Question

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?

Explanation:

Step1: List all possible fractions

The possible fractions using two of 7, 2, 3 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 $3.5>\frac{5}{6}$ (since $\frac{5}{6}\approx0.833$).
• For $\frac{7}{3}\approx2.333$, and $2.333>\frac{5}{6}$.
• For $\frac{2}{7}\approx0.286$, and $0.286<\frac{5}{6}$.
• For $\frac{2}{3}\approx0.666$, and $0.666<\frac{5}{6}$.
• For $\frac{3}{7}\approx0.429$, and $0.429<\frac{5}{6}$.
• For $\frac{3}{2}=1.5$, and $1.5>\frac{5}{6}$.

Answer:

Yes, she can. For example, the fraction $\frac{7}{2}$ (or $\frac{7}{3}$, $\frac{3}{2}$ etc.) is greater than $\frac{5}{6}$.