Multiplication Using Multiples of 10

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.

1. 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: 

1. 2 × 10 = 20
2. 3 × 10 = 30

Try this:

1. 70 x 2 = _____.
2. 40 x 9 = _____.
3. 20 x 8 = ______.

1.2 Patterns to Multiply:

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

1. Place value blocks pattern
2. 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 or80
• 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.

1. 5 x 10
2. 6 x 30
3. 7 x 70
4. 4 x 50
5. 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

Concept Map: