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, ∣−6∣=6 and ∣6∣ 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×+7=−84,
- −12÷+6=−2,
- 12÷3=4 and so on.
Exercises for Mixed Integer Computations
1) (−4) × (−3) =
2) 36 ÷ (−4) =
3) −14 ÷ 2 =
4) 36 ÷ 6 =
5) −24 ÷ (−3) =
6) 2 ÷ 2 =
7) −56 ÷ (−8) =
8) 24 ÷ (−4) =
9) 8 ÷ (−1) =
10) 4 × (−7) =
1) (−4) × (−3) =12
2) 36 ÷ (−4) =−9
3) −14 ÷ 2 =−7
4) 36 ÷ 6 =6
5) −24 ÷ (−3) =8
6) 2 ÷ 2 =1
7) −56 ÷ (−8) =7
8) 24 ÷ (−4) =−6
9) 8 ÷ (−1) =−8
10) 4 × (−7) =−28
Mixed Integer Computations Practice Quiz
