## How to Do Mixed Integer Computations

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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 \(6\).

**How to Add and Subtract Integers**

To add or subtract two integers, follow these steps:

- In the first case, if two integers have the
**same**sign (either both are positive or both are negative), add up those integers and put the common sign. - In the second case, if two integers have an
**opposite**sign (one is positive and the other one negative), then subtract them and put the sign of the bigger number.

**Example:**

- \(-12 +13 = +1,\)
- \(-12 -13 = -25,\)
- \(12 – 13 = -1\) and so on.

**How to Multiply and Divide Integers**

To Multiply or Divide two integers, follow these steps:

- Firstly, perform general multiplication or division between the two integers and ignore their sign.
- Next, we have to decide the sign. So, if both signs are opposite, then we must always put a negative sign. Also, if both signs of the integers are same, we must use a positive sign.

**Example:**

- \(-12 \times +7 = -84,\)
- \(-12 \div +6 = -2,\)
- \(12 \div 3 = +4\) and so on.

## Free printable Worksheets

### Exercises for Mixed Integer Computations

**1)** \((-4) \ \times \ (-3) \ = \)

**2) **\(36 \ \div \ (-4) \ = \)

**3) **\(-14 \ \div \ 2 \ = \)

**4) **\(36 \ \div \ 6 \ = \)

**5) **\(-24 \ \div \ (-3) \ = \)

**6) **\(2 \ \div \ 2 \ = \)

**7) **\(-56 \ \div \ (-8) \ = \)

**8) **\(24 \ \div \ (-4) \ = \)

**9) **\(8 \ \div \ (-1) \ = \)

**10) **\(4 \ \times \ (-7) \ = \)