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\\October 8, 2025 12:09 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

5. Find the actual and the estimated product of 1439 × 784.
6. 23,52,167 votes were cast in the Constituency A election, whereas 30,14,184 votes
were cast in the Constituency B election. Estimate the difference between the votes
cast in these two constituencies.

SiMPlifiCation of nuMEriCal ExPrESSionS

We have already learnt how to perform arithmetic operations (addition, subtraction,
multiplication and division) on the numbers.

Sometimes we need to solve an expression which Math Insight

contains more than one operation; we can get different Numbers connected together
results depending on the order in which the operations by one or more operations
form a numerical expression.
are carried out.

Let us simplify 5 + 5 + 45 ÷ 5 × 4 – 1

Possibility 1 Possibility 2 Possibility 3

= (5 + 5 + 45) ÷ 5 × 4 – 1 = 5 + 5 + 45 ÷ 5 × (4 – 1) = 5 + 5 + (45 ÷ 5) × 4 – 1
[Add the first three numerals] [Subtract: 4 – 1 = 3 ] [Divide: 45 ÷ 5 = 9]

= 55 ÷ (5 × 4) – 1 = 5 + 5 + 45 ÷ (5 × 3) = (5 + 5 + 9) × 4 – 1
[Multiply: 5 × 4 = 20] [Multiply: 5 × 3 = 15] [Add: 5 + 5 + 9 = 19]

= 55 ÷ (20 – 1) = 5 + 5 + (45 ÷ 15) = (19 × 4) – 1
[Subtract: 20 – 1 = 19] [Divide: 45 ÷ 15 = 3] [Multiply: 19 × 4 = 76]

= 55 ÷ 19 = 5 + 5 + 3 = 76 – 1

[Divide: 55 by 19 = 2 17 ] [Add: 5 + 5 + 3 = 13] [Subtract: 76 – 1 = 75]
19
= 2 17 = 13 = 75
19

We can simplify the above expression in many more ways and get different results. But can
you tell which is the correct answer to the above expression?

Hence, it is very important that we follow a certain order to solve such a problem correctly.

There is a rule to solve such numerical expressions that have more than one mathematical
operations.

dMaS

A numerical expression is simplified to get the answer by following the rule of DMAS.

According to this rule, operations are performed in the following order to solve numerical
expressions:

First - division Second - Multiplication Third - Addition Fourth - Subtraction

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