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 

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 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.

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