Page 178 - New Medley 4 Semester 1

Simplification of Expressions with

Two or More Operations (DMAS)

Consider the expressions: 2 × 5 – 7; 3 + 5 × 7 – 6; 2 × 12 ÷ 3 – 6 + 1, etc.

Some times two or more operators occur simultaneously in an expression.

To simplify such expressions we use the rule of DMAS

(Divide – Multiply – Add – Subtract). We first perform division, next

multiplication, then addition and finally subtraction.

Example 11: Simplify the following.

(a) 2 × 12 ÷ 3 – 6 + 1 (b) 72 × 9 ÷ 3 – 150

Solution: (a) 2 × 12 ÷ 3 – 6 + 1

We first divide [12 ÷ 3 = 4] = 2 × 4 – 6 + 1

Next we multiply [2 × 4 = 8] = 8 – 6 + 1

Now we add [8 + 1 = 9] = 9 – 6

Finally we subtract [9 – 6 = 3] = 3

(b) 72 × 9 ÷ 3 – 150

We first divide [9 ÷ 3 = 3] = 72 × 3 – 150

Next we multiply [72 × 3 = 216] = 216 – 150

We have no ‘addition’ so we skip it.

Finally we subtract = 66.

Note: If an operator is not present it is skipped, keeping the order of
operations same.

EXERCISE 4.8

Simplify.

1. 426 – 210 × 4 ÷ 2 2. 248 ÷ 62 + 8 × 12
3. 64 × 2 – 85 ÷ 17 4. 245 – 75 × 9 ÷ 3

5. 110 – 50 × 4 ÷ 2 + 3

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