Order of operations with fractions

Definition

We combine the order operations PEMDAS with adding, subtracting, multiplying, and dividing fractions.

Rules for Order of Operations with Fractions

• First, we simplify any parentheses if any in the expression.
• Next, we simplify any exponents if present in the expression.
• We do multiplication and division before addition and subtraction.
• We do multiplication and division based on order of appearance from left to right in the problem.
• Next, we do addition and subtraction based on order of appearance from left to right in the problem.

Consider the following problems involving PEMDAS with adding, subtracting, multiplying, and dividing fractions.

Example 1

Evaluate 45[17−32(14)2]

Solution

Step 1:

As per the PEMDAS rule of operations on fractions we simplify the brackets or the parentheses first.

Step 2:

Within the brackets, the first we simplify the exponent as (14)2=116

Step 3:

Within the brackets, next we multiply as follows

17−32(14)2=17−32×116=17−2

Step 4:

Within the brackets, next we subtract as follows

17 – 2 So, [17−32(14)2]=15

Step 5:

45[17−32(14)2]=45[15]=45×15

So, simplifying we get

45×15=4×3=12

Step 6:

So, finally 45[17−32(14)2]=12

Example 2

Evaluate (367−117)×85−97

Solution

Step 1:

As per the PEMDAS rule of operations on fractions we simplify the brackets or the parentheses first.

Within the brackets, the first we subtract the fractions as follows

Step 2:

Next, we multiply as follows

(367−117)×85−97=257×85−97=407−97

Step 3:

We then subtract as follows

407−97=(40−9)7=317

Step 4:

So, finally (367−117)×85−97=317=437