If you"re teaching math to students that are ready to learn about absolute value, typically roughly Grade 6, here"s review of the topic, in addition to two lessons to introduce and also develop the ide with your students.

You are watching: The distance a number is from zero

## What does Absolute worth Mean?

Absolute value defines the distance native zero the a number is on the number line, without considering direction. The absolute value of a number is never ever negative. Take a watch at part examples.

The absolute worth of 5 is 5. The distance from 5 to 0 is 5 units.

The absolute value of –5 is 5. The distance from –5 to 0 is 5 units.

The absolute worth of 2 + (–7) is 5. When representing the sum on a number line, the resulting suggest is 5 devices from zero.

The absolute worth of 0 is 0. (This is why we don"t say that the absolute worth of a number is positive. Zero is neither an unfavorable nor positive.)

## Absolute value Examples and also Equations

The many common method to represent the absolute worth of a number or expression is come surround it v the absolute worth symbol: 2 vertical right lines.

|6| = 6 means “the absolute worth of 6 is 6.”|–6| = 6 means “the absolute value of –6 is 6.|–2 – x| means “the absolute value of the expression –2 minus x.–|x| means “the an adverse of the absolute value of x.

The number heat is not simply a means to display distance from zero; it"s additionally a useful method to graph equalities and inequalities the contain expressions v absolute value.

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Consider the equation |x| = 2. To display x top top the number line, you require to present every number whose absolute value is 2. Over there are exactly two places where the happens: in ~ 2 and also at –2:

Now consider |x| > 2. To show x ~ above the number line, you require to present every number who absolute worth is higher than 2. As soon as you graph this on a number line, use open up dots at –2 and 2 to suggest that those numbers are not part of the graph:

In general, you get two to adjust of values for any type of inequality |x| > k or |x| ≥ k, whereby k is any number.

Now take into consideration |x| ≤ 2. Friend are looking for numbers whose absolute values are less than or same to 2. This is true for any kind of number in between 0 and 2, consisting of both 0 and also 2. That is additionally true for all of the opposite numbers in between –2 and also 0. When you graph this top top a number line, the closeup of the door dots in ~ –2 and also 2 suggest that those numbers space included. This is because of the inequality utilizing ≤ (less 보다 or same to) instead of

Math activities and Lessons grades 6-8