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?

## Step 1: Write the ratios as fractions<br />### Convert the given ratios into fractions. For $16 : 40$, write it as $\frac{16}{40}$. Similarly, for $55 : 22$, write it as $\frac{55}{22}$.<br /><br />## Step 2: Simplify both fractions<br />### Simplify $\frac{16}{40}$ by dividing both numerator and denominator by their greatest common divisor (GCD), which is 8:<br />\[<br />\frac{16}{40} = \frac{16 \div 8}{40 \div 8} = \frac{2}{5}.<br />\]<br />For $\frac{55}{22}$, divide both numerator and denominator by their GCD, which is 11:<br />\[<br />\frac{55}{22} = \frac{55 \div 11}{22 \div 11} = \frac{5}{2}.<br />\]<br /><br />## Step 3: Compare the simplified fractions<br />### The simplified forms of the two ratios are $\frac{2}{5}$ and $\frac{5}{2}$. These fractions are not equal because $\frac{2}{5} \neq \frac{5}{2}$.<br /><br />## Step 4: Conclude whether the ratios are equivalent<br />### Since the simplified fractions are not equal, the ratios $16 : 40$ and $55 : 22$ are not equivalent.