**Operations**

**Multiplication
**

Multiplication is a primary operation and it is used to find the product of two or more numbers.

- The symbol which is used to denote multiplication is ‘X’.

**Multiplication as repeated addition**

The multiplication of two numbers can be represented as **repeated addition**.

Example:

- Multiplication of 3 by 4 = 3 + 3 + 3 + 3 = 3 × 4 =12
- Multiplication of 7 by 5 = 7 + 7 + 7 + 7 + 7 = 7 × 5 = 35

**Multiplication on Number Line**

We can do multiplication using a number line.

Example:

- 3 × 4
- 6 × 3

**Answer:**

- To multiply 3 by 4, we need to take four jumps of 3 in the right direction.
- To multiply 6 by 3, we need to take three jumps of 6 in the right direction.
6 × 3 = 18

So,

3 × 4 = 12

**Multiplication Table up to 15**

**Multiplication of 2-digit numbers with a single digit number**

Multiplication of a 2-digit number with a single digit number can be categorise as:

- Without regrouping
- With regrouping

Example:

Find the product.

- 42 × 2
- 56 × 2

**Answer:**

- 42 × 2
Hence, 42 × 2 = 84

- 26 × 3
Hence, 26 × 3 = 78

**Multiplication of 2-digit numbers with 2-digit numbers**

Example:

Find the product.

- 33 × 11
- 56 × 12

**Answer:**

- 33 × 11

**Step 1****Step 2****Step 3**Hence, 33 × 11 = 363

- 56 × 12
**Step 1****Step 2****Step 3**Hence, 56 × 12 = 672

Alternative Method

In this method, we split the numbers in tens and ones and then use a grid to multiply.

Example:

Find the product.

- 65 × 23
- 74 × 17

**Answer:**

- 65 × 23 = (60 + 5) × (20 + 3)
Hence, 65 × 23 = 1495

- 74 × 17 = (70 + 4) × (10 + 7)
Hence, 74 × 17 = 1258

**Word Problems**

Example:

- Ram has 4 mango trees in his garden. Each tree has 35 mangoes. How many mangoes are there in the garden?
- Danish has 45 pens. He sold all of his pens for Rs 8 each. How much he earned after selling all of his pens?

**Answer:**

- Each tree has 35 mangoes.

Then the total number of mangoes is

35 × 4 = 140

Hence, the total number of mangoes in his garden is

140. -
Price of each pen is Rs 8.

The total price of 45 pens is

45 × Rs 8 = Rs 360

Hence, the total money he gets from selling his pens is

Rs 360.