Solve Fraction Division: Calculate 3/4 ÷ 5/6 Step-by-Step

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

Video Solution

Solution Steps

00:00 Solve

00:03 Instead of division, use multiplication by the reciprocal

00:08 Flip between the numerator and denominator of the fraction

00:16 Make sure to multiply numerator by numerator and denominator by denominator

00:22 Calculate the multiplications

00:25 Reduce the fraction as much as possible

00:29 Make sure to divide both numerator and denominator

00:33 Calculate the quotients

00:36 And this is the solution to the question

Step-by-Step Solution

To solve the problem of dividing two fractions, we apply the method of multiplication by the reciprocal:

Step 1: The given problem is $\frac{3}{4} \div \frac{5}{6}$ .
Step 2: Find the reciprocal of the divisor $\frac{5}{6}$ , which is $\frac{6}{5}$ .
Step 3: Multiply the dividend $\frac{3}{4}$ by the reciprocal of the divisor: $\frac{3}{4} \times \frac{6}{5}$
Step 4: Perform the multiplication: $\frac{3 \times 6}{4 \times 5} = \frac{18}{20}$
Step 5: Simplify the resulting fraction $\frac{18}{20}$ : $\frac{18 \div 2}{20 \div 2} = \frac{9}{10}$

Therefore, the correct result of the division $\frac{3}{4} \div \frac{5}{6}$ is $\frac{9}{10}$ .