Absolute value and opposite numbers – with practice

Distance from zero

The absolute value of a number is its distance from zero on the number line. Just count how many steps it takes to get from the number to zero. It is written with two vertical bars.

|-5| = 5

From −5 to zero it is 5 steps.

What is

|-12|

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$12$ – from −12 to zero it is 12 steps.

The opposite number sits across from it

If you mirror a number across zero, you get its opposite number. It is just as far from zero, but on the other side. So the sign always switches.

1
Opposite of 3
$3 \rightarrow -3$
2
Opposite of −3
$-3 \rightarrow 3$
3
Opposite of 0
Zero is its own mirror image. Its opposite is $0$ .

Two different questions

The absolute value asks: how far is the number from zero? The opposite asks: what is on the other side?

For $-5$ both answers look the same. For $5$ they differ: $|5| = 5$ , but the opposite of $5$ is $-5$ .

1
First the absolute value inside
$|-4| = 4$
2
Then the minus in front
$-|-4| = -4$

Thinking backwards

Which number has the absolute value $5$ ? Two of them! Both $5$ and $-5$ are 5 steps away from zero.

|x| = 5 \quad\Rightarrow\quad x = 5 \text{ or } x = -5

Two numbers share the same distance from zero.

Which numbers have the absolute value

7

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$7$ and $-7$ .

Try it

In the app you get questions on this topic that reshuffle every time – with checking and a worked solution.

You need this first

The number linesoon

What comes next

Adding integerssoon
Betrag und Betragsgleichungensoon