The Order of Operations: Why 2 + 3 x 4 Isn't 20
Try this: 2 + 3 x 4. One friend says the answer is 20. Another says it's 14. They both used the same numbers — so how can they get different answers? Here's the trick: the friend who got 20 added first (2 + 3 = 5, then 5 x 4 = 20). The friend who got 14 multiplied first (3 x 4 = 12, then 2 + 12 = 14). Only ONE of them is right, because math has a rulebook that tells everyone the SAME order to work in. That rulebook is called the order of operations, and 14 is the correct answer.
What You'll Learn
- Why math needs one agreed-upon order (so everyone gets the same answer) - The order: parentheses, then multiply and divide, then add and subtract - How to solve a problem step by step without skipping ahead - How parentheses can change the answer on purpose
Why We Need a Rule
Imagine a recipe that says 'add eggs and flour and bake.' If you bake FIRST and add eggs after, you get a mess! The order matters. Math is the same. If everyone solved 2 + 3 x 4 in their own order, bridges would fall down and money would be counted wrong. So mathematicians long ago agreed on one order that everybody in the world follows. Now a student in Ohio and a student in Japan both get 14.
The Order: Multiply Before You Add
Here is the rule for the math you do now: 1. Do anything inside PARENTHESES ( ) first. 2. Then do all MULTIPLYING and DIVIDING, going left to right. 3. Then do all ADDING and SUBTRACTING, going left to right. So for 2 + 3 x 4: there are no parentheses, so we multiply first. 3 x 4 = 12. Then we add: 2 + 12 = 14. Done! The multiplying always jumps ahead of the adding.
Parentheses Change the Game
What if you WANT to add first? You use parentheses to say 'do this part first.' (2 + 3) x 4 tells you to add inside the parentheses first: 2 + 3 = 5. Then multiply: 5 x 4 = 20. So (2 + 3) x 4 = 20, but 2 + 3 x 4 = 14. Same numbers, different answers, all because of those little curved marks. Parentheses are like a spotlight saying 'me first!'
Remember the order with this sentence: 'Please Excuse My Dear Aunt Sally.' Parentheses, Exponents, Multiply/Divide, Add/Subtract. In 3rd-5th grade you mostly use Parentheses, Multiply/Divide, and Add/Subtract — you'll meet exponents later!
Match each problem to its correct answer. Watch the parentheses!
Terms
Definitions
Drag terms onto their definitions, or click a term then click a definition to match.
Solve: 5 + 6 x 2. What is the correct answer?
Why does the whole world agree on one order of operations?
Parentheses power challenge
Grab a partner. Write down these four numbers in this order: 4, 2, 3, 5, with a + between the first two and a x between the rest, like this: 4 + 2 x 3. Step 1: Solve it with NO parentheses using the order of operations. Step 2: Now try putting parentheses in DIFFERENT places — like (4 + 2) x 3 or 4 + (2 x 3) — and solve each one. Step 3: Write down how many DIFFERENT answers you can make just by moving the parentheses. Step 4: Show a family member your favorite one and explain why the answer changed.
Flashcards — click each card to reveal the answer
Want to keep learning?
Sign up for free to access the full curriculum — all subjects, all ages.
Start Learning Free