# Operations with absolute value: Problem type 1

The absolute value of a number ‘*a*’ is denoted as |*a*|

|*a*| = *a*, if *a* is positive

|*a*| = −*a*, if *a* is negative

|0| = 0

**Absolute value** of a number is the distance of the number on the number line from 0. The absolute value of a number is never negative.

For example, the absolute value of both 5 and −5 is 5. The absolute value of 0 is 0.

Finding absolute value of a number is like removing any negative sign in front of a number, and considering all numbers as positive.

In this lesson, we solve problems involving operations with absolute values.

**Evaluate the following**

|13 − 19| − |11|

### Solution

**Step 1:**

Simplifying

|13 − 19| − |11| = |−6| − 11 = 6 – 11

**Step 2:**

It is a subtraction of integers problem

The signs are different. So, we take the difference of absolute values

|−11| − |6| = 11 – 6 = 5

**Step 3:**

The sign of the numbers with larger absolute value (−11) is −.

We keep this sign with the difference obtained in above step

So, |13 − 19| − |11| = − 5

**Evaluate the following**

|7 − 23| − |−6|

### Solution

**Step 1:**

Simplifying

|7 − 23| − |−6| = |−16| − 6 = 16 – 6

**Step 2:**

It is a subtraction of integers problem

The signs are different. So, we take the difference of absolute values

|16| − |−6| = 16 – 6 = 10

**Step 3:**

The sign of the numbers with larger absolute value (16) is +.

We keep this sign with the difference obtained in above step

So, |7 − 23| − |−6| = + 10