## What is Fraction Rules?

**Fraction**: A fraction is a part of a whole or a collection and it consists of a numerator and denominator.

**Example**: If we serve1 part of a cake with 8 equal parts, we have served ^{1}⁄_{8} of the cake.

Let us see how to solve operations involving fractions.

## Adding or subtracting fractions with the same denominator

While adding or subtracting two fractions; we need to make sure that the denominators are the same.

**Steps**:

- Add or subtract the numerators.
- Keep the denominator the same.
- Reduce the answer, if possible.

**Example**: Solve ^{1}⁄_{4 }+ ^{1}⁄_{4}

**Example**: Subtract ^{1}⁄_{4} from ^{3}⁄_{4}

## Adding or subtracting fractions with the different denominators:

If the denominators are not the same:

- First, make them the same
- Then add or subtract like fractions with the same denominators.

**Example**: To solve ^{1}⁄_{4} + ^{1}⁄_{2} , we first make the denominators the same.

We change the denominator 2 and make it 4 by multiplying it by 2. However, we need to multiply the numerator and denominator both by 2 to keep the value of the fraction unchanged.

Multiplying ^{1}⁄_{2} ✕ ^{2}⁄_{2} = ^{2}⁄_{4}

Since the denominators are the same we can now add both the fractions.

Similarly, we use these rules for subtraction.

## Multiplying Fractions

To multiply two fractions we simply multiply the numerators and denominators.

**Example**:

^{2}⁄_{3} ✕ ^{3}⁄_{15} = ?

First, simplify the fraction ^{3}⁄_{15} to its lowest term.

## Dividing Fractions

While dividing two fractions:

- Inverse the second fraction, that is, interchange its numerator and denominator to get the reciprocal.
- Multiply the first fraction by the reciprocal of the second fraction.

**Example**:

## Solving improper fractions:

Fractions with a numerator larger than the denominator are called improper fractions. When we solve improper fractions, the result can be a mixed number (a fraction with a whole number and a proper fraction).

**Example**:

^{38}⁄_{7 }= ?

- Divide the numerator by the denominator.

38 ÷ 7 = 5 Quotient and 3 Remainder

- Write down the whole number answer.

5

- Then write down the remainder above the denominator.

5 ^{3}⁄_{7}

Therefore, ^{38}⁄_{7} = 5 ^{3}⁄_{7}

Thus, by solving an improper fraction ^{38}⁄_{7} we get a mixed number 5 ^{3}⁄_{7}

Fun Facts– We can multiply two fractions with different denominators, but we cannot add and subtract them. |