31/8 divided by 2/3 in Fraction Form

The result of 31/8 divided by 2/3 is: 5 13/16

Step-by-Step Solution

Step 1: Understand the Problem

We need to divide the fraction $\frac{3}{1} 8$ by $\frac{2}{3}$ .

Step 2: Use the Division Rule

To divide fractions, we multiply by the reciprocal of the second fraction:
$\frac{3}{1} 8 \div \frac{2}{3} = \frac{3}{1} 8 \times \frac{3}{2}$

Step 3: Multiply the Fractions

Multiply the numerators: 31 × 3 = 93
Multiply the denominators: 8 × 2 = 16

Step 4: Convert to Mixed Number

The fraction $\frac{9}{3} 16$ can be written as the mixed number $5 \frac{1}{3} 16$ .

Final Answer

The result of 31/8 divided by 2/3 is:

\frac{31}{8} \div \frac{2}{3} = 5 \frac{1}{3} 16

Understanding Fraction Division

How to Divide Fractions

To divide fractions, you multiply by the reciprocal of the divisor:

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a d}{b c}$

This technique is often remembered as "keep, change, flip" - keep the first fraction, change division to multiplication, and flip the second fraction.

Why Simplify Fractions?

Simplifying fractions makes them easier to work with and understand. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

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