In maths, multiplication is denoted by ‘×’ to find the product of two or more values. The first number is called multiplicand and the second number is called the multiplier. The multiplier will increase the value of the number. The increase in a number depends on the multiplier. It is the repeated addition of the number with respect to one another.

Multiplication is one of the fundamental topics in maths. Here we will learn about the multiplier with different numbers. Get the examples on Multiplier by 10, 100, 1000, 10000 with step by step explanation. Also, the students can know in detail about the properties of multiplication.

**Do Refer:**

- Divide by 10, 100 and 1000 Divisors
- Worksheet on Divide by 10, 100 and 1000 Divisors
- Multiplicand and Multiplier

## How to Multiply by 10, 100, 1000, 10000?

In this concept, we multiply the multiplicand by the non-zero digit of the multiplier. Then we add the same number of zero to the extreme right of the product as the multiplier.

We can understand this concept by following the below steps.

Step 1: We count the zeros first.

Step 2: We multiply the non-zero numbers.

Step 3: We place the same number of zero to the extreme right of the product.

### Properties of Multiplication

1. Commutative Property

2. Associative Property

3. Distributive Property

4. Identity Property

5. Zero Property

**1. Commutative Property:** The commutative property of multiplication, if A and B are any two integers then,

a × b = b × a

Example: 2 × 3 = 3 × 2

**2. Associative Property:** As per the associative property of multiplication, if a, b, c are three integers then,

a × (b × c) = (a × b) × c

Example: 2 × (3 × 5) = (2 × 3) × 5

**3. Distributive Property:** According to the distributive property of multiplication, if a, b and c are three integers then,

a × (b + c) = (a × b) + (a × c)

Example: 2 × (3 + 5) = (2 × 3) + (2 × 5)

**4. Identity Property:** As per the identity property of multiplication, if we multiply any integer by 1, then its value remains unchanged, such that,

a × 1 = 1 × a

Example: 2 × 1 = 1 × 2

**5. Zero Property:** Zero property of multiplication states that any number multiplied by 0 is always 0.

a × 0 = 0

Example: 5 × 0 = 0

### Examples on Multiplying by Multiples of 10 100 1000 and 10000

Let us see some examples of multiply by 10, 100, 1000, 10000 with explanations.

**Example 1.**

Find the product of the following

i. 12 × 10

ii. 24 × 20

**Solution:**

i. 12 × 10

Follow the steps to find the product of the given numbers.

Step 1: We count the zeros first.

There is one zero

Step 2: We multiply the non-zero numbers.

12 × 1 = 12

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 120.

So, 12 × 10 = 120

ii. 24 × 20

Follow the steps to find the product of the given numbers.

Step 1: We count the zeros first.

There is one zero

Step 2: We multiply the non-zero numbers.

24 × 2 = 48

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 480.

So, 24 × 20 = 480

**Example 2.**

Find the product of the following

i. 34 × 100

ii. 12 × 200

**Solution:**

i. 34 × 100

Step 1: We count the zeros first.

There are two zeros.

Step 2: We multiply the non-zero numbers.

34 × 1 = 34

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 3400.

So, 34 × 100 = 3400

ii. 12 × 200

Step 1: We count the zeros first.

There are two zeros.

Step 2: We multiply the non-zero numbers.

12 × 2 = 24

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 2400.

So, 12 × 200 = 2400

**Example 3.**

Find the product of the following

i. 2 × 1000

ii. 5 × 3000

**Solution:**

i. 2 × 1000

Step 1: We count the zeros first.

There are three zeros.

Step 2: We multiply the non-zero numbers.

2 × 1 = 2

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 2000.

So, 2 × 1000 = 2000

ii. 5 × 3000

Step 1: We count the zeros first.

There are three zeros.

Step 2: We multiply the non-zero numbers.

5 × 3 = 15

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 15000.

So, 5 × 3000 = 15000

**Example 4.**

Find the product of the following

i. 6 × 10000

ii. 15 × 50000

**Solution:**

i. 6 × 10000

Step 1: We count the zeros first.

There are four zeros.

Step 2: We multiply the non-zero numbers.

6 × 1 = 6

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 60000.

So, 6 × 10000 = 60000

ii. 15 × 50000

Step 1: We count the zeros first.

There are four zeros.

Step 2: We multiply the non-zero numbers.

15 × 5 = 75

Step 3: We place the same number of zero to the extreme right of the product.

Now add zero to the extreme right.

Thus it becomes 750000.

So, 15 × 50000 = 750000

**Example 5.**

Jai earns $24 per hour. What are his earnings for 10 hours?

**Solution:**

Given that,

Jai earns $24 per hour.

We have to find his income for 10 hours.

24 × 10 = $240

Thus Jai earns $240 for 10 hours.