7 + 7 ÷ 7 + 7 × 7 − 7: the answer is 50
It is 50. Work out 7 ÷ 7 = 1 and 7 × 7 = 49 first, and the expression becomes 7 + 1 + 49 − 7 = 50. Reading left to right gives 56, which is the usual wrong answer.
See it worked out
Order of operations
× and ÷ come before + and −.
= 50
Written out: 7 + 7 ÷ 7 + 7 × 7 − 7
Strictly left to right
Every operator treated as equal. This is the common mistake.
= 56
Written out: ((((7 + 7) ÷ 7) + 7) × 7) − 7
The whole trick is the sevens
Every number is 7, so it is easy to lose track of which 7 belongs to which operation. Copy the expression out, underline 7 ÷ 7 and 7 × 7, and replace them with their values. That leaves 7 + 1 + 49 − 7.
Then add and subtract from left to right: 7 + 1 = 8, 8 + 49 = 57, 57 − 7 = 50.
Where 56 comes from
Left to right: 7 + 7 = 14, 14 ÷ 7 = 2, 2 + 7 = 9, 9 × 7 = 63, 63 − 7 = 56. Each step is correct arithmetic, but the order is wrong, because the division and the multiplication were done too late.
Why repeated numbers make it harder
When every number is the same, the structure of the expression is all that is left, and it is hard to see. Puzzles like this are good practice for that reason. The daily puzzle uses the same idea with varied numbers.
Answers people give
| Answer | How you get there |
|---|---|
| 50 | Multiplication and division first, then 7 + 1 + 49 − 7. |
| 56 | Strictly left to right: ((((7 + 7) ÷ 7) + 7) × 7) − 7. |
Try your own expression
Type anything, including brackets, fractions and exponents, and get the steps.
Questions
Is it 50 or 56?
It is 50. The 56 comes from going strictly left to right, which ignores the fact that multiplication and division are done before addition and subtraction.
What changes if there are brackets?
Brackets go first, before everything else. For example, (7 + 7) ÷ 7 + 7 × 7 − 7 works out as 2 + 49 − 7 = 44.