What are Fractions?
Fractions are numbers that are used to represent a portion of a whole. Usually represented in a form which shows the numerator being divided by the denominator, that is in a pq format, and in this case ‘q’ should not be zero.
In math, there are two types of fractions: like fractions and unlike fractions. Fractions that have the same denominators are called like fractions. On the other hand, fractions with different denominators are called unlike fractions. The following image illustrates the difference between like and unlike fractions.
How do we Subtract Fractions with Unlike Denominators?
Subtracting two or more fractions indicates that we need to find the difference between them. It is possible to subtract fractions with like as well as unlike denominators.
The steps for subtracting fractions with different denominators are:
Step 1: Multiply both the numerator and the denominator of each fraction with a certain number to obtain equivalent fractions, that is, the fractions are converted into like fractions.
Step 2: Subtract the numerators of all the fractions and keep the denominator the same.
Step 3: If required, we can simplify the fraction to its simplest form.
Rapid Recall
Solved Examples
Example 1:
Find the difference between the fractions \(\frac{8}{9}\) and \(\frac{2}{3}\).
Solution:
We have to find the value of: \(\frac{8}{9}-\frac{2}{3}\)
Here, both the fractions have unlike denominators. Convert them into like fractions and subtract them.
\(\Rightarrow \frac{8}{9}-\frac{2\times 3}{3 \times 3}\) [Find equivalent fractions]
\(\Rightarrow \frac{8}{9}-\frac{2}{3}=\frac{8}{9}-\frac{6}{9}\) [Rewrite \(\frac{2}{3}\) as \(\frac{6}{9}\)]
\(\Rightarrow \frac{8-6}{9}\) [Subtract the numerators]
\(\Rightarrow \frac{2}{9}\)
Therefore, the difference between \(\frac{8}{9}\) and \(\frac{2}{3}\) is \(\frac{2}{9}\)
Example 2:
Find the value of this operation involving fractions: \(\frac{17}{20}-\frac{11}{20}-\frac{4}{5}\).
Solution:
We have to find the value of: \(\frac{17}{20}-\frac{11}{20}-\frac{4}{5}\)
Converting unlike fractions into like fractions and subtract
\(\Rightarrow \frac{17}{20}-\frac{11}{20}-\frac{4}{5}=\frac{17}{20}-\frac{11}{20}-\frac{4\times 5}{5\times 5}\) [Rewrite \(\frac{4}{5}\) as \(\frac{16}{20}\)]
\(=\frac{17}{20}-\frac{11}{20}-\frac{16}{20}\)
\(= \frac{17-11-16}{20}\) [Subtract the numerators]
\(= \frac{17-27}{20}\) [Simplify]
\(= \frac{-10}{20}\) [Simplify]
\(= \frac{-1}{2}\) [Divide numerator and denominator by 10]
Therefore, \(\frac{17}{20}-\frac{11}{20}-\frac{4}{5}= \frac{-1}{2}\)
Example 3:
The height of the smallest dog in the world is recorded as \(\frac{19}{5}\) inches tall. The previous record was \(\frac{31}{5}\) inches. How much shorter is the dog with the current world record than the previous one?
Solution:
The current world record for the smallest dog in the world = \(\frac{19}{5}\) inches
And, the previous record = \(\frac{31}{5}\) inches
The difference between current and previous record is,
\(=\frac{31}{5}-\frac{19}{5}\) [The fractions have like denominators]
\(=\frac{31-19}{5}\) [Subtract the numerators]
\(=\frac{12}{5}\)
As a result, the dog with the current world record is \(\frac{12}{5}\) inches shorter than the previous record.
Yes, we can subtract mixed numbers with unlike denominators by finding a common denominator and rewriting each fraction as an equivalent fraction. Then, subtract the fractions and simplify.
Fractions which have the same denominators are called like fractions and the fractions with different denominators are known as unlike fractions.
Addition, subtraction, multiplication, and division are the math operations that can be performed on fractions. Operations with fractions differ from operations with whole numbers, integers, and natural numbers.