Notes 28

1. Notes 28 Using Properties with Rational Numbers 6-3

2. Orlando works part-time at a moving company to earn money for a car. He earns $12.75 per hour. You can use the Distributive Property to calculate Orlando’s total earnings two different ways. The Distributive Property can be used to help you perform calculations more easily by writing equivalent expressions.

3. Remember The Distributive Property states: a(b + c) = ab + ac a(b - c) = ab - ac

4. Additional Example 1: Writing Equivalent Expressions An art teacher pays $13.89 for one box of watercolor brushes. She buys 6 boxes in March and 5 boxes in April. Use the Distributive Property to write equivalent expressions showing two ways to calculate the total cost of the watercolor boxes. Write an expression to show how much the teacher pays for a box and how many boxes purchased. Then use the Distributive Property to write an equivalent expression

5. Method 1 $13.89(6 + 5) $13.89(11) $152.79 Method 2 $13.89(6) + $13.89(5) $83.34 + $69.45 $152.79 Both methods result in a calculation of $152.79 for the amount of money spent of watercolor brushes.

6. Check It Out : Example 1 Jamie earns $8.75 per hour. Last week she worked 15 hours and next week she will work 20 hours. Use the Distributive Property to write equivalent expressions showing two ways to calculate how much money she earned. Write an expression to show how much Jamie earns and the number of hours she works. Then use the Distributive Property to write an equivalent expression.

7. 3 4 5 6 X + 7 = 3 4 5 6 x + 7 = 3 4 5 6 12 x+ 7 = 12 3 1 4 5 1 6 12 2 3 12 x + 12 (7) = Additional Example 2 : Writing Equivalent Expressions Write an equivalent equation for that does not contain fractions. Then solve the equation. The LCM of denominators is 12. Multiply both sides by 12. Simplify.

8. -84 -84 9 9 2 9 x = -8 An equivalent equation is 9x + 84 = 10 and the solution is 2 9 x = -8 Additional Example 2 : Continued 9x + 84 = 10 is an equivalent expression 9x + 84 = 10 9x + 84 = 10 Subtract 84 from both sides. 9x = -74 Divide both side by 9

9. 1 2 4 6 X + 9 = Check It Out: Example 2 Write an equivalent equation for that does not contain fractions. Then solve the equation.

10. Helpful Hint 75 100 0.75 can also be written as

11. Additional Example 3: Construction Application The soccer team uses a 36.75-liter container to take water to games. The team manager fills 0.75 liter bottles from this. He has used 22.5 liters. How many more 0.75 liter bottles can he fill before he runs out of water? Write and solve an equivalent equation without decimals. Write an equation to represent the situation. 0.75x + 22.5 = 36.75

12. Continued: Example 3 Write an equivalent equation without decimals. The equation has decimals to the hundredths, so multiply both sides by 100. 100(0.75x + 22.5) = (36.75)100 Use the Distributive Property 100(0.75x + 100(22.5) = (36.75)100 Simplify to get an equivalent equation without decimals 75x + 2,250 = 3,675

13. Continued: Example 3 75x + 2,250 = 3,675 -2250 -2250 75x = 1,425 75 75 x = 19 The number of 0.75 liter bottles that he can fill before he runs out of water is 19.

14. Check It Out: Example 3 …If the soccer team uses a 42.5-liter container, about how many 0.75 liter bottles can the manager fill before he runs out of water? Write an equation to represent the situation. 0.75x + 22.5 = 42.5