Question

1. benjamin and his sister shared a large sandwich. benjamin ate $\frac{3}{5}$ of the sandwich and his sister ate $\frac{1}{7}$ of the sandwich.

a. estimate how much more benjamin ate than his sister. explain how you found your estimate.
b. how much more did benjamin eat than his sister? find the exact amount.

Explanation:

Part A:

Step1: Estimate each fraction

$\frac{3}{5} \approx \frac{1}{2}$ (since $\frac{3}{5}=0.6$, close to 0.5), $\frac{1}{7} \approx 0$ (small value)

Step2: Subtract estimates

$\frac{1}{2} - 0 = \frac{1}{2}$
Alternative estimate: $\frac{3}{5}=\frac{21}{35}$, $\frac{1}{7}=\frac{5}{35}$, $\frac{21-5}{35}\approx\frac{16}{35}\approx0.46$, close to $\frac{1}{2}$

Part B:

Step1: Find common denominator

Common denominator of 5 and 7 is 35.

Step2: Rewrite fractions

$\frac{3}{5} = \frac{3\times7}{5\times7} = \frac{21}{35}$, $\frac{1}{7} = \frac{1\times5}{7\times5} = \frac{5}{35}$

Step3: Subtract fractions

$\frac{21}{35} - \frac{5}{35} = \frac{16}{35}$

Answer:

A. Estimate: $\frac{1}{2}$ (or close to $\frac{1}{2}$)
B. Exact amount: $\frac{16}{35}$