ‘16 Printing 804 N. 2nd Ave. E. Rock Rapids, IA 51246-1759 800-622-3070 www.aop.com
ISBN 978-0-86717-458-8
9 780867 174588
4th Grade | Unit 8
Unit 8 | WHOLE NUMBERS AND FRACTIONS
MATH 408 WHOLE NUMBERS AND FRACTIONS
1. Signs and Fractions....................................3 Operation Signs |5 Fractions |6
Self Test 1 |9
2. Division of Two-Digit Numbers............ 11 Fractions with Unlike Denominators |13 Missing Number Problems |15 Self Test 2 |18
3. Multiply a Four-Digit Number............. 20 Division |22 Polygons |25
Self Test 3 |27
4. Metric Measurements............................ 29 _1_ Add and Subtract Fractions |34
Digital Clock |36 Self Test 4 |38
4
5. Application and Review......................... 40 Circle Graphs |45 Self Test 5 |47 LIFEPAC Test |Pull-out
_3_ 4 |1
WHOLE NUMBERS AND FRACTIONS | Unit 8
Author: Carol Bauler, B.A. Editor: Alan Christopherson, M.S. Media Credits: Page 3: © Magdalenawd, iStock, Thinkstock; 11: © RTsubin, iStock, Thinkstock; 20: © sumkinn, iStock, Thinkstock; 29: © valeo5, iStock, Thinkstock; 40: © scyther5, iStock, Thinkstock; 43: © KakigoriStudio, iStock, Thinkstock; 46: © Marvid, iStock, Thinkstock.
804 N. 2nd Ave. E. Rock Rapids, IA 51246-1759 © MCMXCVII by Alpha Omega Publications, Inc. All rights reserved. LIFEPAC is a registered trademark of Alpha Omega Publications, Inc. All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
2|
Unit 8 | WHOLE NUMBERS AND FRACTIONS
1. SIGNS AND FRACTIONS Objectives Read these objectives. When you have completed this section, you should be able to: Multiply by a 2-digit number. Recognize operation signs. Simplify fractions.
Complete these activities. 1.1 1.2
A prime number can be divided only by 1 and itself. Circle the prime numbers. 6
11
17
20
27
29
32
A composite number can be divided by 1, itself, and other numbers. Circle the composite numbers. 7
19
21
24
31
35
36
1.3
Factors are numbers that when multiplied together produce a given number. Write all of the factors of these numbers.
6 _____________________________ 12 _______________________________
1.4
Multiples are the multiplication facts for a given number. Write five multiples of each number.
3 _____________________________
7 _______________________________
Section 1 | 3
WHOLE NUMBERS AND FRACTIONS | Unit 8 1.5
Follow the steps to multiply to tens’ place by two-digits. Solve.
48 × 63 144 2,880 3,024
1. Multiply 48 by 3 ones. 2. Put a 0 place holder in the ones’ place below the 4. 3. Multiply 48 by 6 tens. 4. Total the products.
1.6
Follow the steps to multiply to tens’ place by two-digits. Solve.
68 × 24
752 × 45 3,760 30,080 33,840
32 × 38
19 × 67
58 × 26
1. Multiply 752 by 5 ones. 2. Put a 0 place holder in the ones’ place below the 0. 3. Multiply 752 by 4 tens. 4. Total the products. 630
189 × 36
× 85
782 × 24
936 × 12
1.7
Write the largest number possible using the digits 3, 2, 5, 9, 1, 0.
_________________________
1.8
Write the numbers in order from smallest to largest.
352,649
__________ __________ __________ __________ __________ __________
1.9
Write the number in number words. Remember hyphens and commas.
a. 325,462 _________________________________________________________
b. 405,650 _________________________________________________________
4 | Section 1
325,649
25,469
525,694
52,699
365,649
Unit 8 | WHOLE NUMBERS AND FRACTIONS 1.10
Write the number words in digits.
three hundred thousand, fifty-six
_________________
seventeen thousand, two hundred three
_________________
Operation Signs 1.11
Perform the operations and circle the correct operation sign. (not all of these signs are equality / inequality signs some are > , < ) 7 × 5
16 – 3 ( > , < ) 4 + 8
d. 5 + 7 ( > , < ) 5 × 3
66 ÷ 11 ( > , < ) 6 × 2
1.12
Write the answer to the number sentence.
a. 3 + 8 – 6 = _____________
5 + 9 + 6 + 2 = _____________
b. 22 + 5 – 3 = _____________
63 – 2 + 8 = _____________
c. 9 + 3 + 8 + 4 = _____________
12 – 3 + 6 – 2 = _____________
d. 18 + 5 – 4 + 2 = _____________
4 + 4 + 2 + 10 = _____________
1.13
Circle the number ...
a. in the hundreds’ place.
638,742
b. in the ten thousands’ place.
890,361
c. in the ones’ place.
256,183
d. in the hundred thousands’ place.
745,102
1.14
What is the value of the underlined number?
a. 362,491 ______________
b. 462,108 ______________
c. 775,036 ______________
d. 963,482 ______________
1.15
Find the product.
a. 7 × 3 × 0 = _____________
c. 4 × 4 × 2 × 0 = _____________ d. 3 × 6 × 0 × 8 = _____________
b. 5 × 0 × 2 = _____________
Section 1 | 5
WHOLE NUMBERS AND FRACTIONS | Unit 8
Fractions Proper fractions have smaller numerators than denominators. They are less than a 2 __ whole number. 1 3
Mixed numbers are written with a whole number and a fraction. They are greater than 1 a whole number. >1 1__ 3
Complete this activity. 1.16
Describe each one of the following as: a) a proper fraction, b) an improper fraction, or c) a mixed number.
_______________ _______________ _______________
3 1 __ 5
_______________ _______________ _______________
6 | Section 1
15 ___ 8
5 __ 9
7 __ 4
1 1 __ 2__ 8 3
Unit 8 | WHOLE NUMBERS AND FRACTIONS Fractions can be simplified by:
• changing improper fractions to whole numbers or mixed numbers. (Divide denominator into numerator.)
• changing proper fractions to the smallest equivalent fraction. (Divide numerator and denominator by same factor.)
9 __ 4
=
2 R1 4 ) 9 8 1
=
1 2__ 4
3 ÷ 3 __ 9 ÷ 3
1 = __ 3
Complete these activities. 1.17
Simplify or reduce these fractions to lowest terms. Show your work.
a.
4 ___ = 12
10 ___ = 20
12 ___ = 18
b.
13 ___ = 8
11 ___ = 6
9 __ 7
=
Section 1 | 7
WHOLE NUMBERS AND FRACTIONS | Unit 8 We add or subtract fractions by drawing the fraction bar, writing the denominator, adding or subtracting the numerators, and simplifying the answers. 1.18
Add or subtract.
a. +
b. +
c. –
d. –
7 __ 9 1 __ 9
3 __ 8 2 __ 8
10 ___ 12 5 ___ 12
10 ___ 12 6 ___ 12
+
+
–
–
3 __ 4 2 __ 4
6 ___ 12 4 ___ 12
14 ___ 15 6 ___ 15
8 __ 9 6 __ 9
+
+
–
–
4 __ 5 3 __ 5
5 __ 8 4 __ 8
5 __ 9 2 __ 9
7 __ 9 2 __ 9
+
+
–
–
7 ___ 10 2 ___ 10
3 __ 7 2 __ 7
6 __ 8 4 __ 8
6 ___ 10 4 ___ 10
Review the material in this section to prepare for the Self Test. The Self Test will check your understanding of this section. Any items you miss on this test will show you what areas you will need to restudy in order to prepare for the unit test. 8 | Section 1
Unit 8 | WHOLE NUMBERS AND FRACTIONS
SELF TEST 1 Complete these activities (each question, 1 point). 1.01
Circle the prime numbers.
1.02
Circle the composite numbers.
3
6
8
14
14
19
17
25
21
31
25
29
35
33
Fill in the blanks (each question, 2 points). 1.03
Write all of the factors of these numbers.
1.04
Write five multiples of each number.
9 ________________________
14 ________________________
6 ________________________
8 ________________________
Solve these problems (each answer, 2 points). 1.05
Find the product a. b. 67 18 × 35 × 28
c.
d. 372 × 63
515 × 76
Write the answer for these questions (each question, 1 point). 1.06
Write the number in number words. Remember hyphens and commas.
402,391
1.07
Write the number word in digits.
three hundred thousand, fifty-six _________________
_________________________________________________________
Section 1 | 9
WHOLE NUMBERS AND FRACTIONS | Unit 8 Complete these activities (each answer, 1 point unless otherwise noted). 1.08
Circle the correct operation sign.
a. 18 ÷ 3 ( = , ≠ ) 2 × 3
8 × 3 ( = , ≠ ) 29 – 6
b. 48 – 3 ( > , < ) 39 + 5
15 ÷ 5 ( > , < ) 12 ÷ 3
1.09
Write the answer to the number sentence.
a. 3 + 6 – 5 = _____________
13 – 5 + 6 = _____________
b. 83 + 5 – 4 + 2 = _____________
76 – 3 – 3 + 7 = _____________
1.010 Circle the number ...
a. in the one thousands’ place.
546,728
b. in the hundred thousands’ place.
172,934
1.011 What is the value of the underlined number?
a. 831,492 ______________
b. 648,081 ______________
1.012 Describe each one of the following as: a) a proper fraction, b) an improper fraction, or c) a mixed number. 13 ___ 6
7 2 __ 1__ 4 3
4 __ 5
_____________ _____________ _____________ _____________
1.013 Add or subtract. Simplify answers. (each problem, 2 points)
+
10 | Section 1
2 __ 6 1 __ 6
+
4 __ 7 3 __ 7
–
8 __ 12 4 __ 12
–
4 __ 9 1 __ 9
Teacher check:
Initials ____________
Score ______________________
Date
____________
32 40
MAT_Gr3-5
MAT0408 – Jan ‘16 Printing 804 N. 2nd Ave. E. Rock Rapids, IA 51246-1759 800-622-3070 www.aop.com
ISBN 978-0-86717-458-8
9 780867 174588
