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Unit 13: Order of Operations

Why the same expression needs one agreed-upon order, or two people get two different right-looking answers.

4 topics · 17 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Why Order of Operations Rules Even Exist

  1. How it worksWalk me through solving 3 + 4 x 2 left to right and getting 14, one step at a time.
  2. How it worksWalk me through solving 3 + 4 x 2 by multiplying first and getting 11, one step at a time.
  3. Worked exampleFind the answer to 5 + 6 x 3 using the correct order of operations.
  4. Common mistakeWhy isn't the answer to 8 + 2 x 5 the same as solving strictly left to right?
  5. Going furtherWhat happens to the answer of 10 - 2 x 3 if you ignore the order of operations rule?
Your turn1 of 2
Nina saves 14 dollars, then earns 6 dollars an hour for 8 hours doing chores. Using the correct order of operations, how much does she have in total?

Parentheses First

  1. How it worksWalk me through solving (2 + 3) x 4 by doing the parentheses first.
  2. Common mistakeWhy doesn't 6 x (1 + 2) equal 6 x 1 plus 2?
  3. Worked exampleFind the value of (7 - 2) x 5 by solving the parentheses first.
  4. Going furtherWhat changes about 4 x (3 + 6) if you move the parentheses to (4 x 3) + 6?
Your turn1 of 2
A theater has 15 rows of seats, but 3 rows are roped off for cleaning. The rest are reset to hold 9 seats each. Solving the parentheses first, how many seats are usable?

Multiplication and Division Before Addition and Subtraction

  1. How it worksWalk me through solving 4 + 6 divided by 2 by dividing before you add.
  2. Common mistakeWhy isn't 12 - 2 x 3 solved by subtracting 2 from 12 first?
  3. Going furtherWhat happens to 18 divided by 3 x 2 if you multiply before you divide instead of going left to right?
Your turn1 of 2
Ben already has 14 stickers, and a teacher splits 40 more evenly among 9 kids, including him. Dividing before adding, how many stickers does Ben have now?

Working Through Multi-Step Expressions

  1. How it worksWalk me through solving 2 x (3 + 4) - 5 one step at a time in the correct order.
  2. Worked exampleShow me how to evaluate 6 + 2 x (5 - 3) so every step follows the rules.
  3. Worked exampleWalk me through solving 9 + (12 - 4) x 3, step by step in the right order.
  4. Common mistakeWhy isn't 2 x (3 + 4) - 5 solved by working strictly left to right through every symbol?
  5. Going furtherWhat happens to 3 x (4 + 2) - 5 if you move the parentheses to 3 x 4 + (2 - 5)?
Your turn1 of 2
A theater already has 11 seats filled. Then 6 buses arrive, each bringing 19 minus 2 passengers who take a seat. How many seats are filled in total?