1. The Distributive Property Objective: 5.04 Develop fluency in the use of formulas to solve problems.

2. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca Example 2 Simplify each expression. c.(8 + x)5 + 2x

3. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca

4. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca Example 2 Simplify each expression. c.(8 + x)5 + 2x (8 + x)5 + 2x = 8. 5 + x. 5 + 2x Distributive Property

5. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca Example 2 Simplify each expression. c.(8 + x)5 + 2x (8 + x)5 + 2x = 8. 5 + x. 5 + 2x Distributive Property = 40 +5x + 2x Substitution Property

6. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca Example 2 Simplify each expression. c.(8 + x)5 + 2x (8 + x)5 + 2x = 8. 5 + x. 5 + 2x Distributive Property = 40 +5x + 2x Substitution Property = 40 +(5 + 2)xDistributive Property

7. The Distributive Property 1.a(b + c) = ab + ac 2.(b + c)a = ba + ca Example 2 Simplify each expression. c.(8 + x)5 + 2x (8 + x)5 + 2x = 8. 5 + x. 5 + 2x Distributive Property = 40 +5x + 2x Substitution Property = 40 +(5 + 2)xDistributive Property = 40 + 7xSubstitution Property

8. Using Formulas Objective: 5.04 Develop fluency in the use of formulas to solve problems.

9. Using Formulas A formula shows the relationship between certain quantities. Variables are used to represent these qualities.

10. Using Formulas Write a formula for the diameter of a circle, given it radius r. It is often helpful to draw a picture. Let d = diameter. Let r = radius The radius is equal to half the diameter of a circle. r = ½ d So, d = 2r.

11. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. 18m.

12. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. r = ?

13. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. 18 = 2rSubstitute 18 for d.

14. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. r = ?

15. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. 18 = 2rSubstitute 18 for d. 18/2 = 2r/2Divide each side by 2.

16. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. 18 = 2rSubstitute 18 for d. 18/2 = 2r/2Divide each side by 2. 9 = r r = 9

17. Using Formulas Example Use the formula d = 2r to find the radius of a circle that has a diameter of 18 meters. d = 2rDiameter formula. 18 = 2rSubstitute 18 for d. 18/2 = 2r/2Divide each side by 2. 9 = r A circle with a diameter of 18 meters has a radius of 9 meters.

18. Using Formulas Integration An equilateral triangle is a triangle whose three sides are all equal in length. Give a formula for the perimeter of any equilateral triangle. ss s

19. Using Formulas Integration An equilateral triangle is a triangle whose three sides are all equal in length. Give a formula for the perimeter of any equilateral triangle. Answer: p = 3s where p = perimeter and s = length of each side.

20. Using Formulas The speed limit along a particular highway increased from 55 mph to 65 mph. How much time will be saved on a 100-mile trip? Think! d = rt (distance = rate X time 100 (d) = 65 (rate) t 100d = 65t 100 (d) = 55 (rate) t 100 d = 55 t

21. Using Formulas The formula F = n/4 + 37 can be used to find the degrees Farenheit when n is the number of cricket chirps per minute. If a cricket chirps 126 times per minute, determine the temperature.