1. Ratios and Proportion UMI: July 9, 2015

6. Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk. So the ratio of flour to milk is 3 : 2 To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4: 3×4 : 2×4 = 12 : 8 In other words, 12 cups of flour and 8 cups of milk. The ratio is still the same, so the pancakes should be just as yummy.

7. "Part-to-Part" and "Part-to-Whole" Ratios: Example: There are 20 students, 5 are girls, and 15 are boys Part-to-Part: The ratio of boys to girls is 15:5=3:1 or 3/1 The ratio of girls to boys is 5:15=1:3 or 1/3

8. Part-to-Whole: The ratio of boys to all students is 15:20=3:4 or 3/4 The ratio of girls to all students is 5:20=1:4 or 1/4

9. Try It Yourself Answer the following regarding the English alphabet: 1.Determine the ratio vowels to constants. 2.What is ratio of constants to vowels? 3.What is ratio of constants to letters in the English alphabet? 4.Write a word that has a ratio of 2:3 of vowels to constants. Part-to-Part: The ratio of boys to girls is 15:5=3:1 or 3/1 The ratio of girls to boys is 5:15=1:3 or 1/3

11. Proportions Proportion says that two ratios (or fractions) are equal. Example : So 1-out-of-3 is equal to 2-out-of-6 The ratios are the same, so they are in proportion.

15. Practice: 1.The ratio of the weight of Meg’s cat to the weight of Anne’s cat is 5:7. Meg’s cat weighs 20 kg. How much more does Anne’s cat weigh?

17. Practice: 2.Pat the Painter mixed 3 pints of yellow paint with 4 pints of green paint to make a nifty new color. He used 27 pints of yellow paint. How many pints of green paint will he need?

19. Practice: 3.The ratio of boys to girls at the basketball game is 8:5. There are 30 girls. How many more boys are there than girls?

21. Practice: 4.Ben and Matt received votes in the ratio 2:3. The total number of votes cast was 60. How many votes did Ben get?

23. Thank You References: 1.A problem solving approach to mathematics for elementary school teachers by Billstein, Libeskind, Lott 2.Math Playground: http://www.mathplayground.com/http://www.mathplayground.com/ 3.Math is Fun : https://www.mathsisfun.com/index.htmhttps://www.mathsisfun.com/index.htm