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Name: ______________________ Period:______ Date: __________ 1.7 Distributive Property AREA Compare = length x width 3 x 14 and 3 x (10 + 4) 14 = 10 + 4 10 3 3 3(10 + 4) = 3 x 14 = 42 4 3 3(10 + 4) = 3 x 10 + 3 x 4 = 30 + 12 = 42 Add, Multiply Multiply, Add The Distributive Property combines addition and multiplication, "multiplication distributes over addition". Formally, they write this property as "a(b Examples + c) = ab + ac". a. 2(6 + 3) = 2 · 6 + 2 · 3 = b. 7(24) = 7(20 + 4)= 140 + 28 = 168 12 + 6 = 18 c. 7(m - 5) = 7m - 35 d. (m + n - 8)3 = 3m + 3n - 24 Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression, if possible. 1. 3(8 + 2) 24 + 6 = 30 2. 2(9 + 11) 18 + 22 = 40 3. (19 – 6)5 95 – 30 = 65 3 _ 8 _ 3 _ 2; 30 2 _ 9 _ 2 _ 11; 40 5 _ 19 _ 5 _ (_6); 65 4. 6(27) 6(20 + 7)= 120 +42= 142 5. 3(38) 3(30 + 8) = 90 + 24= 114 6. (5 + 3)7 7(5) + 7(3) = 35 + 21 = 56 7. 3(d + 4) 8. (w – 5)4 9. 2(c + d + 7) 3d + 12 4w – 20 2c + 2d + 14 Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. 1. 8(24) = 8(20 + 4) 3. 2(64) = 2( 60 + 2. 19 · 5 = (20 - 1)5 ) 4. 7(43) = 7( + ) 400 _ 32; 432 100 _ 45; 145 120 _ 8; 128 280 _ 14; 266 5. 4(100 – 2) 6. 4(17) = 7. 8(10 + 1) 8. 9 x 24 = 1600 _ 8; 1592 _64 _ 20; _84 _32 _ 8; _40_ 9; _66 294 _ 154; 140 _2000 _ 50; _2050 13,950 _ 558; 13,392 Use the Distributive Property to write each expression as an equivalent algebraic expression. 9. 7( y + 11) 10. 6(t – 1) 11. 8(u – 2) 12. (r + 9)(4) 7y _ 77 _6t _ 6 _8u _ 16 _4r _ 36 13. 1(h + 5) 14. 2( f + g + 3) 15. 4(b – 1) 16. (7 – v)· 1 17. 5(1 – b) 19. 8(q – 5) 20. 4(h – 16) h _ 5 _2f _ 6 _4b _4 7 _ v 21. 2(d – 5) 22. 2(n + 10 - m) 23. 50(z - 1) 24. 12( g + 12) _2d _ 10 22n _ 220 _50z _ 50 _12g _ 144 25. 1(2 - y) 26. 0(a + 1) = 0 27. (-8 - s)(9) 28. 9(r – 1) 18. 0(x + 12) _2 _ y _7a _7 11k _ 220 _9r _ 9_ 19 _r _ 27 53x _ 583 17n _ 17 37. PLANTS A planter weighs 2 pounds and holds 3 pounds of soil. Write two equivalent expressions for the total weight of nine planters. Then find the weight. 9(2 + 3) = 9(5) = 45 OR 9(2) + 9(3) = 18 + 27 9(2 _ 3), 9(2) _ 9(3); 45 pounds 38. UNIFORMS A uniform costs $42 for the sweater and $29 for the slacks. Write two equivalent expressions for the total cost of six uniforms. Then find the cost.