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We can simplify the above expression in many more ways getting all 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 follow 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
Here are the first letters of the operations in the order in which they are performed.

Division Multiplication Addition Subtraction

D M A S

Now let us solve the expression 5 + 8 + 45 ÷ 5 × 4 – 1 using the rule of DMAS.

5 + 8 + 45 ÷ 5 × 4 – 1
First - Division = 5 + 8 + (45 ÷ 5) × 4 – 1 [45 ÷ 5 = 9]

Second - Multiplication = 5 + 8 + (9 × 4) – 1 [9 × 4 = 36] Remember
Third - Addition = (5 + 8 + 36) – 1 [5 + 8 + 36 = 49] If any operation is
missing, skip to the
Fourth - Subtraction = 49 – 1 = 48 [49 – 1 = 48] next operation.

Hence, 5 + 8 + 45 ÷ 5 × 4 – 1 = 48
Example 1: Simplify: 26 ÷ 2 × 4 + 1 – 8

Solution: We have, 26 ÷ 2 × 4 + 1 – 8
= 13 × 4 + 1 – 8 (Division: 26 ÷ 2)

= 52 + 1 – 8 (Multiply: 13 × 4) Remember
= 53 – 8 (Addition: 52 + 1) (Dear Mother and Sister)
D M A S
= 45 (Subtraction: 53 – 8)

Thus, 26 ÷ 2 × 4 + 1 – 8 = 45
Example 2: Simplify: 15 + 24 ÷ 3 – 1 × 6

Solution: We have, 15 + 24 ÷ 3 – 1 × 6

= 15 + 8 – 1 × 6 (Division: 24 ÷ 3)

= 15 + 8 – 6 (Multiply: 1 × 6)

= 23 – 6 (Addition: 15 + 8)

= 17 (Subtraction: 23 – 6)

48 Mathematics-5