How to Find Absolute Value of Numbers

We have two general cases when it comes to find the absolute value of numbers.

Case 1: |m|

Case 2: |-m|  , m is any real number

In both cases, the answer would be positive of a real number.

Is that not clear? Let us see the above cases with numbers.

Choose any real number, say m = -2.

So, -m = -(-2) = 2

Case 1: |-2| = ??

Case 2: |-(-2)| = |2| = ??

Answer is 2 in both cases.

Keeping straight, just ignore the sign you have in front of numbers. Absolute value of 2 is 2 and absolute value of -2 is 2 as well.

Find the value:

a) | 4 | b) | -4 | c) - | 4 | d) - | -4 |

Solution:

In a) and b), it is enough to find the absolute value of numbers. However, in c) and d), we should find the absolute value and then apply the negative sign.

a) | 4 |

Absolute value of any real number is positive.

So, | 4 | = 4

b) | - 4 |

Same rule is applied here as in (a).

So, | -4 | = 4

c) - | 4 |

As we seen in a), | 4 | = 4

So, - | 4 | = - 4

d) - | -4 |

As we seen in b), | -4 | = 4

So, - | - 4 | = - 4

Evaluate the absolute value:

a) | 5 | + | 6 | = 5 + 6 = 11

b) | 2 | - | -8 | = 2 - (8) = 2 - 8 = -6

c) -| -9 | - | -14 | = -(9) - (14) = -9 - 14 = -23

d) -| -3 | x | -4 | = -(3) x (4) = -3 x 4 = -12

e) | 15 | / | -3 | = (15) / (3) = 15 / 3 = 5

Try Yourself: Absolute Value Worksheets