## 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

### Example: 1

### Example: 2

**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 Multiplicatio**n** 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.

### Concept Map

### 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