1. Using Proportions Math 8 Feb. 9

2.  We can use what we know about ratios and proportions to solve word problems Ratio  A comparison of two or more quantities with the same unit Proportion  A statement that two ratios are equal Think: equivalent ratios!

3.  How can we find the value of x? 5 : x = 40 : 56 Two methods: 1. Use proportions 2. Use equivalent fractions

4. 5 : x = 40 : 56 Rewrite your ratio as fractions 5 = 40 x 56 Cross multiply 5 * 56 = 40x Solve for x 280 = 40x 40 7 = x

5. 5 : x = 40 : 56 Think: 5 is less than 40 so we must divide to find x. What do we divide 40 by to get 5? Divide 56 by the same number 5 : x = 40 : 56 /8 x = 7

6. X : 3 = 12 : 36 Method 1: x = 12 3 36 12 * 3 = 36x 36 = 36x 36 x = 1 Method 2: 3 is less than 36 so we must divide X : 3 = 12 : 36 /12 x = 1

7. 49 : 35 = 14 : n Method 1: 49 = 14 35 n 35 * 14 = 49n 490 = 49n 49 n = 10 Method 2: 49 : 35 = 14 : n Since 14 is less than 49, we must divide What do we divide 49 by to get 14? Nothing! We must simplify the known ratio first 49 : 35 = 7 : 5 7 : 5 = 14 : n x 2 n = 10

8.  You have now learned 2 methods to solve a ratio problem  The most common is to use proportions  We will continue to use this method, however, use the method that you feel is most comfortable to you!

9. The photograph is a picture of a father and his daughter. In the photo, that father’s height is 8 cm and the daughter’s height is 6 cm. The father’s actual height is 1.8 m. What is the actual height of his daughter? Father : Daughter 8 : 6 = 180 : h 8 = 180 6 h 6 * 180 = 8h 1080 = 8h 8 h = 135 The daughter’s actual height Is 135 cm. Photo = Actual

10. A bike is in fourth gear. When the pedals turn 3 times, the rear wheel turns 7 times. When the pedal turns twice, how many times does the rear wheel turn? Pedal Turns : Wheel Turns 3 : 7 = 2 : t 3 = 2 7 t 7 * 2 = 3t 14 = 3t 3 t = 3.67When the pedals turn twice, The wheel turns 3.67 times.

11.  Please complete the following questions. Pg. 291 Part A  # 4a, 5a, 6a, 7a, 8 Part B  #4b, 5b, 6b 7b, 9 Part C  #4c, 5c, 6c, 7c, 10 Ask any questions you have!