Solve Fraction Division: 7/8 ÷ 2⅜ Step-by-Step

To solve this problem, we will follow these steps:

• Step 1: Convert the mixed number $2\frac{3}{8}$ into an improper fraction.
• Step 2: Divide $\frac{7}{8}$ by the improper fraction by multiplying with its reciprocal.
• Step 3: Simplify the resulting fraction.

Now, let's go through each step:

Step 1: Convert the mixed number $2\frac{3}{8}$ to an improper fraction. We do this by multiplying the whole number part by the denominator and adding the numerator:

$2\frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}$.

Step 2: To divide by a fraction $\frac{19}{8}$, we multiply by its reciprocal $\frac{8}{19}$:

$\frac{7}{8} : \frac{19}{8} = \frac{7}{8} \times \frac{8}{19}$.

Step 3: Simplify the resulting expression. Multiply the numerators and the denominators:

$\frac{7 \times 8}{8 \times 19} = \frac{56}{152}$.

The $8$s cancel out, leaving us with:

$\frac{56}{152} = \frac{7}{19}$.

Therefore, the solution to the problem is $\frac{7}{19}$.