Adding integers calculator
-7 + 12 - (-5) + (-3) = 7 in the adding integers calculator, with the sign rule for each step: 5, then 10, then 7.
Answer
- Your expression
- -7 + 12 - (-5) + (-3)
- Step 1: add -7 + 12 = 5. Addition and subtraction are one level, done left to right. Different signs: subtract the smaller size from the larger, 12 - 7 = 5, and keep the sign of 12: 5.
- 5 - (-5) + (-3)
- Step 2: subtract 5 - (-5) = 10. Addition and subtraction are one level, done left to right. Subtracting is adding the opposite: 5 - (-5) = 5 + 5. Same signs: add the sizes, 5 + 5 = 10, and keep the sign: 10.
- 10 + (-3)
- Step 3: add 10 + (-3) = 7. Addition and subtraction are one level, done left to right. Different signs: subtract the smaller size from the larger, 10 - 3 = 7, and keep the sign of 10: 7.
- 7
- Answer 3 operations, in order.
- 7
- PEMDAS read letter by letter What you get by doing every multiplication before any division, and every addition before any subtraction. It is the commonest misreading of the mnemonic: M and D are one level, as are A and S, and each pair is worked left to right.
- 13
| Level | Covers | In this expression |
|---|---|---|
| 1. Brackets | ( ), [ ], { }, innermost first | 2 pairs |
| 2. Exponents | ^, right to left | 0 |
| 3. Multiply and divide | ×, ÷ and implicit, left to right | 0 |
| 4. Add and subtract | +, -, left to right | 3 |
- Order: brackets (innermost first), exponents (right to left), multiplication and division (left to right), addition and subtraction (left to right). PEMDAS, BODMAS and BIDMAS all name this same order.
How the Order of Operations Calculator works
Adding integers comes down to two rules and one rewrite.
Same signs: add the sizes and keep the sign. 8 + 5 = 13, and -8 + (-5) = -13. Two debts of $8 and $5 make a debt of $13.
Different signs: subtract the smaller size from the larger and keep the sign of the larger. For -7 + 12 the sizes are 7 and 12, 12 - 7 = 5, and 12 is the larger, so the answer is 5. For -15 + 9, 15 - 9 = 6 and -15 is the larger in size, so the answer is -6. A number and its opposite cancel: -6 + 6 = 0.
Subtracting is adding the opposite. a - b = a + (-b), so every subtraction becomes an addition and one of the two rules finishes it. 3 - 8 = 3 + (-8) = -5, and 5 - (-5) = 5 + 5 = 10, which is why two minus signs in a row make a plus.
Worked example: -7 + 12 - (-5) + (-3), left to right.
1. -7 + 12: different signs, 12 - 7 = 5, keep the sign of 12: 5. 2. 5 - (-5) = 5 + 5: same signs, 10. 3. 10 + (-3): different signs, 10 - 3 = 7, keep the sign of 10: 7.
On a number line, adding a positive number moves right and adding a negative moves left. Start at -7 and move 12 right to 5; subtracting -5 becomes moving 5 right, to 10; adding -3 moves 3 left, to 7.
Once every subtraction is rewritten as adding the opposite, the terms can be added in any order. Add the positives, 12 + 5 = 17, then the negatives, -7 + (-3) = -10, and combine them: 17 + (-10) = 7.
Order of Operations Calculator FAQ
What is a negative plus a negative?
A negative. Add the sizes and keep the minus sign: -4 + (-6) = -10.
Why does subtracting a negative make a positive?
Because subtracting a number is adding its opposite, and the opposite of -4 is 4. So -6 - (-4) = -6 + 4 = -2. Taking away a debt of $4 leaves you $4 better off.
Does the order matter when adding integers?
Not for addition: -7 + 12 and 12 + (-7) are both 5. Subtraction is different, since 3 - 8 = -5 but 8 - 3 = 5. Rewriting each subtraction as adding the opposite turns the whole expression into addition, which can then be done in any order.