Name
LESSON
Date
Class
Problem Solving
1-4 Properties of Numbers
Write the correct answer.
1. Jo makes and sells jewelry. She sold
three bracelets for $45, $17, and
$25. Write an expression for the total
Jo received. Explain how you can
use properties and mental math to
simplify the expression.
2. Use parentheses to show two ways of
grouping the numbers in 12 • 8 • 25.
Tell which expression you think would
be easier to simplify, and why. Then
simplify the expression.
3. The distance from Mark’s apartment
to his job is 27 miles. Mark works 5
days per week. How many miles
does Mark drive to and from work
each week?
4. Jane said that 6(64) 6(50) 6(14).
Is she correct? Use the Distributive
Property to explain your answer.
Choose the letter for the best answer.
5. Maxine works 8 hours at a rate of
$16 per hour. Which expression could
not be used to find her total earnings
in dollars?
A 8 • (10 • 6)
B 8 • (20 4)
C 8 • (10 6)
D 8 • (8 8)
6. Rosemary runs 16 miles on Friday, 8
miles on Saturday, and 14 miles on
Sunday. How many miles does
Rosemary run in all?
F 22 mi
G 24 mi
H 30 mi
J 38 mi
7. Which of the following represents the
Identity Property?
8. Which of the following shows how the
Distributive Property could be used
to simplify 7(28)?
F 7•2•8
G 7 • (20 • 8)
H 7 • (20 8)
J (7 • 20) 8
A
B
C
D
(8 • 4) • 3 8 • (4 • 3)
16 • 0 0
25 • 1 25
6(26) 6(20) 6(6)
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Holt Mathematics
Problem Solving
1-4 Properties of Numbers
Challenge
1-4 What’s the Expression?
LESSON
LESSON
Write the correct answer.
On each tic-tac-toe board below, exactly one row, column, or
diagonal contains three expressions with the same value.
1. Jo makes and sells jewelry. She sold
three bracelets for $45, $17, and
$25. Write an expression for the total
Jo received. Explain how you can
use properties and mental math to
simplify the expression.
Predict which row, column, or diagonal of squares will have
three expressions with the same value. Draw a line through
those three squares. Then check your prediction. Find the value
of each expression on the board.
9(80 12)
1 • 621
(2 9)34
612
621
374
2. Use parentheses to show two ways of
grouping the numbers in 12 • 8 • 25.
Tell which expression you think would
be easier to simplify, and why. Then
simplify the expression.
Possible answer: $45 $17 $25;
Possible answer: (12 • 8) • 25,
use the commutative and associative
12 • (8 • 25); 12 • (8 • 25) is easier
properties to rewrite the expression as
to multiply, because 12 • 200 is easier
($45 $25) $17, then add mentally.
9(30 4)
2 • 9 • 34
(3 • 3)60
306
612
540
2(9 34)
9(70 – 2)
9(60 8)
86
612
612
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to multiply than 96 • 25; 2,400
4. Jane said that 6(64) 6(50) 6(14).
Is she correct? Use the Distributive
Property to explain your answer.
3. The distance from Mark’s apartment
to his job is 27 miles. Mark works 5
days per week. How many miles
does Mark drive to and from work
each week?
Possible answer: Yes. Since
50 14 64, 6(64) 6(50 14) 6(50) 6 (14).
270 mi
Choose the letter for the best answer.
(4 • 3)(8 • 8)
12(80 8)
768
12(60 12)
864
864
12(60 4)
(2 • 2)64
1 • (12 • 72)
768
256
864
(70 6)4
4 • (3 72)
(4 • 3)72
256
300
864
33
5. Maxine works 8 hours at a rate of
$16 per hour. Which expression could
not be used to find her total earnings
in dollars?
A 8 • (10 • 6)
B 8 • (20 4)
C 8 • (10 6)
D 8 • (8 8)
6. Rosemary runs 16 miles on Friday, 8
miles on Saturday, and 14 miles on
Sunday. How many miles does
Rosemary run in all?
F 22 mi
G 24 mi
H 30 mi
J 38 mi
7. Which of the following represents the
Identity Property?
8. Which of the following shows how the
Distributive Property could be used
to simplify 7(28)?
F 7•2•8
G 7 • (20 • 8)
H 7 • (20 8)
J (7 • 20) 8
A (8 • 4) • 3 8 • (4 • 3)
B 16 • 0 0
C 25 • 1 25
D 6(26) 6(20) 6(6)
Holt Mathematics
34
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Holt Mathematics
Puzzles, Twisters, & Teasers
1-4 Make the Connection!
Reading Strategies
1-4 Use a Flowchart
LESSON
LESSON
Use a flowchart to help you simplify an expression, such as (25 89) 15.
Draw a line to connect each equation to the property it represents.
Step 1: Choose two numbers that are easy to add.
(25 89) 15
Step 2: Rewrite the expression so the two numbers are next to each other.
Use the Commutative Property. (25 89) 15 (89 25) 15)
Step 3: Rewrite the expression so the two numbers are grouped together.
Use the Associative Property. (89 25) 15 89 (25 15)
Identity Property
R
2. 1 • 15 15
Commutative Property
Y
3. 9(4 6) 9(4) 9(6)
Associative Property
E
4. 38 7 7 38
Distributive Property
P
Draw a line to connect expressions with the same value.
Step 4: Add.
89 (25 15) 89 40 129
Use the expression 16 (39 14) for Exercises 1-4.
16 and 14
1. Which two numbers are easy to add?
1. 3 • (8 • 5) (3 • 8) • 5
2. Rewrite the expression so that the numbers that are easy
to add are next to each other. What property lets you do this?
16 (14 39); Commutative Property
3. Rewrite the expression so that the numbers that are easy to add
are grouped together. What property lets you do this?
5. 5 (7 6)
5(7) 5(6)
S
6. 5(70 6)
5(70) 5(6)
H
7. 5 70 6
(5 7) 6
T
8. 5 • 7 • 6
(5 • 70) • 6
I
9. 5(13)
7 • (5 • 6)
D
10. 5(70 6)
70 11
L
11. 5 • (70 • 6)
5(70) 5(6)
K
Start with number 1. Find the letter next to the answer. Use the
letters to find out why potatoes are good detectives.
(16 14) 39); Associative Property
69
4. Simplify the expression.
Use the expression 35 47 5 for Exercises 5-8.
35 and 5
5. Which two numbers are easy to add?
6. Rewrite the expression so that the numbers that are easy to add
are next to each other. What property lets you do this?
47 35 5; Commutative Property
T
H
E
Y
K
E
E
P
5
10
1
4
6
1
1
3
T
H
E
I
R
E
Y
E
S
5
10
1
11
2
1
4
1
9
P
E
E
L
E
D
3
1
1
7
1
8
7. Rewrite the expression so that the numbers that are easy to add
are grouped together. What property lets you do this?
47 (35 5); Associative Property
87
8. Simplify the expression.
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All rights reserved.
35
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
112
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Holt Mathematics
Holt Mathematics