Page 38 - Maths Skill - 6

36 Maths

INTRODUCTION
In this chapter, we shall study use of brackets, simplification of brackets, multiples and factors, divisibility rule of
numbers, even/odd numbers, prime and composite numbers, co-prime numbers, prime factorization of numbers
and many more.

SIMPLIFICATION
Upto now, we have learnt how the four fundamental operations – addition, subtraction, multiplication and division
are performed on numbers. But we performed only one operation at Fact-o-meter
a time.

For example, 4 – 3, 0 + 2, 3 × 15, 14 ÷ 2, etc. � An expression involving
Sometimes, we have the situations where we have to apply two or numbers and their operations
more operations on numbers and to write a numerical expression as is called numerical expression.
single numeral. This is called the simplification of the expression.

While simplifying an expression, we have to take care of some rules. If we do not follow them, we may not find
the right answer.
For example, consider the expression: But, Pranshi simplified same expression as

50 – 20 ÷ 5 + 3 × 2 50 – 20 ÷ 5 + 3 × 2 = 50 – 4 + 3 × 2
Soumya, simplified the above expression as (Dividing 20 by 5)
50 – 20 ÷ 5 + 3 × 2 = 30 ÷ 5 + 3 × 2 = 50 – 4 + 6 (Multiplying 3 and 2)
(Subtracting 20 from 50) = 56 – 4 (Adding 50 and 6)

= 6 + 3 × 2 (Dividing 30 by 5) = 52 (Subtracting 4 from 56)
= 9 × 2 (Adding 6 and 3)
= 18 (Multiplying 9 and 2)

Now, it is clear from above that both girls have got different answers. Why? Because they performed
operations: addition, subtraction, multiplication and division in different order.
In order to avoid this kind of confusion in simplification, an international convention has been accepted which is
stated as follows:
In a mathematical expression, the operations are performed in the following order: division, multiplication,
addition and subtraction (DMAS) sequentially from left to right in order.
The following example will clear the above statement:

20 ÷ 4 + 25
As we know the order in which the four fundamental operations to be performed is first division, then multiplication,
then addition and at last subtraction.
We look for the operation of division (÷) first of all and carry out the same.
Thus, 20 ÷ 4 + 25 = 5 + 25 [Dividing 20 by 4]
= 30 [Adding 25 and 5]

USE OF BRACKETS
Can you solve 40 – 1 + 5 × 2? What will be your answer? Is it 88 or 49? The answer is 49 as while calculating
we follow a systematic way to get accurate answers. The rule which is followed in the arithmetic operations is
VBODMAS.