1. Solving Proportions

2. Definitions: Proportion – an equation stating that two ratios are equal Cross Products – are found by multiplying the denominator of each ratio by the numerator of the other ratio

3. Using Unit Rates: 2.45 dollars 5 cards = Step 1: Find the unit price Example: Postcards cost $2.45 for 5 cards. How much will 13 cards cost? $ 0. 49 per card Step 2: You know the cost of one card. Multiply to find the cost of 13 card. $ 0. 49 per card x 13 cards = $6.37

4. Using Unit Rates: 84.36 dollars 12 pairs = Step 1: Find the unit price Example: Goggles cost $84.36 for a case of 12. How much will it cost for 17 pairs? $ 7. 03 per pair of goggles Step 2: You know the cost of one pair of goggles. Multiply to find the cost of 17 pairs. $ 7. 03 per pair x 17 pairs = $119.51

5. Using Unit Rates: 7.75 dollars 5 notebooks = Step 1: Find the unit price Example: The bookstore sales five notebooks for $7.75. At this rate how much would 7 notebooks cost ? $ 1. 55 per notebook Step 2: You know the cost of one notebook. Multiply to find the cost of 7 notebooks. $ 1. 55 per notebook x 7 notebooks = $10.85

6. Using Unit Rates: 144 bricks 3 hours = Step 1: Find the unit price Example: Steven can lay 144 bricks in 3 hours. At this rate, how many bricks can he lay in 8 hours ? 48 bricks per hour Step 2: You know the number of bricks in 1 hour. Multiply to find the number in 8 hours. 48 bricks per hour x 8 hours = 384 bricks

7. m 12 = x 3 Since 12 x 3 = 36 21 36 Find what number times 3 equals 21 m = 7 8 10 = x 4 Since 10 x 4 = 40 k 40 8 x 4 = k k = 32 Using Mental Math:

8. 3 8 = x 3 Since 8 x 3 = 24 b 24 3 x 3 = b b = 9 5 g = x 6 Since 5 x 6 = 30 30 48 g = 8 Find what number times 6 equals 48 Using Mental Math:

9. Examples: S 4 7272 = 1.) Cross Multiply Opposite Numerators and denominators 2s2s =7 4 2.) Multiply 2s2s =28 3.) Divide both sides by 2 2s2s 2 = 28 2 s =14 4.) Simplify Using Cross Products:

10. Examples: 10 5 u3u3 = 1.) Cross Multiply Opposite Numerators and denominators 10 3 =5u 2.) Multiply 30 =5u 3.) Divide both sides by 5 30 5 = 5u 5 u =6 4.) Simplify Using Cross Products:

11. Examples: 20 w 12 3 = 1.) Cross Multiply Opposite Numerators and denominators 20 3 =12w 2.) Multiply 60 =12w 3.) Divide both sides by 12 60 12 = 12w 12 w =5 4.) Simplify Using Cross Products:

12. Examples: 9 30 p 16 = 1.) Cross Multiply Opposite Numerators and denominators 9 16 =30p 2.) Multiply 144 =30p 3.) Divide both sides by 30 144 30 = 30p 30 p =4.8 4.) Simplify Using Cross Products:

13. Writing Proportions: Eight out of ten fish are trout. How many trout are there out of 40 fish? 8 10 n 40 = Trout =32 8 40 =10n 320 10n 320 10 10n 10 = =

14. According to a label, there are 25 calories in a serving of turkey. How many calories are in 2.5 servings? 25 1 x 2.5 = Calories =62.5 25 2.5 = 1x 62.5 1x 62.5 1 1x 1 = = Writing Proportions:

15. Chris drove 200mi in 4 hours. At that rate, how long would it take Chris to drive 340mi? 200 4 340 h = hours =6.8 4 340 =200h 1360 200h 1360 200 200h 200 = = Writing Proportions: