- The sign rule for addition of integers states:
- When we add two integers of the same sign, the sum will have the same sign of the integers.
Positive + Positive = Positive
Negative +Negative = Negative
- But when we add two integers with different signs, we need to find out which integer has a bigger absolute value.
- Suppose, we have a positive and a negative integer then,
- If the positive integer has a bigger absolute value, the sum will be a positive integer.
Example : \(-3+5=?\)
\(|-3|=3,\;|5|=5\)
Here, \(|5|\) has a bigger absolute value than \(|-3|\).
Since \(5\) has a positive sign, so the sum will also have a positive sign.
\(-3+5=\) a positive integer
- If the negative integer has a bigger absolute value, the sum will be a negative integer.
Example : \(7+(-9)=?\)
\(|7|=7\) and \(|-9|=9\)
Here, \(|-9|\) has a bigger absolute value than \(|7|\).
Since \(-9\) has a negative sign, so the sum will also have a negative sign.
\(7+(-9)=\) a negative integer
- The sign rule for subtraction of integers states:
- When we subtract two integers, then consider the following cases:
1. Positive – Positive
- If the first integer is greater than the second, we get a positive integer as the answer.
\(4-2=\) Positive integer
- If the second integer is greater than the first, we get a negative integer as the answer.
\(2-4=\) Negative integer
2. Negative – Positive
- If the first integer is negative and the second integer is positive then we get a negative integer as the answer.
\(-4-2=\) Negative integer
3. Positive – Negative
- If the first integer is positive and the second integer is negative, we get a positive integer as the answer.
\(4-(-2)=\) Positive integer
4. Negative – Negative
- If the absolute value of the first integer is greater than the absolute value of the second integer, we get a negative integer as the answer.
\(-4-(-2)=\) Negative integer
- If the absolute value of the second integer is greater than the absolute value of the first integer, we get a positive integer as the answer.
\(-2-(-4)=\) Positive integer
- The sign rule for multiplication of integers states:
- When we multiply two integers of the same sign, we get a positive integer as the answer.
Positive × Positive = Positive
Negative × Negative = Positive
- But when we multiply two integers with different signs, we get a negative integer as the answer.
Positive × Negative = Negative
Negative × Positive = Negative
- The sign rule for division of integers states:
- When dividend and divisor are of the same sign, we get a positive integer as the answer.
Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
- But when dividend and divisor are of different signs, we get a negative integer as the answer.
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative