The Distributive Property

ALGEBRA 1 LESSON 1-7ALGEBRA 1 LESSON 1-7

(For help, go to Lessons 1-2 and 1-6.)

Use the order of operations to simplify each expression.

1. 3(4 + 7) 2. –2(5 + 6) 3. –1(–9 + 8)

4. –0.5(8 – 6) 5. t(10 – 4) 6. m(–3 – 1)

The Distributive Property

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1. 3(4 + 7) = 3(11) = 33

2. –2(5 + 6) = –2(11) = –22

3. –1(–9 + 8) = –1(–1) = 1

4. –0.5(8 – 6) = –0.5(2) = –1

5. t(10 – 4) = t(6) = (6)t = • 6 t = 3t

6. m(–3 – 1) = m(–4) = –4m

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Solutions

Use the Distributive Property to simplify 26(98).


26(98) = 26(100 – 2) Rewrite 98 as 100 – 2.

= 26(100) – 26(2) Use the Distributive Property.

= 2600 – 52 Simplify.

= 2548


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Find the total cost of 4 CDs that cost $12.99 each.

4(12.99) = 4(13 – 0.01) Rewrite 12.99 as 13 – 0.01.

= 4(13) – 4(0.01) Use the Distributive Property.

= 52 – 0.04 Simplify.

= 51.96

The total cost of 4 CDs is $51.96.



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Simplify 3(4m – 7).

3(4m – 7) = 3(4m) – 3(7) Use the Distributive Property.

= 12m – 21 Simplify.



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Simplify –(5q – 6).

–(5q – 6) = –1(5q – 6) Rewrite the expression using –1.

= –1(5q) – 1(–6) Use the Distributive Property.

= –5q + 6 Simplify.



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Simplify –2w2 + w2.

–2w2 + w2 = (–2 + 1)w2 Use the Distributive Property.

= –w2 Simplify.



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Relate: –6 times the quantity 7 minus m

Write: –6 • (7 – m)

Write an expression for the product of –6 and the quantity 7

minus m.

–6(7 – m)



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Simplify each expression.

1. 11(299) 2. 4(x + 8) 3. – 3(2y – 7)

4. –(6 + p) 5. 1.3a + 2b – 4c + 3.1b – 4a

6. Write an expression for the product of and the quantity b minus .

3289 4x + 32 – 6y + 21

– 6 – p –2.7a + 5.1b – 4c

47

35b –( )


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Documents

The Distributive Property