### Key concepts

- Multiply by multiples of 10
- Types of patterns to multiply
- Using place value of blocks for multiplication
- Using number lines for multiplication

**Introduction:**

### Multiplication

- A mathematical operation performed on a pair of numbers in order to derive a third number called a product.
- In multiplication, the second factor is referred to as the multiplicand. It is the number that is multiplied by the first factor, referred to as the multiplier
**.**

### Multiples:

A multiple is a product that we get when one number is multiplied by another number.

### Multiples of 10:

A multiple of 10 is any number multiplied by 10.

- We will learn about the multiplier by 10

We add a zero to the extreme right of the multiplicand while multiplying by 10.

**For example: **

- 2 × 10 = 20
- 3 × 10 = 30

**Try this:**

- 70 x 2 = _____.
- 40 x 9 = _____.
- 20 x 8 = ______.

### 1.2 Patterns to Multiply:

Two types of patterns are used to multiply by multiples of 10.

- Place value blocks pattern
- Number line pattern

**Place value block pattern:**

A place value block is a method that helps to learn addition, subtraction, multiplication, place values and counting.

E.g., 1: Find 3 x 40 using the place value blocks.

- 1 x 40 is 1 group of 4 tens = 4 tens or
**40** - 2 x 40 is 2 groups of 4 tens = 8 tens or
**80** - 3 x 40 is 3 groups of 4 tens = 12 tens or
**120**

E.g., 2: A pearl anniversary is a period of 30 years. Find the number of years in 5- pearl anniversary by using blocks.

Pearl anniversary = 30 years

The number of years in 5 pearl anniversary = 5 x 30

- 1 x 30 is 1 group of 3 tens = 3 tens or
**30**

- 2 x 30 is 2 groups of 3 tens = 6 tens or
**60**

- 3 x 30 is 3 groups of 3 tens = 9 tens or
**90**

- 4 x 30 is 4 groups of 3 tens = 12 tens or
**120**

- 5 x 30 is 5 groups of 3 tens = 15 tens or
**150**

E.g., 3: Find the value of 8 x 10 by using place value blocks.

**Solution:**

Given 8 x 10. So, we can take 1 group of tens block.

- 1 x 10 is 1 group of 8 tens = 8 tens or
**80**

### 1.3 Number Line Patterns:

A number line is a horizontal line on which numbers are marked at intervals, used to illustrate simple numerical operations.

E.g.: Find 3 x 40 using the number line pattern.

**Solution:**

The below number line shows the relation of 3 x 40.

- 1 Jump of 40 is 40. 1 x 40 = 40

- 2 Jumps of 40 is 80. 2 x 40 = 80

- 3 jumps of 40 is 120. 3 x 40 = 120

**EXAMPLE: 2**

A pearl anniversary is a period of 30 years. Find the number of years in 5- pearl anniversary by using number lines.

**Solution:**

Pearl anniversary = 30 years

The number of years in 5 pearl anniversary = 5 x 30

The below number line shows the relation of 5 x 30.

- 1 Jump of 30 is 30. 1 x 30 = 40

- 2 Jumps of 30 is 60. 2 x 30 = 60

- 3 jumps of 30 is 90. 3 x 30 = 90

- 4 Jumps of 30 is 120. 4 x 30 = 120

- 5 Jumps of 30 is 150. 5 x 30 = 150

**EXAMPLE: 3**

Find the value of 8 x 10, by using number line.

**Solution:**

The below number line shows the relation of 8 x 10.

- 1 Jump of 10 is 10. 1 x 10 = 40

- 2 Jumps of 10 is 20. 2 x 10 = 20

- 3 jumps of 10 is 30. 3 x 10 = 30

- 4 Jumps of 10 is 40. 4 x 10 = 40

- 5 Jumps of 10 is 50. 5 x 10 = 50

- 6 jumps of 10 is 60. 6 x 10 = 60

- 7 Jumps of 10 is 70. 7 x 10 = 70

- 8 Jumps of 10 is 80. 8 x 10 = 80

**EXAMPLE: 4**

On one open number line, show 4 x 30. On the other open number line, show 3 x 40. How are problems alike? How are they different?

**Solution:**

4 x 30 and 3 x 40 representation on the number line is given below.

- Even though the product of 3 x 40 and 4 x 30 is 120. The factors between them are not equal.

- The factors of 4 x 30 are 0, 30, 60, 90, 120.

- The factors of 3 x 40 are 0, 40, 80, 120.

**Example: 5**

Diana has $500. She spends $200 on new computer software. Find how much money is left with Diana.

Sol: Total amount of money Diana has = $500.

The amount of money she spends on computer software = $200

The total amount of money does she had after spending $200 = $500 – $200

= $300

**Assessment**

- What is meant by factors?

- Find the factors of 4 x 5?

- Express 4 x 10 on the number line.

## Exercise:

Find the product of each of the following using patterns.

- 5 x 10
- 6 x 30
- 7 x 70
- 4 x 50
- 3 x 30

### What we have learnt:

- Multiplication by using the multiples of 10.

- Multiplication through place value-box patterns

- Multiplication through number line patterns