**Fractions**

Multiplication and Division of Fractions

**Multiplication of fractions**

To multiply fractions, there is no need to have the same denominators. We can multiply any fractions by the following steps.

**Step 1:** If there is a whole number, write the whole number in the form of a fraction with denominator 1.

**Step 2:** Multiply the numerators.

**Step 3:** Multiply the denominators.

**Step 4:** Simplify the new fraction.

** Multiplication of fraction and a whole number**

**Example:**

**Question:**Find the product:

**Answer:**

**Step 1:** Write the whole number in the form of a fraction.

**Step 2:** Multiply the numerators.

4 × 3 = 12

**Step 3:** Multiply the denominators.

1 × 4 = 4

We can do steps 2 and 3 as:

**Step 4: Simplify the new fraction.**

HCF of 4 and 12 = 4

Divide numerator and denominator by 4.

`÷`

4
/
4 `÷`

4
Therefore,

**Visual representation:**

**Multiplication of two fractions**

**Example:**

**Answer:**

**Step 1:** Multiply the numerators.

**Step 2:** Multiply the denominators.

So,

**Visual representation:**

Division of Fractions

To do division of fractions, we need to know the term ‘reciprocal of a fraction’.

**Reciprocal of a fraction:**

- Reciprocal of a fraction is the fraction obtained by interchanging the numerator and denominator with each other.
- The product of a fraction with its reciprocal is always 1

**Example:**

Reciprocal of

Reciprocal of 5 is

**Steps for division of fractions:**

**Step 1:** If there is a whole number, write the whole number in the form of a fraction

**Step 2:** Find the reciprocal of the second fraction.

**Step 3:** Multiply the first fraction and reciprocal of the second fraction.

**Examples:**

**Question 1:**

`÷`

2 = ?
**Answer:**

`÷`

2 =
`÷`

2=
Now, simplify the answer.

HCF of 9 and 24 = 3

Divide both numerator and denominator by 3.

`÷`

3
/
24 `÷`

3
So,

`÷`

2 =
**Visual representation:**

**Question 2:**

`÷`

**Answer:**

**Step 1:** Find the reciprocal of the second fraction.

**Step 2:** Multiply the first fraction and the reciprocal of the second fraction.

`÷`

**Step 3:** Simplify the fraction.

HCF of 45 and 36 = 9

Divide both numerator and denominator by 9.

`÷`

9
/
36 `÷`

9
`÷`

**Visual representation:**