Compute 7 + 3 × 5.
3 × 5 = 15
Multiplication beats addition: I compute it first, even though it sits on the right.
7 + 15 = 22
Only an addition is left: I finish the calculation.
Result: 7 + 3 × 5 = 22
Back to the path
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Order of operations and brackets
Level 3 · Ages 11–13
Quick recall· Let's wake up what you already know before we start.
Recall: what is 6 × 7?
The whole lesson
Read it again any time, including while you work through the exercises.
What is 7 + 3 × 5? If you compute from left to right, you get 10 × 5 = 50. Your neighbour gets 7 + 15 = 22. Two different answers for the same calculation, impossible! So mathematicians agreed on one rule of the game for everyone.
The rule: multiplications and divisions are done BEFORE additions and subtractions. In 7 + 3 × 5, the multiplication goes first: 3 × 5 = 15, then 7 + 15 = 22. The right answer is 22, and a scientific calculator will tell you the same.
What if you really want to start with the addition? Use brackets: (7 + 3) × 5 = 10 × 5 = 50. Brackets beat everything: whatever sits inside brackets is always computed first.
One last subtlety: when only operations of the same priority remain, like 18 - 6 + 2 or 36 ÷ 6 × 2, you simply compute from left to right. So 18 - 6 + 2 = 12 + 2 = 14, not 18 - 8 = 10.
Let us recap the order: brackets first, then multiplications and divisions, finally additions and subtractions, reading from left to right. With that, all your calculations will speak the same language as the rest of the world!
The worked example, step by step
Compute (8 + 4) × 3 - 10 ÷ 2.
8 + 4 = 12
Brackets first: they beat every other operation.
12 × 3 = 36 et 10 ÷ 2 = 5
Then the multiplications and divisions, each on its own side.
36 - 5 = 31
Finally the subtraction, which comes last.
Result: (8 + 4) × 3 - 10 ÷ 2 = 31