NCERT Solutions Class 6th Maths Chapter – 6 Integers All Examples

Example 1. By looking at the number line, answer the following questions – Which integers lie between –8 and –2? Which is the largest integer and the smallest integer among them?

Solution –

Integers between –8 and –2 are –7, –6, –5, –4, –3. The integer –3 is the largest and –7 is the smallest.

If, I am not at zero what happens when I move?
Let us consider the earlier game being played by Salma and Ruchika.

Suppose Ruchika’s token is at 2. At the next turn she gets a red die which after throwing gives a number 3. It means she will move 3 places to the right of 2.

Thus, she comes to 5.

If on the other hand, Salma was at 1, and drawn a blue die which gave her number 3, then it means she will move to the left by 3 places and stand at – 2.

By looking at the number line, answer the following question-

Example 2. (a) One button is kept at – 3. In which direction and how many steps should we move to reach at – 9?

(b) Which number will we reach if we move 4 steps to the right of – 6.

Solution –

(a) We have to move six steps to the left of – 3.

(b) We reach – 2 when we move 4 steps to the right of – 6.

Example 3. Using the number line, write the integer which is-

(a) 4 more than –1
(b) 5 less than 3

Solution –

(a) We want to know the integer which is 4 more than –1.
So, we start from –1 and proceed 4 steps to the right of –1 to reach 3 as
shown below-

Therefore, 4 more than –1 is 3.

(b) We want to know an integer which is 5 less than 3; so we start from 3 and move to the left by 5 steps and obtain –2 as shown below-

Therefore, 5 less than 3 is –2.

Example 4. Find the sum of (–9) + (+4) + (–6) + (+3)

Solution –

We can rearrange the numbers so that the positive integers and the negative integers are grouped together. We have

= (–9) + (+4) + (–6) + (+3)
= (–9) + (–6) + (+4) + (+3)
= (–15) + (+7) = –8

Example 5. Find the value of (30) + (–23) + (–63) + (+55)

Solution –

= (30) + (+55) + (–23) + (–63)
= 85 + (–86)
= –1

Example 6. Find the sum of (–10), (92), (84) and (–15)

Solution –

= (–10) + (92) + (84) + (–15)
= (–10) + (–15) + 92 + 84
= (–25) + 176
= 151

Example 7. Find the value of –8 – (–10) using number line.

Solution –

–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.

Example 8. Subtract (–4) from (–10)

Solution –

= (–10) – (–4) = (–10) + (additive inverse of –4)
= –10 + 4 = –6

Example 9. Subtract (+3) from (–3)

Solution –

= (–3) – (+3) = (–3) + (additive inverse of +3)
= (–3) + (–3) = –6