Subtraction of Integers Using Number Line

We will learn subtraction of integers using number line.

We know that subtraction is the inverse of addition. Therefore, to subtract an integer, we add its additive inverse.

For example, to find +5 – (+2), we add +5 + (-2). 

So, on the number line, we move to the left of +5 by 2 steps. +5 + (-2) = +3.

We know that to get a predecessor of a number we subtract 1.

So, predecessor of -20 is -20 - 1 = -21 and successor is -20 + 1 = -19

On a number line, the values go on decrease as we move to the left. So, we represent the positive direction while moving towards the right and the opposite direction as negative, i.e., moving towards the left.

For subtraction on number line, we have the following rules:

Rule I: When we subtract a positive integer, we move to the left on the number line.

Rule II: When we subtract a negative integer, we move to the right on the number line.

Solved Examples on Subtraction of Integers:

1. Subtract +4 from +7.

Solution:

+7 – (+4) = +7 + (-4). So, we move 4 steps left to 7 on the number line.

Hence, +7 + (-4) = 3.

2. Subtract (-3) from (-7).

Solution:

-7 – (-3) = -7 + (+3) = -4. So, we move 3 steps to the right of -7 on the number line.

Hence, (-3) from (-7) = -4.

3. Find the difference of the integers using the number line:

(i) (-4) - 6

(ii) 6 - (-2)

(iii) (-3) - (-4)

Solution:

(i) We have to subtract 6 from -4. So, we start from -4 and move 6 steps to the left of -4. 

We end up at -10.

Therefore, (-4) - 6 = -10.

(ii) We have to subtract -2 from 6. So, we start from 6 and move 2 steps to the right of 6.

We end up at 8.

Therefore, 6 - (-2) = 8.

(iii) We have to subtract -4 from -3. So, we start from -3 and move 4 steps to the right of -3. 

We end up at 1.

Therefore, (-3) - (-4) = 1.

Worksheet on Subtracting Integers Using the Number Line:

1. Using the number line, subtract the following:

(i) 3 - (-2)

(ii) (-6) - (-1)

(iii) (-4) - (-2)

(iv) 6 - 7

(v) (-2) - (-3)

(vi) (-3) - (-5)

5th Grade Numbers Page

5th Grade Math Problems

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