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a. Match each ratio from column 1 with the equivalent ratio in column 2. Column 1 \(\qquad\) Column 2 12 out of 27 \(\qquad\) 60 out of 75 28 out of 36 \(\qquad\) 25 out of 40 45 out of 75 \(\qquad\) 21 out of 27 64 out of 80 \(\qquad\) 42 out of 70 35 out of 56 \(\qquad\) 20 out of 45 b. Write each matched pair of equivalent ratios as a percent. If necessary, round to the nearest tenth of a percent.

Short Answer

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Question: Match the equivalent ratios from the columns below and calculate their corresponding percentages. Column 1: 12 out of 27 28 out of 36 45 out of 75 64 out of 80 35 out of 56 Column 2: 60 out of 75 25 out of 40 21 out of 27 42 out of 70 20 out of 45 Answer: The matched pairs of equivalent ratios and their rounded percentages are: 4/9 and 4/9 -> 44.4% 7/9 and 7/9 -> 77.8% 3/5 and 3/5 -> 60% 4/5 and 4/5 -> 80% 5/8 and 5/8 -> 62.5%

Step by step solution

01

Simplify the ratios

First, simplify the ratios in both columns by dividing the numerator and denominator of each ratio by their greatest common divisor (GCD): Column 1: 12 out of 27 -> 12/27 (Divide by 3) -> 4/9 28 out of 36 -> 28/36 (Divide by 4) -> 7/9 45 out of 75 -> 45/75 (Divide by 15) -> 3/5 64 out of 80 -> 64/80 (Divide by 16) -> 4/5 35 out of 56 -> 35/56 (Divide by 7) -> 5/8 Column 2: 60 out of 75 -> 60/75 (Divide by 15) -> 4/5 25 out of 40 -> 25/40 (Divide by 5) -> 5/8 21 out of 27 -> 21/27 (Divide by 3) -> 7/9 42 out of 70 -> 42/70 (Divide by 14) -> 3/5 20 out of 45 -> 20/45 (Divide by 5) -> 4/9
02

Match equivalent ratios

Match the simplified ratios from column 1 with the simplified ratios from column 2: 4/9 matches with 4/9 7/9 matches with 7/9 3/5 matches with 3/5 4/5 matches with 4/5 5/8 matches with 5/8
03

Calculate the percentages

For each matched pair of equivalent ratios, write them as percentages: 4/9 as a percent: (4 / 9) x 100 = 44.4 (rounded to the nearest tenth) 7/9 as a percent: (7 / 9) x 100 = 77.8 (rounded to the nearest tenth) 3/5 as a percent: (3 / 5) x 100 = 60 4/5 as a percent: (4 / 5) x 100 = 80 5/8 as a percent: (5 / 8) x 100 = 62.5 So the matched pairs of equivalent ratios and their rounded percentages are: 4/9 and 4/9 -> 44.4% 7/9 and 7/9 -> 77.8% 3/5 and 3/5 -> 60% 4/5 and 4/5 -> 80% 5/8 and 5/8 -> 62.5%

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