How to Change a Negative to Positive in Math

Changing a negative to a positive in math usually means finding its opposite, also called its additive inverse, or finding its absolute value. For example, both operations turn −8 into 8. They are related but not interchangeable in every expression: multiplying by −1 changes the sign of a number, while absolute value describes its nonnegative distance from zero.

Before you begin, identify the number or expression you need to change and check whether the instruction says to find its opposite, multiply by −1, or evaluate its absolute value. The wording matters, especially when the negative sign is part of a larger expression.

What You’ll Need

The number or expression you want to change
A pencil and paper, or a calculator for more complicated arithmetic
Basic familiarity with negative signs and parentheses

Step-by-Step

Identify the negative value. Locate the minus sign and determine exactly what it applies to. In −6, the negative sign applies to 6. In −(2 + 4), it applies to the entire quantity inside the parentheses. This distinction prevents changing only part of an expression.
Choose the operation the problem asks for. If it asks for the opposite or additive inverse, multiply the value by −1. If it asks for absolute value, find the value’s distance from zero and write that distance as a nonnegative number. For a single negative number, both methods produce the same positive result.
For a single number, remove its negative sign. The opposite of −6 is 6, because (−6) × (−1) = 6. The absolute value is also written |−6| = 6. Do not change the number’s magnitude; only its sign changes.
Keep parentheses around a full expression. To change the sign of −(2 + 4), multiply the entire quantity by −1: (−1) × [−(2 + 4)] = 2 + 4 = 6. More generally, multiplying a sum by −1 changes every term’s sign: −(a + b) = −a − b. Multiplying a difference by −1 gives −(a − b) = −a + b.
Simplify carefully. Apply the multiplication or absolute-value rule first, then perform any remaining arithmetic. For example, |−3 + 1| means evaluate inside the bars first: −3 + 1 = −2, then take the absolute value, giving 2. It does not mean make each term positive before adding.
Check the result. If you found an opposite, add the original number and your result; the sum should be zero. For example, −6 + 6 = 0. If you found an absolute value, check that the answer is zero or positive and equals the original number’s distance from zero.

Common Mistakes

Changing only one term: A minus sign outside parentheses applies to the whole expression. For example, −(x + 3) simplifies to −x − 3, not −x + 3.
Confusing a negative sign with subtraction: In 7 − 4, the minus sign tells you to subtract 4 from 7. It does not mean the number 4 is negative. In 7 + (−4), the value being added is negative.
Assuming every minus sign disappears: A negative multiplied by a negative becomes positive, but a negative multiplied by a positive remains negative. For instance, (−2) × 3 = −6, while (−2) × (−3) = 6.
Taking absolute values too early: Absolute-value bars enclose a complete quantity. In |−3 + 1|, simplify inside the bars before taking the distance from zero.
Thinking the opposite and absolute value are identical ideas: They match for a negative number’s result, but they answer different questions. The opposite reverses a number’s direction; absolute value gives its nonnegative distance from zero.

Tips

Use a number line: Zero is the center. The opposite lies the same distance from zero on the other side. Thus, the opposite of −5 is 5.
Remember zero: Zero is neither positive nor negative. Its opposite and absolute value are both zero, so changing its sign does not produce a positive number.
Use parentheses to show scope: Write −1 × (−4 + 2) when you mean to change the sign of the entire result. Clear grouping makes the intended operation easier to follow.
For decimals and fractions, keep the magnitude: The opposite of −2.5 is 2.5, and the opposite of −3/4 is 3/4. Only the sign changes.
Use a calculator as a check: Enter the expression with parentheses when needed. A calculator can confirm arithmetic, but you still need to know which operation the question requests.

Troubleshooting

If your answer stays negative, check whether you multiplied by a positive number instead of −1, or whether the minus sign applies to a larger grouped expression. If your result has the wrong magnitude, revisit the arithmetic without changing the digits or terms unnecessarily.

If you get different answers from the opposite and absolute-value methods, review the original expression and its parentheses. For example, the opposite of (−2 + 5) is −3, because the expression equals 3; its absolute value is 3. They are not always equal when the entire expression is positive. If the problem’s wording is unclear, write both interpretations and check which one fits the surrounding lesson or instructions.

If an answer is zero, confirm whether the original value was zero or whether positive and negative terms canceled out. Absolute value cannot be negative; if your absolute-value answer is negative, you have likely omitted the bars or applied the operation incorrectly.

Frequently Asked Questions

How do you change a negative number to a positive?

For a single negative number, multiply it by −1 or take its absolute value. For example, (−1) × (−9) = 9 and |−9| = 9.

Is taking the absolute value the same as changing the sign?

Not always. Absolute value gives a nonnegative distance from zero, while changing the sign means finding the opposite. For a negative number, both give the same positive result; for a positive number, its opposite is negative but its absolute value stays positive.

What happens when you change the sign of zero?

Zero remains zero. It has no positive or negative direction, and both its opposite and absolute value equal zero.

How do you change the sign of a number in parentheses?

Multiply the entire parenthetical expression by −1. When distributing that factor, change the sign of every term inside the parentheses.

Can an absolute value be negative?

No. Absolute value represents distance from zero, so it is always zero or positive.

Further reading: none, this is general know-how. Details can change, so check the official page for anything that matters to you. Spotted a mistake? Tell us. How we write an answer.