Dividing fractions is easy

We will solve fraction divisions in the following way:
First step
Let's look at the exercise.

  • If there is any mixed number - we will convert it into a fraction
  • If there is any whole number - we will convert it into a fraction

Second step
We will convert the division into multiplication
Also, we will swap the numerator and denominator in the second fraction.
Third step
We will solve by multiplying numerator by numerator and denominator by denominator.

Suggested Topics to Practice in Advance

  1. Sum of Fractions
  2. Subtraction of Fractions
  3. Multiplication of Fractions

Practice Division of Fractions

Examples with solutions for Division of Fractions

Exercise #1

1×12:2 1\times\frac{1}{2}:2

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we should first solve the exercise from left to right since there are only multiplication and division operations present:

1×12=12 1\times\frac{1}{2}=\frac{1}{2}

12:2=14 \frac{1}{2}:2=\frac{1}{4}

Answer

1/4

Exercise #2

0.52= \frac{0.5}{2}=

Video Solution

Step-by-Step Solution

Let's convert the decimal fraction to a simple fraction:

0.5=510 0.5=\frac{5}{10}

We'll write the division problem as follows:

5102 \frac{\frac{5}{10}}{2}

Let's convert the division problem to a multiplication problem.

We'll multiply 510 \frac{5}{10} by the reciprocal of 2 2 as follows:

510×12 \frac{5}{10}\times\frac{1}{2}

We'll solve it this way:

5×110×2=520 \frac{5\times1}{10\times2}=\frac{5}{20}

We'll reduce both the numerator and denominator by 5 and get:

5:520:5=14 \frac{5:5}{20:5}=\frac{1}{4}

Answer

14 \frac{1}{4}

Exercise #3

0.54= \frac{0.5}{4}=

Video Solution

Step-by-Step Solution

Let's convert the decimal fraction to a simple fraction:

0.54=124 \frac{0.5}{4}=\frac{\frac{1}{2}}{4}

Let's convert the division problem to a multiplication problem.

We'll multiply 12 \frac{1}{2} by the reciprocal of 4 as follows:

12×14 \frac{1}{2}\times\frac{1}{4}

We'll solve it as follows:

1×12×4=18 \frac{1\times1}{2\times4}=\frac{1}{8}

Answer

18 \frac{1}{8}

Exercise #4

0.30.5= \frac{0.3}{0.5}=

Video Solution

Step-by-Step Solution

Let's convert the decimal fractions to simple fractions:

0.3=310 0.3=\frac{3}{10}

0.5=510 0.5=\frac{5}{10}

We'll write the division problem as follows:

310510 \frac{\frac{3}{10}}{\frac{5}{10}}

Let's convert the division problem to a multiplication problem.

We'll multiply 310 \frac{3}{10} by the reciprocal of 510 \frac{5}{10} as follows:

310×105 \frac{3}{10}\times\frac{10}{5}

We'll solve it this way:

3×1010×5 \frac{3\times10}{10\times5}

We'll cancel out the 10 in the numerator with the 10 in the denominator and get:

35 \frac{3}{5}

Answer

35 \frac{3}{5}

Exercise #5

Solve the following exercise:

14:12=? \frac{1}{4}:\frac{1}{2}=\text{?}

Video Solution

Answer

12 \frac{1}{2}

Exercise #6

Complete the following exercise:

19:13=? \frac{1}{9}:\frac{1}{3}=\text{?}

Video Solution

Answer

13 \frac{1}{3}

Exercise #7

Complete the following exercise:

89:23=? \frac{8}{9}:\frac{2}{3}=\text{?}

Video Solution

Answer

113 1\frac{1}{3}

Exercise #8

Complete the following exercise:

34:12=? \frac{3}{4}:\frac{1}{2}=\text{?}

Video Solution

Answer

112 1\frac{1}{2}

Exercise #9

Complete the following exercise:

16:13=? \frac{1}{6}:\frac{1}{3}=\text{?}

Video Solution

Answer

12 \frac{1}{2}

Exercise #10

Solve the following exercise:

24:22=? \frac{2}{4}:\frac{2}{2}=\text{?}

Video Solution

Answer

12 \frac{1}{2}

Exercise #11

Solve the following exercise:

412:24=? \frac{4}{12}:\frac{2}{4}=\text{?}

Video Solution

Answer

23 \frac{2}{3}

Exercise #12

Solve the following exercise:

84:42=? \frac{8}{4}:\frac{4}{2}=\text{?}

Video Solution

Answer

1 1

Exercise #13

Complete the following exercise:

12:12=? \frac{1}{2}:\frac{1}{2}=\text{?}

Video Solution

Answer

1 1

Exercise #14

Solve the following exercise:

610:25=? \frac{6}{10}:\frac{2}{5}=\text{?}

Video Solution

Answer

112 1\frac{1}{2}

Exercise #15

Solve the following exercise:

34:16=? \frac{3}{4}:\frac{1}{6}=\text{?}

Video Solution

Answer

412 4\frac{1}{2}

Topics learned in later sections

  1. Comparing Fractions
  2. Operations with Fractions