Table of Contents
Table of Contents
- Trick 1: Dealing with numbers close to multiples of 10
- Trick 2: Dealing with multiples of 5
- What’s Next?
In our previous segment, we learnt about the Distributive property of whole numbers and how it can be used to solve multiplication problems. In this segment, we will learn some more tricks to add, subtract and multiply whole numbers.
Trick 1: Dealing with numbers close to multiples of 10
The presence of numbers such as ten, hundred, thousand, ten thousand, most of the time makes multiplication a bit easier. Hence, whenever possible, we should try to bring these numbers into our calculations. We will now look at some examples to see how this can be done.
Example 1: ?? × ??
In this problem, we will use the distributive property of multiplication over subtraction. We
will express 99 as 100 -1
59 × 99 = 59 × (100 − 1)
= (59 × 100) − (59 × 1)
= 5900– 59
= 5841
Example 2: ?? × ?
Here, again we will use the distributive property of multiplication over subtraction.
87 × 9 = 87 × (10 − 1)
= (87 × 10) − (87 × 1)
= 870– 87
= 783
Example 3: 565 + 98
Instead of adding this directly, we can split 98 as 100 – 2, and then use the associative property of whole numbers.
565 + 98 = 565 + (100 – 2)
= (565 + 100) – 2
= 665 – 2
= 663
Trick 2: Dealing with multiples of 5
But sometimes, there may not be any number that is close to 10, 100 or 1000. For example: 86 × 5
Writing the above expression as 86 × (10 − 5) ?? (100 − 14) × 5, will not simplify the
calculation.
We know that when there is nothing in the denominator, it is assumed to be 1.
That means 5 is same as 5
1
So multiplying 5 with 2 gives 10,making the problem easy to solve.
1 2 2
So we have, 86 × 5 = 86 × 10/2
To simplify this, we will divide 86 by 2 to get 43. Then multiply 43 with 10 to get 430.
Thus, in such cases, we try to convert the multiple of 5 to a multiple of 10 by multiplying the
number with 2.
2
Let us look at a few more examples to understand this.
Example 1: ?? × ??
55 is a multiple of 5. We multiply it with2 .
2
26 × 55 = 26 × 55 × (2/2)
= 26 × (55 × 2)/2
= 26/2 × 110
= 13 × 110
= 1430
Example 2: ?? × ??
66 × 35 = 66 x 35 x (2/2)
= 33 × 70
= 2310
Note :
This method cannot be applied for all multiplications where multiples of five are involved. For example, this method will not work for 87 × 5,as 87 is not divisible by 2, as it is an odd number.
It works only when the other number in the expression is an even number.
What’s next?
In the next segment of Class 6 Maths, we look at some interesting patterns of whole numbers.
