NCERT Solutions Ganita Prakash Chapter 10 & 254Back to the number line — Figure it Out
Book page 253 Updated on2026-09-05
Q1.
Mark 3 positive numbers and 3 negative numbers on the number line above.
Answer
Any three numbers on each side will do. Here is one choice — positives 2, 5, 8 and negatives – 1, – 3, – 7.
Three positive numbers A = 2, B = 5, C = 8 (right of 0, in green) and three negative numbers P = – 1, Q = – 3, R = – 7 (left of 0, in red).
Tip: Every positive number must be marked to the right of 0 and every negative number to the left of 0. Your friend's three numbers may be different — that is perfectly fine.
Q2.
Write down the above 3 marked negative numbers in the following boxes:
Answer
Write them in the order in which they appear on the number line, that is smallest first (left to right):
– 7 < – 3 < – 1
Why this is the increasing order: – 7 lies furthest to the left, so it is the smallest; – 1 is nearest to 0, so of the three it is the greatest. All three are still less than 0.
Q3.
Is 2 > – 3? Why? Is – 2 < 3? Why?
Answer
Yes to both.
2 > – 3 — on the number line 2 lies to the right of – 3, and whatever is further right is greater. In the building, Floor 2 is above Floor – 3.
– 2 < 3 — here – 2 lies to the left of 3, and whatever is further left is smaller. Floor – 2 is below Floor 3.
– 3 < 0 < 2 → 2 > – 3 – 2 < 0 < 3 → – 2 < 3
Tip: A positive number is always greater than a negative number — you never even need to look at the digits.
Q4.
What are a. – 5 + 0 b. 7 + (– 7) c. – 10 + 20 d. 10 – 20 e. 7 – (– 7) f. – 8 – (– 10)?
Answer
Expression
Working
Answer
a.
– 5 + 0
Adding 0 changes nothing
– 5
b.
7 + (– 7)
A number plus its inverse
0
c.
– 10 + 20
From – 10 move 20 forward: 10 to reach 0, 10 beyond
+ 10
d.
10 – 20
10 + (– 20): from 10 move 20 backward
– 10
e.
7 – (– 7)
= 7 + 7; from – 7 to 7 is 14 steps
+ 14
f.
– 8 – (– 10)
= – 8 + 10; from – 10 up to – 8 is 2 steps
+ 2
Compare (b) and (e): 7 + (– 7) = 0 but 7 – (– 7) = 14. Adding the inverse cancels; subtracting the inverse doubles. The sign in front of the bracket makes all the difference.