Subtracting Fractions with the Same Denominator
To subtract fractions with the same denominator, subtract the numerators and keep the common denominator. Simplify the result if possible.
The numerators are \(a\) and \(b\), and the common denominator is \(d\).
$${a \over d} – {b \over d} = {{a – b} \over d}$$
Example 1: \(\large{{7 \over 8} – {3 \over 8}}\)
Since they share the same or a similar denominator, we can subtract the numerators without any issues. Specifically, \(7 – 3 = 4\). The common denominator is \(8\). Noticing that \(4\) is the Greatest Common Factor (GCF), we can simplify the fraction to its 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 \(3\).
$$\eqalign{
{{32} \over {42}} – {{23} \over {42}} &= {{32 – 23} \over {42}} \cr
& = {9 \over {42}} \cr
& = {{9 \div 3} \over {42 \div 3}} \cr
& = {3 \over {14}} \cr} $$