1. Math 015 Section 7.4 Proportions

2. Obj: To determine whether a proportion is true A proportion is a statement of equality between two ratios or between two rates. 50 miles 25 miles 4 gallons 2 gallons = Notice that the units in the numerators of these rates are the same and the units in the denominators are the same. 3 1 6 2 =

3. Obj: To determine whether a proportion is true A proportion is true if the fractions are equal when written in simplest terms.  A proportion is true if the cross products are equal 2 8 3 12 = 3  8 = 24 2  12 = 24 The proportion is true. 4 8 5 9 = 5  8 = 40 4  9 = 36 The proportion is not true.

4. State whether the following are true proportions. 62 miles 33 miles 4 gallons 2 gallons 6 9 10 15 = = 132 124 The proportion is not true The proportion is true = 90 =

5. Obj: To solve a proportion Use the cross product rule to rewrite the equation Solve the new equation Check your answer Example: Solve n 25 12 60 = 60 n = 300 n = 5

6. Obj: To solve a proportion Use the cross product rule to rewrite the equation Solve the new equation Check your answer Example: Solve 9 n 7 21 = 7n 189 = n = 27

7. Obj: To solve a proportion Example: Solve n + 2 1 5 2 = 2n = 1 n = 1/2 2n + 4 = 5

8. Obj: To solve a proportion Solve: x + 5 2 x 3 = 3x + 15= 2x x + 15 = 0 x = -15

9. Obj: To solve a proportion Example: Solve n 14 5 9 = 9n 70 = n = 7 7979

10. Obj: To solve a proportion Example: Solve 1.9 13 Round to the nearest 7 nhundredth = 1.9n 91 = n = 47.8947368 n = 47.89

11. Obj: To solve application problems Three tablespoons of a liquid fertilizer are to be added to every 4 gallons of water. How many tablespoons of fertilizer are required for 10 gallons of water? 3 tablespoons n tablespoons 4 gallons 10 gallons = 4n 30 = n = 7.5 Answer: 7.5 tablespoons should be added to 10 gallons

12. Obj: To solve application problems When engineers designed a new car, they first built a model of the car. The ratio of the size of a part on the model to the actual size of the part is 2:5. If a door is 1.3 feet long on the model, what is the length of the door on the car? 2 1.3 5 n = 2n 6.5 = n = 3.25 Answer: The door on the real car will be 3.25 feet long Model 2 Real 5 =