Subtraction of Integers with the help of a Number Line
We have added positive integers on a number line. For example, consider 6+2. We start from 6 and go 2 steps to the right side. We reach at 8. So, 6 + 2 = 8.

We also saw that to add 6 and (–2) on a number line we can start from 6 and then move 2 steps to the left of 6. We reach at 4. So, we have, 6 + (–2) = 4.

Thus, we find that, to add a positive integer we move towards the right on a number line and for adding a negative integer we move towards left. We have also seen that while using a number line for whole numbers, for subtracting 2 from 6, we would move towards left.

i.e. 6 – 2 = 4

Ex.1     Find the value of – 8 – (–10) using number line
Sol.:    – 8 – (– 10) is equal to – 8 + 10 as additive inverse of –10 is 10.
On the number line, from – 8 we will move 10 steps towards right.

We reach at 2. Thus, –8 – (–10) = 2
Hence, to subtract an integer from another integer it is enough to add the additive inverse of the integer that is being subtracted, to the other integer.

Ex.2 Subtract the sum of 998 and – 486 from the sum of – 290 and 732.
Sol. Sum of 998 and – 486 is 998 + (– 486) = (998 – 486) = 512
Sum of – 290 and 732 is  – 290 + 732  = 732 – 290 = 442
Now, 442 – 512 = 442 +(–512) = – 70
[We subtract 442 from 512 and give minus sign to  the result]

Ex.3  On a particular day, the temperature at Dehradun at 10 AM was 20ºC but by midnight , it fell down to 11ºC. The temperature at Bangaluru at 10AM the same day was 30º C but fell down to 18º C by the midnight . Which fall is greater ?
Sol.    Fall in temperature at Dehradun = 20ºC – 11ºC = 9ºC
Fall in temperature at Bangaluru= 30ºC – 18ºC = 12ºC
The fall in temperature at Bangaluru is greater and is 12ºC.

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