Mixed operation problems are composed of various arithmetic equations, including addition, subtraction, multiplication and division, combined into one expression or equation. To perform them successfully, we must understand the order of operations (PEMDAS/BODMAS).

Parentheses / Brackets
Exponents / Orders (this topic will not be discussed here)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
To better understand how to easily solve mixed-operations problems, let us take a look at some examples.

Example 1: Solving an Expression Containing Parentheses

Problem
What is 7 + (5 x 3) – 47 + (5 x 3) – 4?
Solution
Step #1 – Perform the multiplication 5 x 3 = 15 5 x 3 = 15
Next, replace the parentheses with the result:
7 + 15 – 47 + 15 – 4
Now, perform addition/subtraction; therefore, it would be:
7 + 15 = 22
22 – 4 = 18
Final Answer: 18

Example 2: Real World Application (Toys in Boxes)
Problem
If I have six boxes, each containing eight toys, and I give away five toys, how many toys do I have left?
Solution
Step #1 – Calculate total number of toys by multiplying: 6 boxes x 8 toys per box = 48 toys
Step #2 – Calculate the total number of toys by taking away the five toys that were given away = 48 toys – 5 toys = 43 toys left.
Final Answer: 43 Toys

Example 3: Reading Advancement Through a Novel

Question:
A novel comprises 120 total pages; a pupil would read 15 each day, thus over the course of four days, the pupil will read 15 x 4 pages (60) with 120 – 60 (60) still to be read after this.
60 pages read over four days
60 pages remaining after the pupil has completed 60 pages from the total of 120 pages in the novel. (Word count = 49)

Example 4: Dividing 12 Apples Equally Between 4 Friends

Question:
Maria has 12 apples and purchased 4 more. When she divides the apples equally among the 4 friends, what is the number of apples each friend receives?
(Initial apples + apples purchased) 12 + 4 = 16 total apples (word count = 15)
(16 total apples) ÷ 4 (number of friends) = 4 apples per friend. (Word count = 15)