Informative line

# Addition of Integers (Same Signs)

• A negative number means loss and when we add two losses then the sum represents more loss.
• A positive number means gain and when we add two gains then the sum represents more gain.
• To add two integers having same signs:
• Ignore the signs.
• Find the sum of the given numbers.
• The answer will have the same sign of the numbers.

For example: We want to add two negative numbers, $$-5$$ and $$-15$$.

$$-5+(-15)=-20$$

The answer is $$-20$$.

Note: We can add the integers just like the whole numbers and keep the sign same.

#### Find:​ $$(-75)+(-24)$$

A $$-99$$

B $$99$$

C $$100$$

D $$75+24$$

×

When we add two integers with the same sign, the sign stays same for the sum as well.

Ignore the signs and add directly.

$$\begin{array}\ &7&5\\ +&2&4\\ \hline &9&9\\ \hline \end{array}$$

Thus, $$(-75)+(-24)=-99$$

Hence, option (A) is correct.

### Find:​ $$(-75)+(-24)$$

A

$$-99$$

.

B

$$99$$

C

$$100$$

D

$$75+24$$

Option A is Correct

# Addition of Integers (Different Signs)

• We can add the integers with different signs.

Steps to add integers having different signs:

1. Ignore the signs.
2. Find the difference of the given numbers.
3. The answer will have the sign of the greater number.
• For example: Add $$-9$$ and $$3$$.

$$-9+3=\Box$$

• First, ignore the sign and find the difference of $$9$$ and $$3$$.

$$9-3=6$$

• Now, $$6$$ will have the sign of the greater addend.

$$9$$ is greater than $$3$$.

So, the sum will have the sign same as $$9,$$ i.e. '–'

Thus, $$-9+3=-6$$

• Example:

$$-15+3=-12$$

$$12+(-7)=5$$

$$-5+2=-3$$

#### What is the sum of $$35$$ and $$-25$$ ?

A $$10$$

B $$-10$$

C $$-60$$

D $$60$$

×

To find the sum of $$35$$ and $$-25$$,

first, ignore the signs and find the difference of $$35$$ and $$25$$.

$$35-25=10$$

Now $$10$$ will have the sign of the greater addend.

$$35$$ is greater than $$25$$  with a positive sign.

So, $$10$$ will also have the positive sign.

Thus, $$35+(-25)=10$$

Hence, option (A) is correct.

### What is the sum of $$35$$ and $$-25$$ ?

A

$$10$$

.

B

$$-10$$

C

$$-60$$

D

$$60$$

Option A is Correct

# Subtraction of Integers (Same Signs)

• We can subtract the integers having same signs.
• Follow the given steps to subtract the integers:

Step 1: Look at the integer being subtracted.

Step 2: Take the opposite of that integer (which is being subtracted).

Step 3: Add the opposite to the first integer.

For example: Subtract $$-9$$ from $$-15$$.

$$-15-(-9)=\Box$$

• The integer being subtracted is $$-9$$, i.e. negative.

Opposite of $$-9$$ is $$9$$.

• Now, add $$-15$$ and $$9$$.

Thus, $$-15+9=-6$$

Examples:

1. $$-8-(-4)=-4$$
2. $$7-12=-5$$
3. $$-20-(-10)=-10$$

#### Find:​ $$-28-(-30)$$

A $$-58$$

B $$2$$

C $$-2$$

D $$58$$

×

The integer being subtracted is $$-30$$, i.e. negative.

Opposite of $$-30$$ is $$30$$.

Now, add $$-28$$ and $$30$$.

$$-28+30=2$$

Hence, option (B) is correct.

### Find:​ $$-28-(-30)$$

A

$$-58$$

.

B

$$2$$

C

$$-2$$

D

$$58$$

Option B is Correct

# Subtraction of Integers (Different Signs)

• We can subtract integers with different signs.
• Follow the given steps to subtract the integers:

Step 1: Look at the integer being subtracted.

Step 2: Take the opposite of that integer (which is subtracted).

Step 3: Add the opposite to the first integer.

• For example: Subtract $$2$$ from $$-5$$.

$$-5\,-2=\Box$$

• The integer being subtracted is $$2$$, i.e. positive.
• Opposite of $$2$$ is $$-2$$.

Now, add $$-2$$ to $$-5$$.

$$-5+(-2)=-7$$

• Examples:
1. $$70-(-30)=100$$
2. $$-15\,-45=-60$$
3. $$55-(-25)=80$$

#### Find:​ $$-456-44$$

A $$-500$$

B $$-412$$

C $$412$$

D $$500$$

×

The integer being subtracted is $$44$$, i.e. positive.

Opposite of $$44$$ is $$-44$$.

Now, add $$-44$$ to $$-456$$,

$$-456+(-44)=-500$$

Hence, option (A) is correct.

### Find:​ $$-456-44$$

A

$$-500$$

.

B

$$-412$$

C

$$412$$

D

$$500$$

Option A is Correct