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:

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 #4

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 #5

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 #6

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 #7

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 #8

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 #9

Complete the following exercise:

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

Video Solution

Step-by-Step Solution

To solve the division of two fractions 12:14 \frac{1}{2} : \frac{1}{4} , follow these steps:

  • Step 1: Identify the operation: The problem involves dividing 12\frac{1}{2} by 14\frac{1}{4}.
  • Step 2: Use the reciprocal: In fraction division, multiply by the reciprocal of the second fraction. Thus, 12:14=12×41\frac{1}{2} : \frac{1}{4} = \frac{1}{2} \times \frac{4}{1}.
  • Step 3: Perform the multiplication: Now compute the multiplication by multiplying the numerators and the denominators: 1×42×1=42 \frac{1 \times 4}{2 \times 1} = \frac{4}{2} .
  • Step 4: Simplify the fraction: The fraction 42\frac{4}{2} simplifies to 22.

Thus, the solution to the division 12:14\frac{1}{2} : \frac{1}{4} is 22. Therefore, the correct answer choice is 22 (Choice 1).

Answer

2 2

Exercise #10

Complete the following exercise:

12:35=? \frac{1}{2}:\frac{3}{5}=\text{?}

Video Solution

Step-by-Step Solution

To solve the division 12÷35 \frac{1}{2} \div \frac{3}{5} , we will follow the multiplication by the reciprocal method. Here are the steps:

  • Step 1: Find the reciprocal of the divisor 35 \frac{3}{5} , which is 53 \frac{5}{3} .
  • Step 2: Multiply the dividend 12 \frac{1}{2} by the reciprocal found in Step 1: 12×53 \frac{1}{2} \times \frac{5}{3} .
  • Step 3: Multiply the numerators: 1×5=5 1 \times 5 = 5 .
  • Step 4: Multiply the denominators: 2×3=6 2 \times 3 = 6 .
  • Step 5: Combine the results to form the fraction 56 \frac{5}{6} .

The simplified result of 12÷35 \frac{1}{2} \div \frac{3}{5} is 56 \frac{5}{6} .

Answer

56 \frac{5}{6}

Exercise #11

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 #12

Complete the following exercise:

15:110=? \frac{1}{5}:\frac{1}{10}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we need to divide the fraction 15\frac{1}{5} by the fraction 110\frac{1}{10}. When dividing fractions, the procedure involves multiplying by the reciprocal of the divisor (the second fraction).

Let's start with the solution:

  • First, determine the reciprocal of 110\frac{1}{10}. The reciprocal of a fraction is obtained by swapping its numerator and denominator. Thus, the reciprocal of 110\frac{1}{10} is 101\frac{10}{1}.
  • Now multiply 15\frac{1}{5} by the reciprocal of 110\frac{1}{10}, which is 101\frac{10}{1}:

15×101=1×105×1=105\frac{1}{5} \times \frac{10}{1} = \frac{1 \times 10}{5 \times 1} = \frac{10}{5}

Simplify the fraction 105\frac{10}{5}:

105=2\frac{10}{5} = 2

Therefore, the result of 15:110\frac{1}{5} : \frac{1}{10} is 22.

Answer

2 2

Exercise #13

Complete the following exercise:

23:38=? \frac{2}{3}:\frac{3}{8}=\text{?}

Video Solution

Step-by-Step Solution

To solve the division of fractions 23\frac{2}{3} by 38\frac{3}{8}, we follow these steps:

  • Step 1: Identify the reciprocal of the second fraction 38\frac{3}{8}. The reciprocal is 83\frac{8}{3}.

  • Step 2: Multiply the first fraction 23\frac{2}{3} by the reciprocal 83\frac{8}{3}:

23×83\frac{2}{3} \times \frac{8}{3}

  • Step 3: Multiply the numerators together and the denominators together:

2×83×3=169\frac{2 \times 8}{3 \times 3} = \frac{16}{9}

  • Step 4: Simplify the resulting fraction, if possible. In this case, 169\frac{16}{9} is already in its simplest form.

  • Step 5: Convert the improper fraction 169\frac{16}{9} to a mixed number:

16÷9=116 \div 9 = 1 remainder 77, so the mixed number is 1791\frac{7}{9}.

Therefore, the solution to the problem is 179 {1\frac{7}{9}} .

Answer

179 1\frac{7}{9}

Exercise #14

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 #15

Complete the following exercise:

24:43=? \frac{2}{4}:\frac{4}{3}=\text{?}

Video Solution

Step-by-Step Solution

To find the result of dividing 24\frac{2}{4} by 43\frac{4}{3}, follow these steps:

  • Step 1: Simplify the fraction 24\frac{2}{4}. This becomes 12\frac{1}{2} because both the numerator and the denominator can be divided by 2.
  • Step 2: Find the reciprocal of the fraction 43\frac{4}{3}. The reciprocal is 34\frac{3}{4} because it exchanges the numerator and the denominator.
  • Step 3: Multiply 12\frac{1}{2} by 34\frac{3}{4}. 12×34=1×32×4=38 \frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
  • Step 4: The result is 38\frac{3}{8}, which is already in its simplest form.

Therefore, the solution to the problem 24:43\frac{2}{4}:\frac{4}{3} is 38\frac{3}{8}.

Answer

38 \frac{3}{8}

Topics learned in later sections

  1. Comparing Fractions
  2. Operations with Fractions