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.
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) \(4 \ \times \ (-7) \ = \)
1) \((-4) \ \times \ (-3) \ = \color{red}{12} \)
2) \(36 \ \div \ (-4) \ = \color{red}{-9} \)
3) \(-14 \ \div \ 2 \ = \color{red}{-7} \)
4) \(36 \ \div \ 6 \ = \color{red}{6} \)
5) \(-24 \ \div \ (-3) \ = \color{red}{8} \)
6) \(2 \ \div \ 2 \ = \color{red}{1} \)
7) \(-56 \ \div \ (-8) \ = \color{red}{7} \)
8) \(24 \ \div \ (-4) \ = \color{red}{-6} \)
9) \(8 \ \div \ (-1) \ = \color{red}{-8} \)
10) \(4 \ \times \ (-7) \ = \color{red}{-28} \)
Mixed Integer Computations Practice Quiz
