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# Multiply by multiples ## Key Concepts

• Associative property of multiplication
• Multiplication through place value

## 3.1.1 Associative property of multiplication:

Associative property over multiplication formula

The rule that involves number grouping is known as the associative property. The rule for the associative property of multiplication is

(A × B) × C = A × (B × C

Associative property over multiplication formula

For example: (3 × 4) × 5 = 3 × (4 × 5)

⇒ 12 × 5 = 3 × 20

⇒ 60 = 60

### Associative property of multiplication

2 × 10, 2 × 100, 2 × 1000

Use associative property of multiplication

2 × 10 = 2 × (1 × 10)

= (2 × 1) × 10

= 2 × 10

= 20

2 × 100 = 2 × (1 × 100)

= (2 × 1) × 100

= 2 × 100

= 200

2 × 1000 = 2 × (1 × 1000)

= (2 × 1) × 1000

= 2 × 1000

= 2000

Place value:

Place value is all about the value of each digit within a number. Each digit has a different value determined by its position.

### 3.1.2 Multiplication through place value:

The following chart shows the place value:

### Example: 1

Find the value of 8 × 549.

Multiplication through place value is shown in the given picture:

### Example: 2

Finding the place value of each number:

The image below indicates the multiplication through the place value of each number.

### Exercise:

1.    Workout

(a)  8 × 10

(b) 6 × 100

(c) 7 × 1000

2.    Multiply and write the product.

(a)   3 × 48                      (b)  8 × 207                   (c)  9 × 2956

3.    Multiply and write the product in the outermost circle.

Fill in the blanks.

(a)  7 × 10 = _________

(b)  8 × __________ = 68000

(c)   5 × 100 = __________

5.    Fill the missing number in the blank.

(a)   10 × (8 × 7) =  ____________

(b)  (4 × 6) × 2 = ____________

(c)   8 × (7 × 3) = ______________

6.    Determine the value of n that makes the equation true.

(a)  9 × (3 × 5) = (n × 3) × 5

(b)  5 × (7 × 8) = (n × 7) × 8

7.    Determine the place value of the digit 3 in the whole number.

(a)   2530 ___________________________

(b)  45,271,903 ___________________

(c)   1392 _________________________

8.    Name the place value of 3 in each of the following:

(a)   23,576

(b)  75,329

9.    Find the place value of the digit 4 in each of the following:

(a)   74983160

(b)  8745836

10. Solve 2 × (4 × 3) and (2 × 4) × 3.

### What have we learnt:

In this chapter, we have learned:

• Associative property of multiplication
• Place value
• Multiplication through place value
• Multiply by multiples of 10, 100, and 1,000

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