Question

use vocabulary in writing
explain how you could determine whether \\(\frac{\frac{3}{120}}{12}\\) and \\(\frac{7}{9}\\) have the same decimal equivalent. use vocabulary words in your explanation.

Explanation:

Step1: Simplify both fractions

Simplify $\frac{21}{120}$: divide numerator and denominator by 3 → $\frac{7}{40}$. Simplify $\frac{7}{9}$: already in simplest form.

Step2: Convert to decimals

$\frac{7}{40} = 0.175$ (terminating decimal). $\frac{7}{9} = 0.\overline{7}$ (repeating decimal).

Step3: Compare decimals

0.175 ≠ $0.\overline{7}$, so they differ.

Answer:

Simplify $\frac{21}{120}$ to $\frac{7}{40}$, convert both to decimals ($0.175$ vs. $0.\overline{7}$), and compare—they do not have the same decimal equivalent.