In this article, we will learn about subtracting fractions with unlike denominators. If you do not know what are fractions with unlike denominators consider reading this article

## Subtracting fractions with unlike denominators

### Definitions and Concepts

#### Fraction

- A fraction represents a part of a whole and consists of a numerator and a denominator. For example, \(\frac{a}{b}\), where \(a\) is the numerator and \(b\) is the denominator.

#### Unlike Denominators

- Two fractions have unlike denominators if the denominators are not the same.

### Subtracting Fractions with Unlike Denominators

#### Step 1: Finding the Least Common Multiple (LCM)

To subtract fractions with unlike denominators, find the least common multiple of the denominators.

##### Example:

LCM of 4 and 6:

\[

\text{LCM}(4, 6) = 12

\]

#### Step 2: Rewriting the Fractions with the Common Denominator

Next, rewrite both fractions using the LCM as the common denominator.

##### Example:

Rewrite \(\frac{3}{4}\) and \(\frac{5}{6}\) with 12 as the common denominator.

\[

\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

\]

\[

\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}

\]

#### Step 3: Subtracting the Fractions

Subtract the numerators and place the result over the common denominator.

\[

\frac{9}{12} – \frac{10}{12} = \frac{9 – 10}{12} = \frac{-1}{12}

\]

## Solved Examples

let us have a look at two examples of subtracting fractions with unlike denominators.

### Example 1: Subtracting \(\frac{2}{7}\) from \(\frac{3}{5}\)

#### Step 1: Finding the Least Common Multiple (LCM)

Find the LCM of 7 and 5:

\[

\text{LCM}(7, 5) = 35

\]

#### Step 2: Rewriting the Fractions with the Common Denominator

\[

\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}

\]

\[

\frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35}

\]

#### Step 3: Subtracting the Fractions

\[

\frac{3}{5} – \frac{2}{7} = \frac{21}{35} – \frac{10}{35} = \frac{11}{35}

\]

### Example 2: Subtracting \(\frac{7}{8}\) from \(\frac{3}{5}\)

#### Step 1: Finding the Least Common Multiple (LCM)

\[

\text{LCM}(8, 5) = 40

\]

#### Step 2: Rewriting the Fractions with the Common Denominator

\[

\frac{7}{8} = \frac{35}{40}

\]

\[

\frac{3}{5} = \frac{24}{40}

\]

#### Step 3: Subtracting the Fractions

\[

\frac{3}{5} – \frac{7}{8} = \frac{-11}{40}

\]

These two examples shows the methodical approach of subtracting fractions with unlike denominators. By finding the LCM, rewriting the fractions, and performing the subtraction, we can obtain the desired results.

### Questions and Answers

1. Subtract \(\frac{2}{3}\) from \(\frac{5}{6}\):

\[

\frac{5}{6} – \frac{2}{3} = \frac{5}{6} – \frac{4}{6} = \frac{1}{6}

\]

2. What if the fractions are mixed numbers?

Convert them into improper fractions and then follow the steps above.

### Further Reading

If you are interested in building a strong foundation in mathematics, particularly focusing on basics suitable for younger grades, we invite you to explore our resources tailored for students. Visit Class 6 Maths for fundamental concepts, and Class 7 Math to continue your learning journey.