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

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

When we approach solving such questions, we need to know the rule of dividing fractions,

When we need to divide a fraction by a fraction, we use the method of multiplying by the reciprocal.

This means we flip the numerator and denominator of the second fraction, and then perform fraction multiplication.

Instead of:

1/4 : 1/2 =

We get:

1/4 * 2/1 =

We'll remember that in fraction multiplication we multiply numerator by numerator and denominator by denominator

1*2 / 4*1 =
2/4 =

We'll reduce the fraction and get:

1/2

Answer

12 \frac{1}{2}

Exercise #2

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 #3

3434=? \frac{\frac{3}{4}}{\frac{3}{4}}=\text{?}

Video Solution

Step-by-Step Solution

We will use the formula:

aa=1 \frac{a}{a}=1

Therefore the answer is 1

Answer

1 1

Exercise #4

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 #5

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 #6

5+472= 5+\frac{\frac{4}{7}}{2}=

Video Solution

Step-by-Step Solution

To simplify the fraction exercise, we will multiply 47 \frac{4}{7} by 12 \frac{1}{2}

We will arrange the exercise accordingly and following the order of operations rules, we will first solve the multiplication exercise:

5+47×12= 5+\frac{4}{7}\times\frac{1}{2}= Note that in the multiplication exercise we can reduce 4 in the numerator and 2 in the denominator by 2:

5+27×11=5+27+1 5+\frac{2}{7}\times\frac{1}{1}=5+\frac{2}{7}+1

We will combine the whole numbers and get:

5+1+27=627 5+1+\frac{2}{7}=6\frac{2}{7}

Answer

627 6\frac{2}{7}

Exercise #7

1072+278= \frac{\frac{10}{7}}{2}+\frac{2}{\frac{7}{8}}=

Video Solution

Step-by-Step Solution

To solve the expression 1072+278 \frac{\frac{10}{7}}{2}+\frac{2}{\frac{7}{8}} , we need to perform operations in the correct order as per the rules of the order of operations (PEMDAS/BODMAS - Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 1: Simplify the complex fraction 1072 \frac{\frac{10}{7}}{2}
A complex fraction can be simplified by multiplying the numerator by the reciprocal of the denominator. In this case, the numerator is 107 \frac{10}{7} and the denominator is 2 (which means 21 \frac{2}{1} ).


1072=107×12=10172=1014 \frac{\frac{10}{7}}{2} = \frac{10}{7} \times \frac{1}{2} = \frac{10 \cdot 1}{7 \cdot 2} = \frac{10}{14}


Simplify 1014 \frac{10}{14} by dividing both the numerator and the denominator by their greatest common divisor (2):


1014=57 \frac{10}{14} = \frac{5}{7}

Step 2: Simplify the complex fraction 278 \frac{2}{\frac{7}{8}}
Again, multiply the numerator by the reciprocal of the denominator:
The reciprocal of 78 \frac{7}{8} is 87 \frac{8}{7} .


278=2×87=287=167 \frac{2}{\frac{7}{8}} = 2 \times \frac{8}{7} = \frac{2 \cdot 8}{7} = \frac{16}{7}

Step 3: Add the simplified fractions 57+167 \frac{5}{7} + \frac{16}{7}
Since the fractions have like denominators, we can add the numerators directly:


57+167=5+167=217 \frac{5}{7} + \frac{16}{7} = \frac{5 + 16}{7} = \frac{21}{7}


Simplify 217 \frac{21}{7} by dividing the numerator by the denominator:


217=3 \frac{21}{7} = 3

Thus, the solution to the expression is 3 3 .

Answer

3 3

Exercise #8

60.752×3= \frac{6}{0.75}-2\times3=

Video Solution

Step-by-Step Solution

To solve the expression 60.752×3 \frac{6}{0.75} - 2 \times 3 , we need to carefully follow the order of operations. The order of operations is often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, there are no parentheses or exponents, so we focus on multiplication, division, subtraction in the given order.

  • Step 1: Division
    First, perform the division: 60.75 \frac{6}{0.75} . To divide by a decimal, convert it to a fraction or adjust the dividend and divisor by a power of 10 to make the divisor a whole number. Here, 60.75 \frac{6}{0.75} becomes 6×1000.75×100=60075 \frac{6 \times 100}{0.75 \times 100} = \frac{600}{75} .
    Next, simplify 60075 \frac{600}{75} . Both numbers are divisible by 15:
    600÷15=40 600 \div 15 = 40 and 75÷15=5 75 \div 15 = 5 , so 60075=40÷5=8 \frac{600}{75} = 40 \div 5 = 8 .
  • Step 2: Multiplication
    Next, perform the multiplication: 2×3 2 \times 3 which equals 6 6 .
  • Step 3: Subtraction
    Finally, subtract the results of the previous operations: 86 8 - 6 . This gives 2 2 .

By carefully following the order of operations, the final answer to the expression 60.752×3 \frac{6}{0.75} - 2 \times 3 is 2 2 , which matches the correct answer provided.

Answer

2 2

Exercise #9

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 #10

35910+7913= \frac{\frac{3}{5}}{\frac{9}{10}}+\frac{\frac{7}{9}}{\frac{1}{3}}=

Video Solution

Step-by-Step Solution

To solve the expression 35910+7913 \frac{\frac{3}{5}}{\frac{9}{10}}+\frac{\frac{7}{9}}{\frac{1}{3}} , we need to apply the division of fractions and simplify the resulting expressions.

First, consider the expression 35910 \frac{\frac{3}{5}}{\frac{9}{10}} :

  • When dividing by a fraction, multiply by its reciprocal. The reciprocal of 910 \frac{9}{10} is 109 \frac{10}{9} .
  • Therefore, 35910=35×109 \frac{\frac{3}{5}}{\frac{9}{10}} = \frac{3}{5} \times \frac{10}{9} .
  • Multiplying the numerators and the denominators, we get 3×105×9=3045 \frac{3 \times 10}{5 \times 9} = \frac{30}{45} .
  • Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 15: 30÷1545÷15=23 \frac{30 \div 15}{45 \div 15} = \frac{2}{3} .

Next, consider the expression 7913 \frac{\frac{7}{9}}{\frac{1}{3}} :

  • The reciprocal of 13 \frac{1}{3} is 31 \frac{3}{1} .
  • Therefore, 7913=79×31 \frac{\frac{7}{9}}{\frac{1}{3}} = \frac{7}{9} \times \frac{3}{1} .
  • Multiplying the numerators and the denominators, we get 7×39×1=219 \frac{7 \times 3}{9 \times 1} = \frac{21}{9} .
  • Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3: 21÷39÷3=73 \frac{21 \div 3}{9 \div 3} = \frac{7}{3} .

Now add the simplified fractions: 23+73 \frac{2}{3} + \frac{7}{3} .

  • The fractions have a common denominator, 3, so we can simply add the numerators: 2+73=93 \frac{2 + 7}{3} = \frac{9}{3} .
  • Simplify 93 \frac{9}{3} by dividing both the numerator and the denominator by 3: 9÷33÷3=3 \frac{9 \div 3}{3 \div 3} = 3 .

Therefore, the final solution to the expression is 3 3 .

Answer

3 3

Exercise #11

3121316= 3\frac{1}{2}-\frac{\frac{1}{3}}{\frac{1}{6}}=

Video Solution

Step-by-Step Solution

When we have a fraction over a fraction, in this case one-third over one-sixth, we can convert it to a form that might be more familiar to us:

1/3:1/6 1/3 : 1/6

It's important to remember that a fraction is actually another sign of division, so the exercise we have is one-third divided by one-sixth.
When dealing with division of fractions, the easiest method for solving is performing "multiplication by the reciprocal", meaning:

1/3×6/1 1/3\times6/1

Multiply numerator by numerator and denominator by denominator and get:

63 \frac{6}{3}

Which when reduced equals

21 \frac{2}{1}

Now let's return to the original exercise, to solve it we need to take the mixed fraction and convert it to an improper fraction,
meaning move the whole numbers back to the numerator.

To do this we'll multiply the whole number by the denominator and add to the numerator

3×2=6 3\times2=6

6+1=7 6+1=7

And therefore the fraction is:

72 \frac{7}{2}

Now we want to do the subtraction exercise, but we see that we have another step on the way.
We subtract fractions when both fractions have the same denominator,
so we'll expand the fraction 21 \frac{2}{1} to a denominator of 2, and we'll get:

42 \frac{4}{2}

And now we can perform subtraction -

7242=32 \frac{7}{2}-\frac{4}{2}=\frac{3}{2}

We'll convert this back to a mixed fraction and we'll see that the result is

Answer

112 1\frac{1}{2}

Exercise #12

Complete the following exercise:

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

Video Solution

Answer

13 \frac{1}{3}

Exercise #13

Complete the following exercise:

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

Video Solution

Answer

113 1\frac{1}{3}

Exercise #14

Complete the following exercise:

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

Video Solution

Answer

112 1\frac{1}{2}

Exercise #15

Complete the following exercise:

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

Video Solution

Answer

12 \frac{1}{2}

Topics learned in later sections

  1. Comparing Fractions
  2. Operations with Fractions