Use properties of Multiplication to find a product

Introduction:

How can you find 5 x 30?

Till now, we have learned two different methods:

1. Number line method
2. Block pattern method

Number Line Method:

1 Jump of 30 is 30 ​    1x 30= 30

2 Jumps of 30 is 60​    2x 30= 60

3 Jumps of 30 is 90     3x 30=90

4 Jumps of 30 is 120 ​ 4x 30= 120

5 Jumps of 30 is 150    5 x 30= 150

Block Pattern Method:

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​

Now we will learn more properties of multiply numbers.

You can use different properties to explain a rule for finding a product when one factor is a multiple of 10.

1. Associative property
2. Distributive Property

Associative Property:

Multiplication:

Example 1:

Find 4 x 20 using associative property.

Sol:

You can use the associative property of multiplication to group the factors.

4 x 20 = 4 x (2 x 10)

4 x 20 = (4 x 2) x 10

4 x 20 = 8 x 10

 4 x 20 =   80

Example 2:

A pearl anniversary is a period of 30 years. Find the number of years in 5 pearl anniversaries by using associative property.

Sol:

We need to find 5 x 30.

5 x 30= 5 x (30)

5 x 30 = 5 x (3 x 10)

5 x 30 = (5 x 3) x 10

5 x 30 = 15 x10

5 x 30 = 150

Distributive Property:

Example 1:

Find 4 x 20 using the distributive property.

Sol:

You can use the distributive property to decompose a factor.

4 x20= (2+2) x 20

4 x 20= (2x 20) + ( 2 x 20)

4 x 20 = 40 + 40

4 x 20 = 80

Example 2:

Find the product of 9 x 30 using the distributive property.

Solution:

9x 30= 9 x 30

9 x 30 = (4 + 5) x 30

9 x 30 = (4 x 30) + (5 x 30)

9 x 30 = (120) + (150)

9 x 30 = 270

TRY IT!

A regular box of pencils has 20 pencils. A jumbo box holds 40 pencils. There are 4 boxes of regular pencils on one shelf and 4 boxes of jumbo pencils on another shelf. How many pencils are there on each shelf?​

Answer:

The number of pencils in a regular box = 20 pencils​

The number of boxes of regular pencils on one shelf = 4 boxes

4 x 20 = 4 x ( 2 x 10)

4 x 20 = (4 x2) x 10

4 x 20 = 8 x 10

4 x 20 =  80

Number of pencils in one shelf = 80

The number of pencils in the jumbo box = 40 pencils

The number of boxes of jumbo pencils on another shelf = 4 boxes​

4 x 40 = ( 2+2) x 40

4 x 40 = ( 2 x 40) + ( 2 x 40)

4 x 40 = ( 80) + ( 80)

4 x 40  =  160

The number of pencils on another shelf = is 160​ ​

Exercise:

1. A Bicycle costs $ 210. How much will be paid for 20 bicycles?
2. A carton holds 2 Packets of biscuits. Each packet has 10 biscuits.  How many packets can be packed in 30 packets?
3. 4 folders have 50 papers each. How many papers are there altogether?
4. Use associative Property to solve 9 x 50.
5. Use the distributive property to solve 7 x 40.
6. Is 3 x 60 and 6 x 30 equal? If yes, Justify.
7. Find the missing number of the equation that makes it true. 9 x —- = 630
8. A pearl anniversary is a period of 40 years. Find the number of years in 6- Pearl Anniversary by using number lines.
9. How distributive and associative property are related? Explain with an example.
10. Without finding the product, how can you tell whether 4 x 60 or 7 x 40 is greater? ​

Concept Summary:

What Have We Learnt:

• Associative Property
• Distributive Property.
• Multiplication of any two numbers.