Solve Fraction Division: 2/5 ÷ 1/4 Step-by-Step

Complete the following exercise:

$\frac{2}{5}:\frac{1}{4}=\text{?}$

Video Solution

Solution Steps

00:00 Solve

00:03 Instead of division, we'll use multiplication by reciprocal

00:08 We'll swap the numerator and denominator of the fraction

00:14 Make sure to multiply numerator by numerator and denominator by denominator

00:20 Calculate the multiplications

00:29 Break down 8 into 5 plus 3

00:33 Break down the fraction into a whole number and remainder

00:41 Any number divided by itself always equals 1

00:45 Convert to a mixed fraction

00:50 And this is the solution to the question

Step-by-Step Solution

To solve the problem of dividing $\frac{2}{5}$ by $\frac{1}{4}$ , we need to follow these steps:

Step 1: Identify the reciprocal of $\frac{1}{4}$ .
This reciprocate is $\frac{4}{1}$ .
Step 2: Convert the division of fractions to multiplication with the reciprocal:
$\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1}$ .
Step 3: Perform the multiplication:
$\frac{2 \times 4}{5 \times 1} = \frac{8}{5}$ .
Step 4: Simplify $\frac{8}{5}$ into a mixed number:
$\frac{8}{5}$ can be written as $1\frac{3}{5}$ because 5 goes into 8 once with 3 remaining.

Therefore, the solution to the problem is $1\frac{3}{5}$ .