## How to Solve Integers and Absolute Value Problems

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The term integers represent the meaning **“intact”** or **“whole”**. So, you can generally refer an integer as a whole number, except integers can be negative also!

**What is an Integer?**

An integer is a **whole** number (not any decimal or fraction numbers) which can be zero, positive or negative numbers. Some examples of integers can be \(7 \ , \ 3 \ , \ 0 \ , \ -5 \ , \ -15,\) etc. Moreover, we can represent integers by the denotation \(Z\) which comprises of:**Positive Integers:** As the name suggests, any integer that is **greater** than zero is termed as a **positive** integer.**Negative Integer:** As from the name, any integer that is **less** than zero is termed as a **negative **integer.**Zero:** Zero is neither a positive integer or a negative integer. It is just a whole number.

So, we can write \(Z = \{….,-5 \ , \ -4 \ , \ -3 \ , \ -2 \ , \ -1 \ , \ 0 \ , \ 1 \ , \ 2 \ , \ 3 \ , \ 4 \ , \ 5,……\}\)

Also, we can place all integers on a number line where the negative ones are placed on the **left **of \(“0”\) and the positive ones on the **right**. Moreover, we can perform the 4 basic mathematic properties with integers. They are:

- Addition
- Subtraction
- Multiplication
- Division

We often see that negative integers are always written as \(-5 \ , \ -9\) and so on. But it is **not** generally considered necessary to write positive integers like \(+5 \ , \ +9\) and so on. So, when we write just \(5,\) we mean \(+5\).

Another thing to note is, that an **absolute value **of any integer is always **positive**. So, \(\lvert -6 \rvert=6\) and \(\lvert 6 \rvert\) is also \(6\).

**What is the Absolute Value of an Integer?**

If we plot an integer on the number line, then the absolute value of that integer would be its **distance **from zero. Since distance can’t be negative, therefore the absolute value of any number is **always **a **positive **quantity. Absolute value is sometimes even referred to as magnitude. Absolute of the integer \(x\) is shown as \(\lvert x \rvert\).

For example, absolute value of \(-4\) is \(\lvert -4 \rvert= 4\). This is pretty obvious as when we plot the integer \(4\) on the number line, we can clearly see that the distance from zero is \(“4”\).

### Exercises for Integers and Absolute Value

**1)** \(-14 \ + \ |-8| \ = \)

**2) **\(-7 \ + \ |0| \ = \)

**3) **\(0 \ + \ |9| \ = \)

**4) **\(15 \ + \ |7| \ = \)

**5) **\(|-15| \ = \)

**6) **\(|0| \ = \)

**7) **\(|7| \ = \)

**8) **\(|-11| \ + \ |4| \ = \)

**9) **\(|-18| \ + \ |-4| \ = \)

**10) **\(|4| \ + \ |-6| \ = \)