7 − 1 × 0 + 3 ÷ 3: the answer is 8
It is 8. Do the multiplication and division first: 1 × 0 = 0 and 3 ÷ 3 = 1. Then 7 − 0 + 1 = 8. If you got 1, you read strictly left to right, which is the most common mistake with this puzzle.
See it worked out
Order of operations
× and ÷ come before + and −.
= 8
Written out: 7 − 1 × 0 + 3 ÷ 3
Strictly left to right
Every operator treated as equal. This is the common mistake.
= 1
Written out: (((7 − 1) × 0) + 3) ÷ 3
Why left to right goes wrong
Reading left to right you would do 7 − 1 = 6, then 6 × 0 = 0, then 0 + 3 = 3, then 3 ÷ 3 = 1. That treats every operator as equal. In the real order of operations, multiplication and division outrank addition and subtraction, so the product and the quotient get done first, wherever they sit in the line.
A method that works on any of these
Underline every × and ÷ pair, work each one out, and only then go back to the + and −. Here, 1 × 0 and 3 ÷ 3 are underlined. The expression collapses to 7 − 0 + 1, which is easy.
The zero trap
Multiplying by zero gives zero, so 1 × 0 simply disappears from the sum. Some people stumble because they expect the 0 to wipe out the 7 as well. It only affects the product it belongs to.
Answers people give
| Answer | How you get there |
|---|---|
| 8 | Multiplication and division first, then 7 − 0 + 1. |
| 1 | Strictly left to right: ((7 − 1) × 0 + 3) ÷ 3. |
Try your own expression
Type anything, including brackets, fractions and exponents, and get the steps.
Questions
Does anything times zero always equal zero?
Yes. Any number multiplied by zero is zero, so 1 × 0 = 0. It does not change the numbers around it.
Why do so many people get 1?
Because they work from left to right without giving multiplication and division priority. It feels natural, since that is how we read, but it is not how the rules work.