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Addition And Subtraction Of Integers

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.

Illustration Questions

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.

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

Keep the negative sign in the sum.

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:

\(-15+3=-12\)

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

\(-5+2=-3\)

Illustration Questions

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. \(-20-(-10)=-10\)

Illustration Questions

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. \(55-(-25)=80\)

Illustration Questions

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

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