Opposite Integers

The opposite of an integer is the number that adds to it to make zero. For example, 8 and −8 are opposites. Nonzero opposites have different signs and sit the same distance from zero on opposite sides of a number line. Zero is its own opposite.

Quick answer: Opposite integers are two numbers that sit the same distance from 0 on the number line, but on opposite sides. They have the same absolute value and different signs, and they always add up to 0. For example, 7 and -7 are opposites because 7 + (-7) = 0. The opposite of 0 is 0.

How are integers and their opposites related?

Think of zero as a mirror. The opposite of 5 is −5: each is five units from zero, but one is to the right and one is to the left.

−50+5

• Same distance: a number and its opposite have equal absolute values.
• Different signs: this holds for every nonzero integer.
• Sum of zero: adding a number to its opposite always gives 0.

Remember zero: zero has no positive or negative sign and is not on either side of itself. Its opposite is still 0 because 0 + 0 = 0.

Find an opposite in two steps

1. Work out the value of the given number or expression.
2. Change its sign. Leave zero unchanged.

In symbols, the opposite of n is −n, and n + (−n) = 0. The name for this relationship is additive inverse. The symbol −n means “the opposite of n”; it does not always represent a negative value.

Opposite integers: worked examples

Change the sign, then check the sum

Given integer	Its opposite	Check
9	−9	9 + (−9) = 0
−15	15	−15 + 15 = 0
0	0	0 + 0 = 0

What is the opposite of −(−4)?

First simplify the expression: −(−4) = 4. Now find the opposite of 4, which is −4. Check: 4 + (−4) = 0.

Be careful about the instruction. “Simplify −(−4)” has the answer 4. “Find the opposite of −(−4)” asks for one more sign change and has the answer −4.

Opposite versus absolute value

The opposite changes the direction; absolute value measures distance from zero. For 7, the opposite is −7 and the absolute value is 7. For −7, both calculations give 7. They agree for negative integers and zero, but differ for positive integers.

A temperature example

A temperature is −18°F. The opposite temperature is 18°F. Both are 18 degrees from 0°F, in different directions. Moving from −18°F to 18°F is a rise of 36°F, not 18°F.

Try it yourself: find each opposite

Write an answer before opening the explanation. Check each pair by adding.

1. 12
2. −7
3. −25
4. 0
5. −(−4)
6. A temperature of −18°F

Show answers and explanations

1. −12: 12 + (−12) = 0.
2. 7: −7 + 7 = 0.
3. 25: −25 + 25 = 0.
4. 0: zero is its own opposite.
5. −4: first simplify −(−4) to 4, then take its opposite.
6. 18°F: it is equally far from 0°F on the other side.

Explain your choice: Are −6 and 6 opposites? Yes: they have equal distances from zero, opposite signs, and a sum of zero. Are −6 and 5 opposites? No: their distances differ and their sum is −1.

What to study next

If the direction is still confusing, review integers on a number line. Then compare integers and absolute value before moving into signed-number arithmetic.

For a broader study route, use the free Pre-Algebra Online Center to choose lessons, practice, and further study resources.

Open the existing integer operations calculator

Use the calculator to check arithmetic after explaining the opposite yourself. For example, enter a number plus its opposite and check that the result is zero.

Open the solver in full screen →

Watch the existing video lessons

Use these visual explanations as another way to review opposite and negative numbers.

Definition reference: OpenStax, Introduction to Integers. The explanations and examples on this page are original.

Quick examples of opposite integers

To find an opposite, keep the number and switch its sign. Here are the examples students ask about most.

The row with -(-8) trips people up. First simplify: the opposite of -8 is 8, so -(-8) = 8. Then the opposite of that value is -8.

Opposites show up in real life too. A gain of 15 yards and a loss of 15 yards are opposites, and so are 40 feet above sea level and 40 feet below it. In each pair, the two amounts are the same size but point in opposite directions, so together they cancel out to 0.

Frequently Asked Questions

What are opposite integers?

Opposite integers are two numbers the same distance from 0 on the number line but on opposite sides, such as 11 and −11. They have the same absolute value and different signs, and they always add up to 0. Think of 0 as a mirror: each number is the reflection of its opposite.

What is the opposite integer of 0?

The opposite of 0 is 0. Zero is neither positive nor negative, so there is no sign to change, and 0 + 0 = 0 fits the rule that a number plus its opposite equals zero. It is the only integer that is its own opposite.

What is the opposite integer of 12?

The opposite of 12 is −12. Both are 12 units from 0, one to the right and one to the left, and 12 + (−12) = 0. The same rule works in reverse, so the opposite of −12 is 12. To find any opposite, just change the sign.

How do you add opposite integers?

Adding an integer to its opposite always gives 0. For example, 25 + (−25) = 0 and −3 + 3 = 0. On a number line, you move a certain distance one way and then the same distance back, ending at zero. This is why opposites are also called additive inverses.

How do you subtract opposite integers?

Subtracting a number’s opposite is the same as adding the number itself, so the result is double the first number. For example, 6 − (−6) = 6 + 6 = 12, and −6 − 6 = −12. Rewrite subtraction as adding the opposite first, then work out the sum.

Is the opposite of an integer negative?

Only when the integer is positive. The opposite of 9 is −9, but the opposite of −9 is 9, which is positive, and the opposite of 0 is 0. So the symbol −n means the opposite of n and is not always a negative number. Watch for expressions like −(−4), which equals 4.