1. Ratios and Proportions Foundations of Algebra

2. Ratio and Proportion A ratio is an ordered pair of real numbers, written a:b when b Cannot be 0.

3. Ratio and Proportion Recall that a fraction is always used for part-to-whole comparison, but a ratio can be used for: 1. part-to-part comparison 2. part-to-whole comparison 3. other comparisons such as length-to- width.

4. Ratio and Proportion Equality of ratios: Two ratios a:b and c:d are equal if and only if: a ×d = b ×c i.e. a : b = c : d if and only if: inside×inside = outside×outside This looks like cross multiplication just without fractions.

5. Lets Remember Cross Multiplication Start with two fractions: 4848 =4x = 5 84x = 40 5 x 4x = 40x = 104

6. Proportions A proportion is a statement that two given ratios are equal. Practical example: If you are mixing paint to paint your house, you need to keep the ratio (of color pigments to white paint) constant to ensure that the color will remain exactly the same.

7. Proportions More Practical examples: 1.If city tax rate is $7.75 to every $100 of purchase, then you have to use the same ratio no matter how much your purchase is (because it is the law). 2.If you want to enlarge a 4”×5” picture, then you should keep the same ratio in dimension to avoid distortion.

8. Examples: Write the fraction as a ratio: 1.4/5 2.6/19 3.23/27 Write the ratio as a fraction: 1.5:42 2.3:8 3.6:5

9. Proportions: Are these ratios equivalent? Do they make a proportion? 1.2:9 and 12:54 2.3:5 and 27:45 3.8:3 and 32:12

10. Examples: Find the missing number in the given proportion: 1.2 : 5 = X : 20 1.3 : 7 = 27 : X Solve these proportions: 1. 2.