emma was given three numbers: 7, 2, and 3. she needs to use two of these numbers to make a fraction. can she…
emma was given three numbers: 7, 2, and 3. she needs to use two of these numbers to make a fraction. can she make a fraction that is greater than five - sixths?
Answer
Explanation:
Step1: List all possible fractions
We can form fractions by taking two of the numbers 7, 2, 3. The possible fractions (numerator and denominator are different) are: $\frac{7}{2}$, $\frac{7}{3}$, $\frac{2}{7}$, $\frac{2}{3}$, $\frac{3}{7}$, $\frac{3}{2}$.
Step2: Compare each fraction with $\frac{5}{6}$
- For $\frac{7}{2}$: $\frac{7}{2}=3.5$ and $\frac{5}{6}\approx0.833$, $3.5>\frac{5}{6}$.
- For $\frac{7}{3}\approx2.333$, $2.333>\frac{5}{6}$.
- For $\frac{2}{7}\approx0.286$, $0.286<\frac{5}{6}$.
- For $\frac{2}{3}\approx0.667$, $0.667<\frac{5}{6}$.
- For $\frac{3}{7}\approx0.429$, $0.429<\frac{5}{6}$.
- For $\frac{3}{2} = 1.5$, $1.5>\frac{5}{6}$.
Since there are fractions like $\frac{7}{2}$, $\frac{7}{3}$, $\frac{3}{2}$ which are greater than $\frac{5}{6}$, Emma can make such a fraction.