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1-5 The Distributive Property

1-5 The Distributive Property. Objective: Simplify algebraic expressions using the distributive property. 5-Minute Check. Name the property shown by each statement. (4b)c = 4(bc). 5-Minute Check. Name the property shown by each statement. (4b)c = 4(bc) associative, X. 5-Minute Check.

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1-5 The Distributive Property

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  1. 1-5 The Distributive Property Objective: Simplify algebraic expressions using the distributive property.

  2. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc)

  3. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) associative, X

  4. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0

  5. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0 mult. prop. of 0

  6. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0 Find each sum or product mentally. 3. 18 + 13 + 2 + 7

  7. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0 Find each sum or product mentally. 3. 18 + 13 + 2 + 7 40

  8. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0 Find each sum or product mentally. 3. 18 + 13 + 2 + 7 4. 6 . 7 . 5

  9. 5-Minute Check Name the property shown by each statement. • (4b)c = 4(bc) • (7 + 4)0 = 0 Find each sum or product mentally. 3. 18 + 13 + 2 + 7 4. 6 . 7 . 5 210

  10. 5-Minute Check Find each sum or product mentally. 5. A recent study showed that 63 million Americans choose swimming as their favorite sport, 55 million chose hiking, and 47 million chose camping. How many people chose one of these three sports as their favorite?

  11. 5-Minute Check Find each sum or product mentally. 5. A recent study showed that 63 million Americans choose swimming as their favorite sport, 55 million chose hiking, and 47 million chose camping. How many people chose one of these three sports as their favorite? 165 million

  12. The Distributive Property

  13. The Distributive Property Example 1 Find 11(13) mentally using the distributive property.

  14. The Distributive Property Example 1 Find 11(13) mentally using the distributive property. 11(13) = 11(10 + 3) Replace 13 with 10 + 3.

  15. The Distributive Property Example 1 Find 11(13) mentally using the distributive property. 11(13) = 11(10 + 3) Replace 13 with 10 + 3. =11.10 + 11.3 Think of 110 + 33.

  16. The Distributive Property Example 1 Find 11(13) mentally using the distributive property. 11(13) = 11(10 + 3) Replace 13 with 10 + 3. =11.10 + 11.3 Think of 110 + 33. = 110 + 33 or 143

  17. The Distributive Property • Example 2 • Simplify each expression. • 56x + 73x

  18. The Distributive Property • Example 2 • Simplify each expression. • 56x + 73x • 56x + 73x = (56 + 73)x x is a factor in both 56x and 73x.

  19. The Distributive Property • Example 2 • Simplify each expression. • 56x + 73x • 56x + 73x = (56 + 73)x x is a factor in both 56x and 73x. • = 129x Use the distributive property.

  20. The Distributive Property Example 2 Simplify each expression. b. 5a + a

  21. The Distributive Property Example 2 Simplify each expression. b. 5a + a 5a + a = 5a + 1a a = 1.a by multiplicative property.

  22. The Distributive Property Example 2 Simplify each expression. b. 5a + a 5a + a = 5a + 1a a = 1.a by multiplicative property. = (5 + 1)a Distributive property

  23. The Distributive Property Example 2 Simplify each expression. b. 5a + a 5a + a = 5a + 1a a = 1.a by multiplicative property. = (5 + 1)a Distributive property = 6a

  24. The Distributive Property • Example 2 • Simplify each expression. • (8 + x)5 + 2x

  25. The Distributive Property • Example 2 • Simplify each expression. • (8 + x)5 + 2x • (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property

  26. The Distributive Property • Example 2 • Simplify each expression. • (8 + x)5 + 2x • (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property • = 40 +5x + 2x Substitution Property

  27. The Distributive Property • Example 2 • Simplify each expression. • (8 + x)5 + 2x • (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property • = 40 +5x + 2x Substitution Property • = 40 +(5 + 2)x Distributive Property

  28. The Distributive Property • Example 2 • Simplify each expression. • (8 + x)5 + 2x • (8 + x)5 + 2x = 8.5 + x.5 + 2x Distributive Property • = 40 +5x + 2x Substitution Property • = 40 +(5 + 2)x Distributive Property • = 40 + 7x Substitution Property

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