Question

1. jada threw the ball \\(\frac{3}{4}\\) the length of the gym. clare threw the ball \\(\frac{6}{8}\\) the length of the gym. clare says she threw the ball farther. do you agree? why or why not?

Explanation:

Step1: Convert fractions to common denominator

To compare $\frac{3}{4}$ and $\frac{6}{8}$, find a common denominator. The least common denominator of 4 and 8 is 8. Convert $\frac{3}{4}$: $\frac{3\times2}{4\times2}=\frac{6}{8}$.

Step2: Compare the fractions

Now we have $\frac{3}{4}=\frac{6}{8}$ (since $\frac{3}{4}$ converted to eighths is $\frac{6}{8}$) and Clare's throw is $\frac{6}{8}$ of the gym length. So Jada's throw ($\frac{3}{4}$ or $\frac{6}{8}$) and Clare's throw ($\frac{6}{8}$) are equal.

Answer:

No, I do not agree with Clare. Because when we convert $\frac{3}{4}$ to a fraction with denominator 8, we get $\frac{3\times2}{4\times2}=\frac{6}{8}$. So Jada's throw length ($\frac{3}{4}$ of the gym length) is equal to Clare's throw length ($\frac{6}{8}$ of the gym length), meaning Clare did not throw the ball farther.