Absolute Value

Q: Can the absolute value of a number be negative?

No. The absolute value of a number is always non-negative. It measures distance from zero on the number line, and distance is always positive or zero. Whether the original number is positive, negative, or zero, the absolute value will be zero or a positive value.

Q: Why does the position of absolute value bars matter in an expression?

The absolute value bars tell you which part of the expression to evaluate before removing any negative sign. Moving the bars changes what you calculate first. For example, |−2 × 6 + 3| gives 9, but |−2 × 6| + 3 gives 15, because the second expression applies the absolute value before adding 3.

Q: Do you add or subtract when you have a negative and a positive?

You subtract. Find the absolute value of each number, then subtract the smaller absolute value from the larger. The answer takes the sign of the number with the larger absolute value. For example, 25 − 130 gives −105 because 130 is larger and negative.

Key concept

Absolute value is the distance from zero on the number line. Because distance is never negative, the answer is always positive or zero. A positive number stays as it is, while a negative number drops its minus sign, so |−3| = 3.

Video Lesson

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$Absolute Value poster$

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Flashcards

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The definition of absolute value, examples include |5| = 5, |0| = 0, and |−3| = 3.

Two examples simplifying absolute values, showing final results of 9 and 15 after applying absolute value rules.

Absolute value calculation when both numbers are negative, e.g., −30 − 120 = −150, by adding absolute values and keeping the negative sign.

Absolute value calculation with different signs by subtracting absolute values and keeping the sign of the larger; e.g., −65 + 15 = −50.

What is Absolute Value?

Absolute value is the distance from zero on the number line.
Absolute value is never negative, even for negative numbers.

Practice Questions

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Q1Easy

Calculate $∣ - 3 \times 7∣ + 5$ .

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Interactive Activity

Explore how to evaluate absolute value expressions step-by-step

1Multiply

2Combine terms

3Apply absolute value

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Students Also Ask

The questions students bump into most on this topic

Can the absolute value of a number be negative?

No. The absolute value of a number is always non-negative. It measures distance from zero on the number line, and distance is always positive or zero. Whether the original number is positive, negative, or zero, the absolute value will be zero or a positive value.

What is the absolute value of a negative number?

The absolute value of a negative number is that same number without its negative sign. You simply remove the minus sign. For example, the absolute value of −9 is 9, and the absolute value of −120 is 120. The result is always a positive number.

What is the absolute value of zero?

The absolute value of zero is zero. Zero sits exactly at the origin on the number line, so its distance from zero is zero. It is the only number whose absolute value equals itself and is neither positive nor negative.

Why does the position of absolute value bars matter in an expression?

The absolute value bars tell you which part of the expression to evaluate before removing any negative sign. Moving the bars changes what you calculate first. For example, |−2 × 6 + 3| gives 9, but |−2 × 6| + 3 gives 15, because the second expression applies the absolute value before adding 3.

What is the rule when adding and subtracting negative numbers?

When both numbers are negative, add their absolute values and keep the negative sign. When the numbers have different signs, subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. These two rules cover every case.

Do you add or subtract when you have a negative and a positive?

You subtract. Find the absolute value of each number, then subtract the smaller absolute value from the larger. The answer takes the sign of the number with the larger absolute value. For example, 25 − 130 gives −105 because 130 is larger and negative.

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