5/12 divided by 3/8

Understand the Problem

The question is asking for the process to divide two fractions, specifically 5/12 and 3/8. To solve it, we will multiply the first fraction (5/12) by the reciprocal of the second fraction (8/3).

$\frac{10}{9}$

The result of dividing $\frac{5}{12}$ by $\frac{3}{8}$ is $\frac{10}{9}$.

Steps to Solve

1. Identify the fractions to be divided

We need to divide the fractions $\frac{5}{12}$ and $\frac{3}{8}$.

1. Find the reciprocal of the second fraction

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{3}{8}$ is $\frac{8}{3}$.

1. Set up the multiplication

Now, we can rewrite the division problem as a multiplication problem: $$\frac{5}{12} \div \frac{3}{8} = \frac{5}{12} \times \frac{8}{3}$$

1. Multiply the numerators and the denominators

Next, we multiply the numerators and the denominators:

• Numerators: $5 \times 8 = 40$
• Denominators: $12 \times 3 = 36$

Thus, we have: $$\frac{5 \times 8}{12 \times 3} = \frac{40}{36}$$

1. Simplify the resulting fraction

Now, we simplify $\frac{40}{36}$ by finding the greatest common divisor (GCD) of 40 and 36. The GCD is 4.

Dividing both the numerator and the denominator by 4 gives us: $$\frac{40 \div 4}{36 \div 4} = \frac{10}{9}$$

The result of dividing $\frac{5}{12}$ by $\frac{3}{8}$ is $\frac{10}{9}$.