Order of Operations
Lessons in this chapter
About Order of Operations
Order of Operations is two lessons that settle a question kids have not had to ask before: when an expression has several operations, which one happens first.
Simplify Expressions Using Order of Operations establishes the sequence: exponents, then multiplication and division working left to right, then addition and subtraction left to right. The left-to-right part is the piece most often missed, because 20 − 8 + 3 is 15, not 9.
Simplify Expressions with Parentheses adds the override. Parentheses say do this first regardless, which means 2 × (3 + 4) is 14 while 2 × 3 + 4 is 10. Being able to see that the same digits give different answers is the point of the lesson.
This is a convention rather than a discovery, which is worth saying out loud. Mathematicians agreed on it so an expression has one meaning, and without it every expression with two operations would be ambiguous. It is also the last thing kids need before algebraic expressions arrive in 6th grade.
Both lessons open as a 5th grade math worksheet inside the page. Simplify Expressions Using Order of Operations and Simplify Expressions with Parentheses each set math questions for 5th graders to work one at a time, marked as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Simplify Expressions Using Order of Operations establishes the sequence: exponents, then multiplication and division left to right, then addition and subtraction left to right. The left-to-right part is the piece most often missed, because 20 minus 8 plus 3 is 15, not 9. Simplify Expressions with Parentheses then adds the override, so 2 times (3 + 4) is 14 while 2 times 3 + 4 is 10. The chapter sits in the Common Core domain Operations and Algebraic Thinking (5.OA).
Parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Because addition and subtraction are done left to right, not addition first. 20 − 8 is 12, then 12 + 3 is 15.
Yes, and they are done left to right. In 12 ÷ 3 × 2 the division comes first because it is further left, giving 8, not 2.
Because without it an expression would have more than one meaning. It is an agreed convention, not something discovered, and it exists so everyone reads an expression the same way.
They override the order. Whatever is inside is done first, so 2 × (3 + 4) is 14 while 2 × 3 + 4 is 10.