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Main Idea/Vocabulary

Use the Distributive Property to simplify algebraic expressions. equivalent expressions. constant simplest form simplifying the expression. term coefficient like terms. Main Idea/Vocabulary. Write Expressions With Addition. Use the Distributive Property to rewrite 3( x + 5).

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Main Idea/Vocabulary

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  1. Use the Distributive Property to simplify algebraic expressions. • equivalent expressions • constant • simplest form • simplifying the expression • term • coefficient • like terms Main Idea/Vocabulary

  2. Write Expressions With Addition Use the Distributive Property to rewrite 3(x + 5). 3(x + 5) = 3(x) + 3(5) = 3x + 15 Simplify. Answer: 3x + 15 Example 1

  3. A B C D Use the Distributive Property to rewrite 2(x + 6). A.x + 8 B.x + 12 C. 2x + 6 D. 2x + 12 Example 1

  4. Write Expressions With Addition Use the Distributive Property to rewrite (a + 4)7. (a + 4)7 = a●7 + 4 ●7 = 7a + 28 Simplify. Answer: 7a + 28 Example 2

  5. A B C D Use the Distributive Property to rewrite (a + 6)3. A. 3a + 27 B. 3a + 18 C. 3a + 9 D.a + 18 Example 2

  6. Write Expressions With Subtraction Use the Distributive Property to rewrite (q – 3)9. (q – 3)9 = [q + (–3)]9 Rewrite q – 3 as q + (–3). = (q)9 + (–3)9 Distributive Property = 9q + (–27) Simplify. = 9q – 27 Definition of subtraction Answer: 9q – 27 Example 3

  7. A B C D Use the Distributive Property to rewrite (q – 2)8. A.q – 16 B.q – 10 C. 8q – 16 D. 8q – 10 Example 3

  8. Write Expressions With Subtraction Use the Distributive Property to rewrite –3(z – 7). –3(z – 7) = –3[z + (–7)] Rewrite z – 7 as z + (–7). = –3(z) + (–3)(–7) Distributive Property = –3z + 21 Simplify. Answer: –3z + 21 Example 4

  9. A B C D Use the Distributive Property to rewrite –2(z – 4). A. –2z + 8 B. –2z – 8 C. –2z – 4 D. –2z Example 4

  10. Identify Parts of an Expression Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x. 3x – 5 + 2x – x = 3x + (–5) + 2x + (–x)Definition of subtraction = 3x + (–5) + 2x + (–1x)Identity Property; –x = –1x Answer: The terms are 3x, –5, 2x, and –x.The like terms are 3x, 2x, and –x.The coefficients are 3, 2, and –1.The constant is –5. Example 5

  11. A B C D Identify the terms, like terms, coefficients, and constants in 6x – 2 + x – 4x. A.terms: 6x, 2, x, and –4x; like terms: 6x, x, and –2x; coefficients: 6, –2, and –4;constant: –2 B.terms: 6x, –2, x, and –4x; like terms: 6x, x, and –4x; coefficients: 6, 1, and –4;constant: –2 C.terms: 6x, –2, x, and –4; like terms: 6x, x, and –2; coefficients: 6, 1, and –4;constant: –4 D.terms: 6x, –2, x, and –4x; like terms: 6x, x, and –4x; coefficients: 6, –4, and –2;constant: 6 Example 5

  12. Simplify Algebraic Expressions Simplify the expression 6n – n. 6n – n are like terms. 6n – n = 6n – 1nIdentity Property; n = 1n = (6 – 1)nDistributive Property = 5n Simplify. Answer: 5n Example 6

  13. A B C D Simplify the expression 7n + n. A. 10n B. 8n C. 7n D. 6n Example 6

  14. Simplify Algebraic Expressions Simplify 8z + z – 5 – 9z + 2. 8z, z, and –9z are like terms. –5 and 2 are also like terms. 8z + z – 5 – 9z + 2 = 8z +z + (–5) + (–9z) + 2 Definition of subtraction = 8z +z + (–9z)+ (–5) + 2 Commutative Property = [8 + 1+ (–9)]z+ [(–5) + 2] Distributive Property = 0z + (–3) or –3 Simplify. Answer: –3 Example 7

  15. A B C D Simplify 6z + z – 2 – 8z + 2. A. –z B. –z + 2 C.z –1 D. –2z Example 7

  16. THEATERTickets for the school play cost $5 for adults and $3 for children. A family has the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets. Words$5 each for adults and $3 each for the same number of children. Variable Let x represent the number of adults or children. Equation5● x + 3 ● x Example 8

  17. Simplify the expression. 5x + 3x = (5 + 3)x Distributive Property = 8x Simplify. Answer: The expression $8x represents the total amount of money spent on tickets. Example 8

  18. A B C D MUSEUMTickets for the museum cost $10 for adults and $7.50 for children. A group of people have the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets to the museum. A. $2.50x B. $7.50x C. $15.50x D. $17.50x Example 8

  19. A B C D (over Chapter 7) Find the area of a triangle with base 10 in. and height 15 in. A. 25 in2 B. 50 in2 C. 75 in2 D. 150 in2 Five Minute Check 1

  20. A B C D (over Chapter 7) Find the area of a circle with diameter 14 m. A. 153.9 m2 B. 196.0 m2 C. 307.8 m2 D. 615.6 m2 Five Minute Check 2

  21. A B C D (over Chapter 7) Find the volume of a rectangular prism with length 3 yd, width 5 yd, and height 7 yd. Round to the nearest tenth if necessary. A. 15 yd3 B. 52.5 yd3 C. 71 yd3 D. 105 yd3 Five Minute Check 3

  22. A B C D (over Chapter 7) Find the volume of a cone with diameter 9 ft and height 5 ft. Round to the nearest tenth if necessary. A. 106 ft3 B. 159 ft3 C. 318 ft3 D. 424 ft3 Five Minute Check 4

  23. A B C D (over Chapter 7) Find the surface area of a rectangular prism that is 15 cm long, 20 cm wide, and 25 cm tall. A. 1,175 cm2 B. 2,350 cm2 C. 3,750 cm2 D. 7,500 cm2 Five Minute Check 5

  24. A B C D (over Chapter 7) Find the total surface area of a square pyramid if each side of the base is 9 inches and the slant height is 8 inches. A. 144 in2 B. 225 in2 C. 288 in2 D. 369 in2 Five Minute Check 6

  25. End of Custom Shows

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