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
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