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Order of operations: how to help your child practice

The order of operations is the agreed order for solving an expression: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. So 8 + 4 × 3 = 20, not 36. Most US schools teach it in 5th grade and add exponents in 6th grade.

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What is the order of operations?

The order of operations is a rule everyone agrees on so an expression has only one answer. Without it, 8 + 4 × 3 could be 36 (adding first) or 20 (multiplying first). Mathematicians agreed that multiplication comes before addition, so the answer is 20.

Many kids learn it as PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The catch is that the letters hide two pairs. Multiplication and division are equal partners, done left to right in the order they appear, and the same goes for addition and subtraction.

In most US schools, 5th graders work with parentheses and whole-number expressions, and 6th graders add exponents and expressions with variables. The 5th grade guide shows what else comes up that year, and the math topic guide shows where expressions lead next.

What does a order of operations twin question look like?

Choosing the expression with a given value · Multiple choice

OriginalWhich expression equals 14? A) 2 + 3 × 4 B) (2 + 3) × 4 C) 2 × 3 + 4 D) 2 × 3 × 4

TwinWhich expression equals 26? A) (2 + 6) × 4 B) 2 + 6 × 4 C) 2 × 6 + 4 D) 2 × 6 × 4

Evaluating with parentheses · Number answer

Original(6 + 9) ÷ 3 = ?

Twin(14 − 6) × 5 = ?

Working left to right · Number answer

Original20 − 12 ÷ 4 + 2 = ?

Twin18 ÷ 3 × 2 − 5 = ?

Evaluating with exponents · Number answer

Original3 + 2³ × 4 = ?

Twin4² − 2 × 5 = ?

Illustrative examples of how Easy Twin mirrors a question. The app writes brand-new questions from your own worksheet each time.

How do you use the order of operations, step by step?

Rewrite the expression after every step, so nothing gets lost. Here is 18 − (2 + 4) × 2 + 3²:

  1. Parentheses. 2 + 4 = 6, so it becomes 18 − 6 × 2 + 3².
  2. Exponents. 3² = 3 × 3 = 9, so 18 − 6 × 2 + 9.
  3. Multiplication and division, left to right. 6 × 2 = 12, so 18 − 12 + 9.
  4. Addition and subtraction, left to right. 18 − 12 = 6, then 6 + 9 = 15.

The answer is 15.

The left-to-right rule matters. In 20 − 12 ÷ 4 + 2, divide first (12 ÷ 4 = 3), then work left to right: 20 − 3 = 17, and 17 + 2 = 19. Underlining the next operation to do before solving it keeps kids from jumping ahead.

What order of operations mistakes do kids make most?

Working straight from left to right

A child solves 8 + 4 × 3 by adding first: 12 × 3 = 36. Multiplication comes before addition, so it's 8 + 12 = 20. Have your child underline the multiplication before starting.

Always multiplying before dividing

Reading PEMDAS literally, a child solves 24 ÷ 4 × 2 as 24 ÷ 8 = 3. Multiplication and division are a pair done left to right, so it's 6 × 2 = 12. Writing PEMDAS as P, E, MD, AS helps.

Always adding before subtracting

A child solves 10 − 3 + 2 as 10 − 5 = 5. Addition and subtraction are also a pair done left to right: 10 − 3 = 7, then 7 + 2 = 9.

How can you practice the order of operations at home in 10 minutes?

Pairs of problems that look almost the same show why the order matters.

  • Minutes 1–3: spot the difference. Solve 5 + 6 × 2 (17) and (5 + 6) × 2 (22). Ask your child why the parentheses changed the answer.
  • Minutes 4–8: five mixed problems. One with parentheses, one with multiplication before addition, one left-to-right division and multiplication (30 ÷ 5 × 3 = 18), one left-to-right subtraction and addition (16 − 4 + 3 = 15), and, for 6th graders, one with an exponent (2 × 3² = 18).
  • Minutes 9–10: make a target. Give your child the numbers 3, 4 and 5 and ask them to make 35 using any operations and parentheses ((3 + 4) × 5), then 23 (3 + 4 × 5).

Repeat over the week with new numbers and new targets.

Which grades practice order of operations?

How can Easy Twin help with the order of operations?

Scan your child's worksheet and Easy Twin makes a twin with the same kinds of questions and new numbers, so practice stays on exactly the expressions the class is learning. Every question comes with two hints and worked steps, and your child can play the twin as a quest or you can print it with an answer key.

Frequently asked questions

What grade learns the order of operations?

Most US schools teach the order of operations in 5th grade with parentheses and whole numbers. In 6th grade kids add exponents and use it with variables, and they keep using it through algebra.

What does PEMDAS stand for?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Multiplication and division are done together from left to right, and so are addition and subtraction.

Is PEMDAS the same as BODMAS or GEMDAS?

Yes, they are the same rule with different names. BODMAS says Brackets and Orders, and GEMDAS says Grouping, but the order of the steps is identical.

Why does the order of operations matter?

It makes sure everyone gets the same answer to the same expression. Without it, 8 + 4 × 3 could be 20 or 36 depending on who solved it.

Topic guide

Math

Easy Twin turns your child's math worksheet into a new "twin" worksheet that practices the same skills with new numbers, names, and wording.

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Try Easy Twin on tonight's worksheet

Download free and get 3 free scans. Scan a page and your kid gets a quest to play with their Stuffy, or print the twin with an answer key.

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