Integer rules
In math, a set of whole numbers and their opposite signs is termed as integer. That is, {…-2, -1, 0, 1, 2, 3 …} is a set, called integer. Here 0, 1, 2 … are whole numbers and -1, -2, -3, … are opposites of whole numbers. The integers with positive sign are termed as positive integers (1, 2, 3...). The integers with negative sign are termed as negative integers (-1, -2, -3…). Integer rules are the procedures to be followed for doing problems in integers. For doing arithmetic operations on integers, integer rules are very useful. Based on the sign of integers the rules differ. The integer rules are applicable for arithmetic operations such as addition, subtraction, multiplication and division. This article helps to give the detail explanation to math integer rules with example problems.
Rules of integers
Math addition rule:
Math subtraction rule:
Negative (+) - Positive (+) = Negative (-) + Negative (-) = Negative (-)
Math multiplication rule:
Math division rule:
The above rules for integers in math help to simplify the algebraic problems.
Integers rules - Examples
Example: 1
Add: 6 + (-9)
Solution:
Given: 6 + (-9)
When we are adding 6 and -9, we have to subtract 6 and 9 and then write the answer with the sign of 9. The integer 9 is greatest. Subtraction of 6 and 9 is 3. We need to write the answer 3 with negative sign as -3.
6 + (-9) = -3
I have recently faced lot of problem while learning Integer Word Problems, But thank to online resources of math which helped me to learn myself easily on net.
Example: 2
Subtract: -6 - (-9)
Solution:
Given: -6 - (-9)
When we are subtracting -6 and -9, we need to change the second element -9 into positive 9 and then add it to the first element -6.
-6 - (-9) = -6 + 9
Now, we have two different sign integers. So, we have to subtract 6 from 9 and the insert the sign of 9 to the answer.
-6 + 9 = + 3
Example: 3
Multiply: -9 x 6
Solution:
Given: -9 x 6
When we are multiplying -9 and 6, we get the multiplication answer 54 with negative sign (-54).
-9 x 6 = -54
Example: 4
Divide: -10 ÷ 2
Solution:
Given: -10 ÷ 2
When we are dividing -10 by 2, we get the answer with negative sign.
`(-10)/2 ` = -5
Rules of integers
Math addition rule:
- The addition of two positive integers results another positive integer.
- Positive (+) + Positive (+) = Positive (+)
- The addition of two negative integers results another negative integer.
- Negative (-) + Negative (-) = Negative (-)
- The addition of two different sign integers results the subtraction value with the sign of greatest integer.
- Positive (+) + Negative (-) = Subtract (With sign of greatest integer)
- Negative (+) + Positive (-) = Subtract (With sign of greatest integer)
Math subtraction rule:
- The subtraction of two positive integers results another positive integer.
- Positive (+) - Positive (+) = Positive (+)
- The subtraction of two negative integers becomes the addition of negative with positive integer. So, subtract the integers and write the result with the sign of greatest integer.
- Negative (-) - Negative (-) = Negative (-) + Positive (+) = Subtract (With sign of greatest integer)
- The subtraction of positive and a negative integer becomes addition of two positive integers. So, just add the two positive integers.
- Positive (+) - Negative (-) = Positive (+) + Positive (+) = Positive (+)
- The subtraction of negative and positive integer becomes addition rule of two negative integers. So, just add the two negative integers.
Negative (+) - Positive (+) = Negative (-) + Negative (-) = Negative (-)
Math multiplication rule:
- The multiplication of two positive integers results positive integer.
- Positive (+) x Positive (+) = Positive (+)
- The multiplication of two negative integers results positive integer.
- Negative (+) x Negative (+) = Positive (+)
- The multiplication of two different sign integers results negative integer.
- Positive (+) x Negative (-) = Negative (-)
- Negative (+) x Positive (-) = Negative (-)
Math division rule:
- The division of two positive integers results positive integer.
- Positive (+) ÷ Positive (+) = Positive (+)
- The division of two negative integers results positive integer.
- Negative (+) ÷ Negative (+) = Positive (+)
- The division of two different sign integers results negative integer.
- Positive (+) ÷ Negative (-) = Negative (-)
- Negative (+) ÷ Positive (-) = Negative (-)
The above rules for integers in math help to simplify the algebraic problems.
Integers rules - Examples
Example: 1
Add: 6 + (-9)
Solution:
Given: 6 + (-9)
When we are adding 6 and -9, we have to subtract 6 and 9 and then write the answer with the sign of 9. The integer 9 is greatest. Subtraction of 6 and 9 is 3. We need to write the answer 3 with negative sign as -3.
6 + (-9) = -3
I have recently faced lot of problem while learning Integer Word Problems, But thank to online resources of math which helped me to learn myself easily on net.
Example: 2
Subtract: -6 - (-9)
Solution:
Given: -6 - (-9)
When we are subtracting -6 and -9, we need to change the second element -9 into positive 9 and then add it to the first element -6.
-6 - (-9) = -6 + 9
Now, we have two different sign integers. So, we have to subtract 6 from 9 and the insert the sign of 9 to the answer.
-6 + 9 = + 3
Example: 3
Multiply: -9 x 6
Solution:
Given: -9 x 6
When we are multiplying -9 and 6, we get the multiplication answer 54 with negative sign (-54).
-9 x 6 = -54
Example: 4
Divide: -10 ÷ 2
Solution:
Given: -10 ÷ 2
When we are dividing -10 by 2, we get the answer with negative sign.
`(-10)/2 ` = -5