Division of Fractions - Examples, Exercises and Solutions

Understanding Division of Fractions

Complete explanation with examples

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.

Detailed explanation

Practice Division of Fractions

Test your knowledge with 15 quizzes

Complete the following exercise:

\( \frac{1}{2}:\frac{3}{5}=\text{?} \)

Examples with solutions for Division of Fractions

Step-by-step solutions included
Exercise #1

Complete the following exercise:

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

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}

Video Solution
Exercise #2

Solve the following exercise:

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

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}

Video Solution
Exercise #3

Complete the following exercise:

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

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}

Video Solution
Exercise #4

Complete the following exercise:

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

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

Video Solution
Exercise #5

Solve the following exercise:

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

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}

Video Solution

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