#### Introduction:

**How can you find 5 x 30?**

Till now, we have learned two different methods:

- Number line method
- 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.**

### Associative Property:

**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:

- A Bicycle costs $ 210. How much will be paid for 20 bicycles?
- A carton holds 2 Packets of biscuits. Each packet has 10 biscuits. How many packets can be packed in 30 packets?
- 4 folders have 50 papers each. How many papers are there altogether?
- Use associative Property to solve 9 x 50.
- Use the distributive property to solve 7 x 40.
- Is 3 x 60 and 6 x 30 equal? If yes, Justify.
- Find the missing number of the equation that makes it true. 9 x —- = 630
- A pearl anniversary is a period of 40 years. Find the number of years in 6- Pearl Anniversary by using number lines.
- How distributive and associative property are related? Explain with an example.
- 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.

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