Positive and Negative Numbers

Learn signed numbers and opposites, absolute value.

Lesson 1 of 32 parts Practice Flashcards

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Signed Numbers and Opposites

Objective: Explain signed numbers and opposites, apply the stated method, and check its conditions.

Positive and negative numbers describe opposite directions from zero on a number line. The additive inverse of x is −x, because x+(−x)=0. Comparing signed values depends on their location; a negative value farther left is smaller. A larger negative magnitude represents a smaller signed value.

Formulas

$x+(−x)=0$

Worked examples

Try itWhat is the opposite of −7?Show answer

Step 1: Opposite numbers are equally far from zero on opposite sides. Step 2: Change the sign of the given number. Step 3: The opposite is 7.

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Signed Numbers and Opposites

Objective: Explain signed numbers and opposites, apply the stated method, and check its conditions.

Formulas

$x+(−x)=0$

Worked examples

Try itWhat is the opposite of −7?Show answer

Step 1: Opposite numbers are equally far from zero on opposite sides. Step 2: Change the sign of the given number. Step 3: The opposite is 7.

Absolute Value

Objective: Explain absolute value, apply the stated method, and check its conditions.

The absolute value |x| is the nonnegative distance from x to zero. It equals x for x≥0 and −x for x<0. Absolute value removes direction, not the fact that the original signed number can be negative. Absolute value is always nonnegative.

Formulas

$|x|=x if x≥0; |x|=−x if x<0$

Worked examples

Try itFind |−42|.Show answer

Step 1: Absolute value measures distance from zero. Step 2: Distance is nonnegative. Step 3: |−42|=42.

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