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NCERT Solutions for Class 6th Maths Chapter 7 Figure it Out — Marking Fraction Lengths on the Number Line

Book page 160 Updated on2026-09-19

Q1.
On a number line, draw lines of lengths 1⁄10, 3⁄10, and 4⁄5.
Answer

Divide the length from 0 to 1 into 10 equal parts. Then 1⁄10 is 1 step, 3⁄10 is 3 steps, and 4⁄5 = 8⁄10 is 8 steps.

4/5 = (4 × 2)/(5 × 2) = 8/10
011/103/104/5 = 8/10
The unit from 0 to 1 cut into ten equal steps. The three coloured lines are 1⁄10, 3⁄10 and 4⁄5 (= 8⁄10) long.
Q2.
Write five more fractions of your choice and mark them on the number line.
Answer

Any five fractions may be chosen. Here is one good set, marked with the same tenths scale.

FractionWhere it goesIn tenths
1/2exactly halfway between 0 and 15/10
2/52 steps of one-fifth4/10
7/107 steps of one-tenth7/10
6/5just past 112/10
3/2halfway between 1 and 215/10
Math Talk: compare your five fractions with a friend’s. Write each one as tenths (or twentieths) and you can instantly say whose fraction is bigger.
Q3.
How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
Answer

There are unlimited (infinitely many) fractions between 0 and 1.

Take any denominator you like and you already get new fractions:

halves → 1/2
thirds → 1/3, 2/3
tenths → 1/10, 2/10, …, 9/10
hundredths → 1/100, 2/100, …, 99/100
Why they never run out: pick any two fractions between 0 and 1. Their “midpoint” is again a fraction lying between them — for example between 1⁄2 and 1⁄3 lies 5⁄12. You can keep doing this forever, so no one can ever finish listing them.
Q4.
What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is 1⁄2. So the blue line is 1⁄2 units long. Write the fraction that gives the length of the black line in the box.
01212
The number line with the blue line and the black line drawn above it.
Answer

Each step on this line is 1⁄2 unit. The black line starts at 0 and stops at the mark between 1 and 2, that is at the third half-step.

Blue line = 1 step = 1/2 unit
Black line = 3 steps = 3 times 1/2 = 3/2 unit = 1 1/2 units

Answer: the black line is 3⁄2 (one and a half) units long.

Q5.
Write the fraction that gives the lengths of the black lines in the respective boxes.
Answer

Here the unit is divided into 5 equal parts, so every step is 1⁄5 unit. All four black lines start at 0 and end after 1, at the four empty boxes.

0129/58/57/56/5
The four black lines of the book redrawn: they stop 6, 7, 8 and 9 fifth-steps away from 0.
First box = 6 steps = 6/5
Second box = 7 steps = 7/5
Third box = 8 steps = 8/5
Fourth box = 9 steps = 9/5

Answer: 6⁄5, 7⁄5, 8⁄5, 9⁄5 (that is 11⁄5, 12⁄5, 13⁄5, 14⁄5).

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