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

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division of two fractions 12÷12 \frac{1}{2} \div \frac{1}{2} , we follow these steps:

  • Step 1: Recognize that dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, we replace division with multiplication by flipping the second fraction.
  • Step 2: Thus, 12÷12 \frac{1}{2} \div \frac{1}{2} becomes 12×21 \frac{1}{2} \times \frac{2}{1} .
  • Step 3: Perform the multiplication: Multiply the numerators and the denominators.
    Numerator: 1×2=2 1 \times 2 = 2
    Denominator: 2×1=2 2 \times 1 = 2
  • Step 4: Simplify the result: The fraction 22\frac{2}{2} simplifies to 1.

Thus, the result of the division 12÷12 \frac{1}{2} \div \frac{1}{2} is 1 1 .

Answer

1 1

Exercise #2

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division of fractions problem 16÷13\frac{1}{6} \div \frac{1}{3}, we'll apply the concept of multiplying by the reciprocal.

  • Step 1: Identify the reciprocal of the second fraction. The reciprocal of 13\frac{1}{3} is 31\frac{3}{1}.
  • Step 2: Multiply the first fraction by this reciprocal. Therefore, calculate 16×31\frac{1}{6} \times \frac{3}{1}.
  • Step 3: Perform the multiplication. Multiply the numerators: 1×3=31 \times 3 = 3. Multiply the denominators: 6×1=66 \times 1 = 6.
  • Step 4: Simplify the resulting fraction. The fraction 36\frac{3}{6} simplifies to 12\frac{1}{2} because both the numerator and denominator can be divided by 3.

Therefore, the solution to the problem is 12\frac{1}{2}.

Answer

12 \frac{1}{2}

Exercise #3

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve this problem, we'll break it into these manageable steps:

  • Step 1: Identify the fractions:
    34 \frac{3}{4} and 12 \frac{1}{2} .
  • Step 2: Find the reciprocal of the second fraction:
    • The reciprocal of 12 \frac{1}{2} is 21 \frac{2}{1} .
  • Step 3: Change the division into multiplication:
    • 34÷12 \frac{3}{4} \div \frac{1}{2} becomes 34×21 \frac{3}{4} \times \frac{2}{1} .
  • Step 4: Multiply the numerators and the denominators:
    • Numerator: 3×2=6 3 \times 2 = 6
    • Denominator: 4×1=4 4 \times 1 = 4
    • So, 34×21=64 \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} .
  • Step 5: Simplify the fraction:
    • 64=32 \frac{6}{4} = \frac{3}{2} , since dividing numerator and denominator by 2 gives 32 \frac{3}{2} .
  • Step 6: Convert the fraction to a mixed number:
    • 32 \frac{3}{2} can be written as the mixed number 112 1\frac{1}{2} .

Therefore, the result of the division is 112 1\frac{1}{2} .

Answer

112 1\frac{1}{2}

Exercise #4

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the fraction division 89÷23 \frac{8}{9} \div \frac{2}{3} , follow these steps:

  • Step 1: Identify the given fractions 89 \frac{8}{9} and 23 \frac{2}{3} .
  • Step 2: Find the reciprocal of the second fraction. The reciprocal of 23 \frac{2}{3} is 32 \frac{3}{2} .
  • Step 3: Multiply the first fraction by the reciprocal of the second fraction: 89×32 \frac{8}{9} \times \frac{3}{2} .
  • Step 4: Perform the multiplication: multiply the numerators together and the denominators together.

Let's compute the multiplication:

89×32=8×39×2=2418 \frac{8}{9} \times \frac{3}{2} = \frac{8 \times 3}{9 \times 2} = \frac{24}{18}

Step 5: Simplify the resulting fraction 2418 \frac{24}{18} .

To simplify, find the greatest common divisor (GCD) of 24 and 18, which is 6. Divide both the numerator and the denominator by 6:

2418=24÷618÷6=43 \frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}

Step 6: If necessary, convert the improper fraction to a mixed number.

Since 43 \frac{4}{3} is an improper fraction, it can be converted to a mixed number:

43=113 \frac{4}{3} = 1 \frac{1}{3}

Therefore, the solution to the problem 89:23 \frac{8}{9} : \frac{2}{3} is 113 1 \frac{1}{3} .

Answer

113 1\frac{1}{3}

Exercise #5

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division of the fractions 19 \frac{1}{9} and 13 \frac{1}{3} , we'll employ the method of "invert and multiply":

  • Step 1: Identify the reciprocal of the divisor. The divisor is 13 \frac{1}{3} , and its reciprocal is 31 \frac{3}{1} .
  • Step 2: Convert the division into a multiplication. Therefore, 19÷13 \frac{1}{9} \div \frac{1}{3} becomes 19×31 \frac{1}{9} \times \frac{3}{1} .
  • Step 3: Carry out the multiplication of the two fractions.
    19×31=1×39×1=39\frac{1}{9} \times \frac{3}{1} = \frac{1 \times 3}{9 \times 1} = \frac{3}{9}.
  • Step 4: Simplify the resulting fraction.
    39\frac{3}{9} simplifies to 13 \frac{1}{3} by dividing both the numerator and the denominator by their greatest common divisor, which is 3.

Therefore, the solution to the problem 19÷13 \frac{1}{9} \div \frac{1}{3} is 13 \frac{1}{3} .

Answer

13 \frac{1}{3}

Exercise #6

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division of fractions 24:22 \frac{2}{4} : \frac{2}{2} , follow these steps:

  • Step 1: Identify the fractions — the first fraction is 24 \frac{2}{4} , and the second fraction is 22 \frac{2}{2} .
  • Step 2: Find the reciprocal of the second fraction. The reciprocal of 22\frac{2}{2} is 22\frac{2}{2}, as it simplifies to 1.
  • Step 3: Multiply the first fraction by the reciprocal of the second fraction:

24×22=2×24×2=48 \frac{2}{4} \times \frac{2}{2} = \frac{2 \times 2}{4 \times 2} = \frac{4}{8}

Step 4: Simplify the resulting fraction 48\frac{4}{8}. Since the greatest common divisor of 4 and 8 is 4, divide both numerator and denominator by 4:

48=4÷48÷4=12 \frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}

Therefore, the solution to the problem is 12\frac{1}{2}.

Answer

12 \frac{1}{2}

Exercise #7

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 #8

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division problem 412:24 \frac{4}{12}:\frac{2}{4} , we will follow these steps:

  • Step 1: Identify the fractions involved: 412 \frac{4}{12} and 24 \frac{2}{4} .
  • Step 2: Convert the division into multiplication by the reciprocal of the divisor. The reciprocal of 24 \frac{2}{4} is 42 \frac{4}{2} .
  • Step 3: Multiply the first fraction by this reciprocal:

412×42=4×412×2 \frac{4}{12} \times \frac{4}{2} = \frac{4 \times 4}{12 \times 2}

=1624 = \frac{16}{24}

  • Step 4: Simplify the resulting fraction. The greatest common divisor of 16 and 24 is 8.

16÷824÷8=23 \frac{16 \div 8}{24 \div 8} = \frac{2}{3}

Thus, the solution to the problem is 23 \frac{2}{3} .

Answer

23 \frac{2}{3}

Exercise #9

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 #10

Complete the following exercise:

24:13=? \frac{2}{4}:\frac{1}{3}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, let's follow these steps:

  • Step 1: Simplify the fraction 24 \frac{2}{4} .
  • Step 2: Find the reciprocal of 13 \frac{1}{3} .
  • Step 3: Multiply the simplified fraction by the reciprocal.
  • Step 4: Simplify the resulting fraction if needed.

Now, let's work through each step:
Step 1: Simplify 24 \frac{2}{4} to 12 \frac{1}{2} by dividing both the numerator and the denominator by 2.
Step 2: The reciprocal of 13 \frac{1}{3} is 31 \frac{3}{1} .
Step 3: Multiply 12×31 \frac{1}{2} \times \frac{3}{1} . This gives us 1×32×1=32 \frac{1 \times 3}{2 \times 1} = \frac{3}{2} .
Step 4: 32 \frac{3}{2} is an improper fraction. Convert it to a mixed number, 112 1\frac{1}{2} .

Therefore, the solution to the division 24:13 \frac{2}{4}:\frac{1}{3} is 112 1\frac{1}{2} .

Answer

112 1\frac{1}{2}

Exercise #11

Solve the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division 610÷25 \frac{6}{10} \div \frac{2}{5} , we use the method of multiplying by the reciprocal of the divisor.

First, identify the reciprocal of the divisor 25 \frac{2}{5} . The reciprocal is obtained by swapping the numerator and denominator, resulting in 52 \frac{5}{2} .

Next, replace the division operation with multiplication by the reciprocal:

610×52 \frac{6}{10} \times \frac{5}{2} .

Now, perform the multiplication of the fractions by multiplying numerator by numerator and denominator by denominator:

6×510×2=3020 \frac{6 \times 5}{10 \times 2} = \frac{30}{20} .

Simplify the fraction 3020 \frac{30}{20} by finding the greatest common divisor. Both 30 and 20 can be divided by 10:

30÷1020÷10=32 \frac{30 \div 10}{20 \div 10} = \frac{3}{2} .

The simplified fraction 32 \frac{3}{2} can also be expressed as a mixed number:

112 1\frac{1}{2} .

Therefore, the solution to the problem 610÷25 \frac{6}{10} \div \frac{2}{5} is 112 1\frac{1}{2} , aligning with choice 1.

Answer

112 1\frac{1}{2}

Exercise #12

Complete the following exercise:

46:37=? \frac{4}{6}:\frac{3}{7}=\text{?}

Video Solution

Step-by-Step Solution

To solve the fraction division problem 46:37 \frac{4}{6} : \frac{3}{7} , follow these steps:

  • Step 1: Simplify the first fraction 46 \frac{4}{6} .

Simplify by finding the greatest common divisor (GCD) of 4 and 6, which is 2. Divide both the numerator and denominator by 2:

46=4/26/2=23 \frac{4}{6} = \frac{4/2}{6/2} = \frac{2}{3}

  • Step 2: Find the reciprocal of the second fraction 37 \frac{3}{7} .

The reciprocal of 37 \frac{3}{7} is 73 \frac{7}{3} .

  • Step 3: Multiply the simplified first fraction by the reciprocal of the second.

23×73=2×73×3=149 \frac{2}{3} \times \frac{7}{3} = \frac{2 \times 7}{3 \times 3} = \frac{14}{9}

  • Step 4: Convert the improper fraction 149 \frac{14}{9} to a mixed number.

Divide 14 by 9, which gives a quotient of 1 and a remainder of 5:

149=159 \frac{14}{9} = 1\frac{5}{9}

Therefore, the solution to the problem is 159 1\frac{5}{9} .

Answer

159 1\frac{5}{9}

Exercise #13

Complete the following exercise:

34:56=? \frac{3}{4}:\frac{5}{6}=\text{?}

Video Solution

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 34÷56 \frac{3}{4} \div \frac{5}{6} .
  • Step 2: Find the reciprocal of the divisor 56 \frac{5}{6} , which is 65 \frac{6}{5} .
  • Step 3: Multiply the dividend 34 \frac{3}{4} by the reciprocal of the divisor: 34×65 \frac{3}{4} \times \frac{6}{5}
  • Step 4: Perform the multiplication: 3×64×5=1820 \frac{3 \times 6}{4 \times 5} = \frac{18}{20}
  • Step 5: Simplify the resulting fraction 1820 \frac{18}{20} : 18÷220÷2=910 \frac{18 \div 2}{20 \div 2} = \frac{9}{10}

Therefore, the correct result of the division 34÷56 \frac{3}{4} \div \frac{5}{6} is 910\frac{9}{10}.

Answer

910 \frac{9}{10}

Exercise #14

Complete the following exercise:

13:14=? \frac{1}{3}:\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the fractions involved and their reciprocal.
  • Step 2: Convert the division into multiplication using the reciprocal.
  • Step 3: Simplify the resulting fraction, if needed, converting any improper fraction to a mixed number.

Now, let's work through each step:
Step 1: We are given the fraction 13\frac{1}{3} and we are dividing by 14\frac{1}{4}. The reciprocal of 14\frac{1}{4} is 41\frac{4}{1}.
Step 2: Multiply 13\frac{1}{3} by the reciprocal of 14\frac{1}{4}:

13×41=1×43×1=43 \frac{1}{3} \times \frac{4}{1} = \frac{1 \times 4}{3 \times 1} = \frac{4}{3}

Step 3: Simplify 43\frac{4}{3}. Since 43\frac{4}{3} is an improper fraction, convert it to a mixed number:
Divide 4 by 3, which goes 1 time with a remainder of 1. Therefore, 43=113\frac{4}{3} = 1\frac{1}{3}.

Therefore, the solution to the problem is 113 1\frac{1}{3} .

Answer

113 1\frac{1}{3}

Exercise #15

Complete the following exercise:

25:14=? \frac{2}{5}:\frac{1}{4}=\text{?}

Video Solution

Step-by-Step Solution

To solve the problem of dividing 25\frac{2}{5} by 14\frac{1}{4}, we need to follow these steps:

  • Step 1: Identify the reciprocal of 14\frac{1}{4}.
    This reciprocate is 41\frac{4}{1}.
  • Step 2: Convert the division of fractions to multiplication with the reciprocal:
    25÷14=25×41\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1}.
  • Step 3: Perform the multiplication:
    2×45×1=85\frac{2 \times 4}{5 \times 1} = \frac{8}{5}.
  • Step 4: Simplify 85\frac{8}{5} into a mixed number:
    85\frac{8}{5} can be written as 1351\frac{3}{5} because 5 goes into 8 once with 3 remaining.

Therefore, the solution to the problem is 135 1\frac{3}{5} .

Answer

135 1\frac{3}{5}

Topics learned in later sections

  1. Comparing Fractions
  2. Operations with Fractions