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Subtracting Fractions with the Same Denominator

To subtract fractions with the same or like denominator, we subtract the numerators and then copy the common denominator. Write your answer in the simplest form.

The numerators are \(a\) and \(b\), and the common denominator is \(d\).

$${a \over d} - {b \over d} = {{a - b} \over d}$$

Example 1: \(\large{{7 \over 8} - {3 \over 8}}\)

They have the same or like denominator so we should be able to subtract the numerators without any problem. That is, \(7 - 3 = 4\). The common denominator is \(8\). Upon inspection, there is the Greatest Common Factor (GCF) of \(4\). Use this to reduce to lowest terms.

$$\eqalign{
   {7 \over 8} - {3 \over 8} &= {{7 - 3} \over 8}  \cr 
  &  = {4 \over 8}  \cr 
  &  = {{4 \div 4} \over {8 \div 4}}  \cr 
  &  = {1 \over 2} \cr} $$

Example 2: \(\large{{{32} \over {42}} - {{23} \over {42}}}\)

If we subtract the numerators, we get \(9\). Then we copy the common denominator of \(42\). The GCF of \(9\) and \(42\) is \(3\).

$$\eqalign{
   {{32} \over {42}} - {{23} \over {42}} &= {{32 - 23} \over {42}}  \cr 
  &  = {9 \over {42}}  \cr 
  &  = {{9 \div 3} \over {42 \div 3}}  \cr 
  &  = {3 \over {14}} \cr} $$

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