Download Algebra

Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 8: Distributive Property
The Distributive Property states that the product of a number and the sum
(or difference) of two numbers is equal to the sum (or difference) of the two
products. In other words, you can distribute the value in front of the
parentheses to both values inside the parentheses.
Here’s how it looks: 5(2 1 4) 5 5 • 2 1 5 • 4
5(6) 5
5
30
You can use the distributive property to write equivalent expressions.
EXAMPLE 1
This example shows multiplication with addition.
Given Expression
2(3 1 4) 5 2(7)
Equivalent Expression
2(3) 1 2(4) 5 6 1 8
5 14
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
EXAMPLE 2
5 14
6. ALGEBRA
8. Distributive Property
30
HINT
Either way, you get
the same answer
10 1 20
This example shows multiplication with subtraction.
Given Expression
3(8 2 2) 5 3(6)
5 18
Equivalent Expression
3(8) 2 3(2) 5 24 2 6
5 18
Practice: First Try
Use the distributive property to write an equivalent expression.
Evaluate both expressions.
1. 5(2 1 6)
2. 10(8 2 5)
3. 2(9 1 3)
Use the distributive property to write an equivalent expression.
Simplify whenever possible.
4. 2(x 2 y)
5. 6(a 1 5)
6. 3(m 2 2)
7. 4c 1 4d
8. 7j 2 7k
9. 4z 1 8
McDougal Littell Middle School Math
Remediation Book Lesson 6.8
181
Name ———————————————————————
Date ————————————
Practice: Second Try
Use the distributive property to write an equivalent expression.
Evaluate both expressions.
1. 2(4 2 3)
2. 8(2 1 4)
3. 5(6 1 1)
4. 4(5 2 1)
5. 6(7 2 2)
6. 3(3 1 5)
6. ALGEBRA
8. Distributive Property
Use the distributive property to write an equivalent expression.
Simplify whenever possible.
7. 3(x 1 y)
8. 4(a 2 b)
9. 2(n 2 5)
10. 6(1 1 m)
1
11. }(10 2 x)
2
2
12. }(y 2 9)
3
13. 2a 1 2b
14. 5n 1 5m
15. 8y 2 8z
16. 9n 2 9
17. 3x 2 15
18. 2x 1 12
Extend Your Skills
19. The formula for the perimeter of a rectangle can be written two ways,
P 5 2l 1 2w
P 5 2(l 1w)
Use the distributive property to show that the formulas are equivalent.
Then use both formulas to find the perimeter of a rectangle with length 12 cm
and width 8 cm.
20. Hilary is going to buy 2 CDs and 5 DVDs. Use the distributive property to
show two ways to calculate the total cost if the CD and DVD cost $11 each.
Then find the total cost.
Puzzle
Fill in each circle with the correct variable. Then unscramble the letters in the circles
to form a word that means “dine largely”.
3(s 2 t) 5 3
8a 1 8b 1 8(
2 3t
1 b)
(9 2 f ) 5 9e 2 ef
182
McDougal Littell Middle School Math
Remediation Book Lesson 6.8
5(3 1
) 5 5(3) 1 5f
r(s 1 t) 5 rs 1 r
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
where l is the length and w is the width.
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Name ———————————————————————
SECTION
6
Date ————————————
Algebra
Lesson 8: Distributive Property
The Distributive Property states that the product of a number and the sum
(or difference) of two numbers is equal to the sum (or difference) of the two
products. In other words, you can distribute the value in front of the
parentheses to both values inside the parentheses.
Here’s how it looks: 5(2 1 4) 5 5 • 2 1 5 • 4
5(6) 5
5
30
You can use the distributive property to write equivalent expressions.
EXAMPLE 1
This example shows multiplication with addition.
Given Expression
2(3 1 4) 5 2(7)
Equivalent Expression
2(3) 1 2(4) 5 6 1 8
5 14
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
EXAMPLE 2
5 14
6. ALGEBRA
8. Distributive Property
30
HINT
Either way, you get
the same answer
10 1 20
This example shows multiplication with subtraction.
Given Expression
3(8 2 2) 5 3(6)
5 18
Equivalent Expression
3(8) 2 3(2) 5 24 2 6
5 18
Practice: First Try
Use the distributive property to write an equivalent expression.
Evaluate both expressions.
1. 5(2 1 6)
2. 10(8 2 5)
3. 2(9 1 3)
Use the distributive property to write an equivalent expression.
Simplify whenever possible.
4. 2(x 2 y)
5. 6(a 1 5)
6. 3(m 2 2)
7. 4c 1 4d
8. 7j 2 7k
9. 4z 1 8
McDougal Littell Middle School Math
Remediation Book Lesson 6.8
181
Name ———————————————————————
Date ————————————
Practice: Second Try
Use the distributive property to write an equivalent expression.
Evaluate both expressions.
1. 2(4 2 3)
2. 8(2 1 4)
3. 5(6 1 1)
4. 4(5 2 1)
5. 6(7 2 2)
6. 3(3 1 5)
6. ALGEBRA
8. Distributive Property
Use the distributive property to write an equivalent expression.
Simplify whenever possible.
7. 3(x 1 y)
8. 4(a 2 b)
9. 2(n 2 5)
10. 6(1 1 m)
1
11. }(10 2 x)
2
2
12. }(y 2 9)
3
13. 2a 1 2b
14. 5n 1 5m
15. 8y 2 8z
16. 9n 2 9
17. 3x 2 15
18. 2x 1 12
Extend Your Skills
19. The formula for the perimeter of a rectangle can be written two ways,
P 5 2l 1 2w
P 5 2(l 1w)
Use the distributive property to show that the formulas are equivalent.
Then use both formulas to find the perimeter of a rectangle with length 12 cm
and width 8 cm.
20. Hilary is going to buy 2 CDs and 5 DVDs. Use the distributive property to
show two ways to calculate the total cost if the CD and DVD cost $11 each.
Then find the total cost.
Puzzle
Fill in each circle with the correct variable. Then unscramble the letters in the circles
to form a word that means “dine largely”.
3(s 2 t) 5 3
8a 1 8b 1 8(
2 3t
1 b)
(9 2 f ) 5 9e 2 ef
182
McDougal Littell Middle School Math
Remediation Book Lesson 6.8
5(3 1
) 5 5(3) 1 5f
r(s 1 t) 5 rs 1 r
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
where l is the length and w is the width.