Before knowing the process of dividing fractions, let us first learn what fractions are? Fractions represent the equal part of a whole. Fractions are expressed in the form of , where x and y are integers.

The top number, written above the horizontal line, is known as numerator.  It says how many parts we have. The bottom number, written below the horizontal line, is the denominator. It represents how many equal parts the given item is split into. Hence, in the fraction  (read as five- sixth), 5 is the numerator and 6 is the denominator. This tells us there are 5 parts, each of them is one-fifth (or ) of a whole.

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Steps of Division of Fractions with Unlike Denominators

The process of dividing fractions is the same as multiplying fractions. The only difference is that while dividing fractions, you need to reciprocal the second fraction, i.e. divisor, and change the division sign to multiplication sign and multiply.

 

Example: What is    ?

Solution: The steps to divide the given fraction are:

Step 1: Keep the first and second fraction as it is given in the questions. This gives

 

Step 2: Change the division symbol into a multiplication symbol.

Step 3: Now, reciprocal the second fraction or divisior. As you will reciprocal, the numerator will become the denominator and the denominator will the numerator. Accordingly, this gives:

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Step 4: Multiply the numerators and denominators of a fraction as shown below:
Step 5: Simply the result. Here,  can be simplified further as.
=
Therefore,      = 3

Converting Decimals to Fractions

Converting decimals to fractions can be done by following these simple steps:

  • Write down the given decimal number divided by 1 like this
  • Multiply both numerator and denominator by 10 for every number after the decimal point. For example, if there are two numbers after the decimal point then multiply by 10, if there are three numbers after the decimal point then multiply by 1000, and so on.
  • Simplify the fraction.
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Example 1: Convert 0.65 into Fraction.

Step 1: Write down the given decimal number divided by 1 like this . Accordingly, it gives

Step 2: Multiply both numerator and denominator by 100 as there are two digits after the decimal point. Accordingly, it gives:

=

Step 3: Simplifying the fraction

=

Therefore, 0.65 in fraction will be .

 

Example 2: Convert 0.525 in Fraction

Step 1: Write down the given decimal number divided by 1 like this .Accordingly, it gives

Step 2: Multiply both numerator and denominator by 1000 as there are three digits after the decimal point. Accordingly it gives:

=

Step 3: Simplifying the fraction

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=  =   =

Therefore, 0.65 in fraction will be .

How to Convert Recurring Decimals Into Fraction

Recurring decimal numbers are the number that keeps on repeating the same value after the decimal point. The steps to convert recurring decimals is same as discussed above. Let us understand with an example.

 

Example: Convert 0.555 into fraction

Step 1: Write down the given decimal number divided by 1 like this . Accordingly, it gives

Step 2: Multiply both numerator and denominator by 1000 as there are three digits after the decimal point. Accordingly, it gives:

=

Step 3: Simplifying the fraction

=

Therefore, 0.555 in a fraction will be .

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