NCERT Solutions for Class 6th Maths Chapter 10 Back to the number line — In-text Questions

Book page 252 & 253 Updated on2026-09-19

Q1.

In the other exercises that you did above, did you notice that subtracting a negative number was the same as adding the corresponding positive number?

Answer

Yes — it happened in every single pair.

+ 105 – (– 55) = + 160 and + 105 + (+ 55) = + 160
+ 80 – (– 150) = + 230 and + 80 + (+ 150) = + 230
– 99 – (– 200) = + 101 and – 99 + (+ 200) = + 101

Why it happens: ‘– (– 55)’ asks how far above – 55 is + 105. To climb out of a level that is 55 below the ground you must first come up those 55 levels — so the 55 gets added to the journey, not removed from it. In short, a – (– b) = a + b.

Q2.

Take a look at the ‘infinite lift’ above. Does it remind you of a number line? In what ways?

Answer

Yes — the infinite lift is a number line, only standing up instead of lying down.

Level 0 of the lift is the 0 of the number line.
Levels above 0 are the positive numbers; levels below 0 are the negative numbers.
The levels are equally spaced, just like the marks on a number line.
Pressing ‘+’ is moving forward; pressing ‘–’ is moving backward.
A higher level means a greater number, exactly as a mark further right means a greater number.

Turn the infinite lift through 90° and it becomes
… – 3, – 2, – 1, 0, 1, 2, 3 … — a complete number line.

Math Talk: This is exactly the answer to the question asked at the very start of the chapter — the number ray starting at 0 becomes a full number line once the negative numbers are put to the left of 0.

Q3.

If, from 5 you wish to go over to 9, how far must you travel along the number line?

The number line from 0 to 10, page 252.

Answer

You must travel 4 steps forward (to the right).

Four steps forward take you from 5 to 9.

Starting Number + Movement = Target Number → 5 + 4 = 9
Target Number – Starting Number = Movement needed → 9 – 5 = 4

Q4.

Now, from 9, if you wish to go to 3, how much must you travel along the number line?

The number line from 0 to 10, page 253.

Answer

You must move 6 steps backward, that is a movement of – 6.

Six steps backward take you from 9 to 3, so the movement is – 6.

Starting Number + Movement = Target Number → 9 + (– 6) = 3
Target Number – Starting Number = Movement needed → 3 – 9 = – 6

Why the answer is negative: the sign shows the direction. Forward (right) is +, backward (left) is –. The 6 tells you how far, the minus tells you which way.

Q5.

Now, from 3, if you wish to go to – 2, how far must you travel?

Answer

You must travel – 5, that is 5 steps backward. Three steps bring you to 0, and two more take you to – 2.

From 3 to – 2 is five steps backward — three to reach 0 and two more beyond it.

3 + (– 5) = – 2
The matching subtraction statement: – 2 – 3 = – 5

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