- 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

A \(14+(-13)\)

B \(-12+10\)

C \(-10+12\)

D \(7+(-5)\)

- 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

A \(-6-(-7)\)

B \(6-7\)

C \(-7-(-6)\)

D \(-6-7\)

- 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

A \(-3×4\)

B \(-3×(-4)\)

C \(3×4\)

D \(5×20\)

- 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

A \(12\div(-4)\)

B \(-15\div5\)

C \(-12\div(-4)\)

D \(-12\div4\)