Order of operations with fractions: Problem type 1

We combine the order operations (PEMDAS) with adding, subtracting, multiplying, and spaniding fractions.

Rules for Order of Operations with Fractions

First, we simppfy any parentheses if any in the expression.

Next, we simppfy any exponents if present in the expression.

We do multippcation and spanision before addition and subtraction.

We do multippcation and spanision 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 spaniding fractions.

Evaluate $frac{4}{5}[17-32left ( frac{1}{4} ight )^{2}]$

Solution

Step 1:

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

Step 2:

Within the brackets, the first we simppfy the exponent as $left ( frac{1}{4} ight )^{2} = frac{1}{16}$

Step 3:

Within the brackets, next we multiply as follows

$17-32left ( frac{1}{4} ight )^2 = 17-32 imes frac{1}{16} = 17 - 2$

Step 4:

Within the brackets, next we subtract as follows

17 - 2 So, $[17-32left ( frac{1}{4} ight )^2] = 15$

Step 5:

$frac{4}{5}[17-32left ( frac{1}{4} ight )^2] = frac{4}{5}[15] = frac{4}{5} imes 15$

So, simppfying we get

$frac{4}{5} imes 15 = 4 imes 3 = 12$

Step 6:

So, finally $frac{4}{5}[17-32left ( frac{1}{4} ight )^2] = 12$

Evaluate $left ( frac{36}{7} - frac{11}{7} ight ) imes frac{8}{5} - frac{9}{7}$

Solution

Step 1:

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

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

Step 2:

Next, we multiply as follows

$left ( frac{36}{7} - frac{11}{7} ight ) imes frac{8}{5} - frac{9}{7} = frac{25}{7} imes frac{8}{5} - frac{9}{7} = frac{40}{7} - frac{9}{7}$

Step 3:

We then subtract as follows

$frac{40}{7} - frac{9}{7} = frac{(40-9)}{7} = frac{31}{7}$

Step 4:

So, finally $left ( frac{36}{7} - frac{11}{7} ight ) imes frac{8}{5} - frac{9}{7} = frac{31}{7} = 4frac{3}{7}$