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Integers On Number Line

Addition of Integers (Same Signs)

  • Addition of integers can be easily understood with the help of a number line.
  • When we add two positive integers, we are adding two gains, so we have more gain.
  • Move in forward direction if both the addends are positive integers.
  • \((+)+(+)\longrightarrow\)

For example: Add \(2\) and \(7\) on the number line.

\(2+7=\Box\)

First, draw a number line from \(0\) to \(10\).

Start from zero and move \(2\) points forward to show the number \(2\).

Now, start from \(2\) and move \(7\) points forward to add \(7\) to \(2\).

We reach the number \(9\).

Thus, \(2+7=9\)

  • We can also add negative integers with the help of a number line.
  • When we add two negative integers, we add two losses, so we have more loss.
  • Move in backward direction if both the addends are negative integers.
  • \(\longleftarrow\,(-)+(-)\)

For example: Add \(-2\) and \(-7\) on the number line.

\(-2+(-7)=\Box\)

First, draw a number line from \(-10\) to \(0.\)

Start from zero and move \(2\) points backward to show the number  \(-2\).

Now, start from \(-2\) and move \(7\) points backward to add \(-7\) to \(-2\).

We reach at number \(-9\).

Thus, \(-2+(-7)=-9\)

We reach the number \(-9\).

Thus, \(-2+(-7)=-9\)

Illustration Questions

Which one of the following equations is represented on the given number line?

A \(6+6=12\)

B \(0+(-12)=-12\)

C \(-6+6=0\)

D \(-6+(-6)=-12\)

×

On the given number line, two negative integers are being added.

To find the equation represented on the given number line, we will count the number of units in each move.

First move starts from zero and ends at \(-6\) (in backward direction).

This means that our first addend is \(-6\).

image

Second move starts from \(-6\) and ends at \(-12\).

This means that our second addend is also \(-6\).

image

The sum of \(-6\) and \(-6\) is \(-12\).

 \(-6+(-6)=-12\)

Hence, option (D) is correct.

Which one of the following equations is represented on the given number line?

image
A

\(6+6=12\)

.

B

\(0+(-12)=-12\)

C

\(-6+6=0\)

D

\(-6+(-6)=-12\)

Option D is Correct

Addition of Integers (Different Signs)

  • Adding negative and positive integers means adding losses and gains.
  • We can also add negative and positive integers on the number line.
  • Move in forward direction on a number line, for positive integers.
  • \(+\longrightarrow\)
  • Move in backward direction on a number line, for negative integers.
  • \(\longleftarrow\;–\)

For example: Add \(-4\) and \(6\) on a number line.

\(-4+6=\Box\)

To add \(-4\) and \(6\), first draw a number line from \(-4\) to \(6.\)

Start from \(0\) and move \(4\) points backward to represent \(-4\) (negative integer).

Now, start from \(-4\) and move \(6\) points forward to add \(6\) (positive integer) to \(-4\).

We reach at number \(2.\)

Thus, \(-4+6=2\)

Illustration Questions

Which one of the following equations is represented on the given number line?

A \(-4+4=0\)

B \(8+(-4)=4\)

C \(4+(-8)=-4\)

D \(-4+8=4\)

×

On the given number line, positive and negative numbers are being added.

To find the equation represented on the given number line, we will count the number of units in each move.

First move starts from zero and ends at \(4.\)

So, our first addend is \(4.\)

image

Second move starts from \(4\) and ends at \(-4\).

This means that our second addend is \(-8\).

image

The sum of \(4\) and \(-8\) is \(-4\).

or  \(4+(-8)=-4\)

Hence, option (C) is correct.

Which one of the following equations is represented on the given number line?

image
A

\(-4+4=0\)

.

B

\(8+(-4)=4\)

C

\(4+(-8)=-4\)

D

\(-4+8=4\)

Option C is Correct

Subtraction of Integers on the Number Line (Same Signs)

  • Subtraction of integers can easily be done on a number line.
  • We can subtract a negative number from another negative number with the help of a number line.
  • To show positive integers, move in forward direction.
  • \(+\longrightarrow\)
  • To show negative integers, move in backward direction.
  • \(\longleftarrow\,-\)
  • To subtract positive integers, we move in backward direction.
  • \(\longleftarrow\,(+)-(+)\)
  • To subtract negative integers, we move in forward direction.

\((-)-(-)\longrightarrow\)

  • For example: Subtract \(-7\) from \(-10\) on the number line.

\(-10-(-7)=\Box\)

First, draw a number line from \(-10\) to \(0.\)

Start from zero and move \(10\) points backward to show \(-10\).

Now, start from \(-10\) and move \(7\) points forward to subtract \(-7\) from \(-10.\)

We reach at number \(-3\).

Thus, \(-10-(-7)=-3\)

We reach the number \(-3\).

Thus, \(-10-(-7)=-3\)

Illustration Questions

Which one of the following equations is represented on the given number line?

A \(-6-(-4)=-2\)

B \(2-(-4)=6\)

C \(-4-6=-10\)

D \(-4-(-6)=2\)

×

On the given number line, either a negative number is being subtracted from another negative number, or a positive number is added to a negative number.

 To find the equation represented on the given number line, we will count the number of units in each move.

First move starts from zero and ends at \(-4\).

So, our first number is \(-4\).

image

Second move starts from \(-4\) and ends at \(2.\)

This means that our second number is \(6.\)

image

Either \(6\) is added to \(-4\) 

or \(-6\) is subtracted from \(-4\).

Thus, \(-4+6=2\) 

or  \(-4-(-6)=2\)

Hence, option (D) is correct.

Which one of the following equations is represented on the given number line?

image
A

\(-6-(-4)=-2\)

.

B

\(2-(-4)=6\)

C

\(-4-6=-10\)

D

\(-4-(-6)=2\)

Option D is Correct

Subtraction of Integers on the Number line (Different Signs)

  • We can subtract positive and negative integers with the help of a number line.
  • To show positive integers, move in forward direction.

\(+\longrightarrow\)

  • To show negative integers, move in backward direction.

\(\longleftarrow\,-\)

  • To subtract a negative integer from a positive integer, we move in forward direction.

\((+)-(-)\longrightarrow\)

  • To subtract a positive integer from a negative integer, we move in backward direction.

\(\longleftarrow\,(-)-(+)\)

For example: Subtract \(-2\) from \(4\).

\(4-(-2)=\Box\)

 

First, draw a number line from \(0\) to \(4.\)

 

Start from zero and move \(4\) points forward to show positive \(4.\)

 

Now, to subtract \(-2\) from \(4,\) we move 2 points in the forward direction.

We reach at number \(6.\)

Thus, \(4-(-2)=6\)

We reach the number \(6.\)

Thus, \(4-(-2)=6\)

 

 

Illustration Questions

Which one of the following number lines represents the subtraction of \(-6\) and \(4\)?

A

B

C

D

×

To show the subtraction of \(4\) from \(-6\) on the number line, start from zero and move \(6\) points backward to show \(-6\).

image

Now, move \(4\) points backward to subtract \(4\) from \(-6\).

image

We reach at number \(-10\).

Thus, \(-6-4=-10\)

Hence, option (A) is correct.

Which one of the following number lines represents the subtraction of \(-6\) and \(4\)?

A image
B image
C image
D image

Option A is Correct

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