Solve Fraction Division: 5/8 ÷ 1¾ Step by Step

To solve the problem, we'll follow these steps:

• Step 1: Convert the mixed number, $1 \frac{3}{4}$, into an improper fraction.
• Step 2: Rewrite the division as a multiplication by the reciprocal of the improper fraction.
• Step 3: Perform the multiplication and simplify the resulting fraction.

Now, let's work through each step:
Step 1: Convert the mixed number. $1 \frac{3}{4}$ can be converted as follows:

The whole number $1$ times the denominator $4$ plus the numerator $3$ gives $7$.
Thus, $1 \frac{3}{4} = \frac{7}{4}$.

Step 2: Divide $\frac{5}{8}$ by $\frac{7}{4}$ by multiplying by its reciprocal:
$\frac{5}{8} \div \frac{7}{4} = \frac{5}{8} \times \frac{4}{7}$.

Step 3: Multiply across the numerators and the denominators:
$\frac{5 \times 4}{8 \times 7} = \frac{20}{56}$.

Simplify $\frac{20}{56}$ by finding the greatest common divisor (GCD), which is $4$:
$\frac{20}{56} = \frac{20 \div 4}{56 \div 4} = \frac{5}{14}$.

Therefore, the solution to the problem is $\frac{5}{14}$.