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Understanding Equivalent Ratios and Lowest Terms in Mathematics

This guide explains the concept of equivalent ratios, how to reduce ratios to their lowest terms, and the importance of order in ratios. Ratios compare two numbers, presenting them in various forms such as "1 to 3," "3:1," or "3/1." Learn how to find equivalent ratios by multiplying both sides by the same number or using calculators for simplification. Keep practicing with examples, and discover how to verify if two ratios are equivalent by calculating their cross products.

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Understanding Equivalent Ratios and Lowest Terms in Mathematics

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  1. 2.6 Equivalent Ratios Ratio- compares one number to another. Lowest terms- ratios are reduced to the lowest common denominator.

  2. A ratio is the quotient (dividing) of two numbers and is used to compare one number to another. The order of the numbers in a ratio is important. Ratios can be written in three different ways: 1 to 3 1 : 3 1/3

  3. Write the ratio in 2 other ways: 4 = 7 3 :16 = 5 to 8 =

  4. Ratios can be reduced to lowest terms: the ratio 2 = 1 8 4 2 to 8 = 1 to 4, 2:8 = 1:4 8 ft to 5 ft The ratio is 8 to 5, 8 , 8:5 5

  5. Equivalent Ratios To find a ratio equivalent to another ratio you must multiply by 1: 2/2, 3/3, 4/4, etc 4 × 2 = 8 9 2 18

  6. Another way to find a ratio equivalent to another ratio is to simplify on your calculator (division). a b/c key and EXE. 20 = 2 30 3

  7. To find if 2 ratios are equivalent to each other, you calculate the cross product. 180 180 10 = 15 12 18

  8. Find equivalent ratios for each fraction. 4 8 5 11 18 20 36 30 15 13 27 15 Are the ratios equivalent? 2 = 6 8 = 3 7 = 6 9 23 9 4 9 7

  9. Do Now 2:8 14:12 3:45 12:4 100:300 23:25 10:8 17:12

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