Jennifer and Luca write the ratio of runs to weight training sessions.Their results are below: 16:40=(2)/(5) and 55:22=(5)/(2) Jennifer and Luca believe that these results are equivalent ratios. Is this correct? Why or why not?

Question

Answer 1

### No, Jennifer and Luca's results are not equivalent ratios because

.

Answer 2

## Step 1: Write the ratios as fractions### Convert the given ratios into fractions. For

, write it as

. Similarly, for

, write it as

.## Step 2: Simplify both fractions### Simplify

by dividing both numerator and denominator by their greatest common divisor (GCD), which is 8:

For

, divide both numerator and denominator by their GCD, which is 11:

## Step 3: Compare the simplified fractions### The simplified forms of the two ratios are

and

. These fractions are not equal because

.## Step 4: Conclude whether the ratios are equivalent### Since the simplified fractions are not equal, the ratios

and

are not equivalent.

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