NCERT Solutions Ganita Prakash (Part 2) Chapter 1 In-text Questions — — The FDP Trio: Fractions, Decimals, and Percentages

Book page 8 Updated on2026-09-05

Q1.

Using this observation, mentally calculate how much 15% of the values in the table would be.

Answer

15% = 10% + 5%. Take a tenth, then add half of it.

	100	200	50	80	10	35	287
10%	10	20	5	8	1	3.5	28.7
5%	5	10	2.5	4	0.5	1.75	14.35
15%	15	30	7.5	12	1.5	5.25	43.05

15% of 287 = 28.7 + 14.35 = 43.05

Q2.

Suppose you have to mentally calculate the following percentages of some value: 75%, 90%, 70%, 55%. How would you do it? Discuss.

Answer

Break each one into the two easy pieces, 10% and 25%, and use adding or subtracting from the whole.

75% = 100% – 25%. Or three quarters: halve, halve again, take three of those parts.
90% = 100% – 10%. Take a tenth away from the whole.
70% = 7 × 10%. Or 100% – 30%.
55% = 50% + 5%. Half, plus a twentieth.

Try it on 240:
75% → 240 – 60 = 180
90% → 240 – 24 = 216
70% → 7 × 24 = 168
55% → 120 + 12 = 132

Why it happens: Subtracting from 100% is legitimate because the part and the rest always add to the whole: (100 – x)% of y = y – (x% of y). For percentages near 100, taking the small piece away is far less work than building the large piece up.

Q3.

Similarly, to find 10% of a quantity, what decimal value should be multiplied?

Answer

0.1

10% = 10/100 = 1/10 = 0.1
So 10% of 350 = 0.1 × 350 = 35

Why it happens: Every percentage has one decimal twin, found by dividing by 100 — that is, shifting the decimal point two places left. 50% → 0.5, 10% → 0.1, 7% → 0.07, 125% → 1.25. Multiplying by that decimal and taking that percentage are the same operation written two ways.

Q4.

Complete the following table: [Per cent: 50%, 100%, 25%, 75%, 10%, 1%, 5%, 43%. Fraction row starts with 50/100; Decimal row starts with 0.5.]

Answer

Per cent	50%	100%	25%	75%	10%	1%	5%	43%
Fraction	50/100 = 1/2	100/100 = 1	25/100 = 1/4	75/100 = 3/4	10/100 = 1/10	1/100	5/100 = 1/20	43/100
Decimal	0.5	1.0	0.25	0.75	0.1	0.01	0.05	0.43

Why it happens: The middle row is written straight from the definition x% = x/100; the bottom row is the same fraction carried out as a division. Nothing is converted twice — the three rows are three notations for one number. That is why 100% is 1: the whole thing.

Tip: 43/100 cannot be simplified, because 43 is prime and does not divide 100. That is fine — a percentage does not have to reduce.

Q5.

Activity: How Close Can You Get? Make a pair. Each of you choose a number. Suppose, the numbers chosen are a and b. Share your numbers with each other. Both of you should estimate the percentage equivalent to the fraction a/b (where a < b) and announce your answers by a fixed time, say, 5 seconds. The one whose estimate is the closest wins this round. Play this for 10 rounds.

Answer

The skill this game trains is bracketing — trapping the answer between two percentages you already know, instead of dividing.

Suppose the pair chooses a = 7, b = 24.

Half of 24 is 12, and 7 < 12, so 7/24 < 50%
A quarter of 24 is 6, and 7 > 6, so 7/24 > 25%
A third of 24 is 8, and 7 < 8, so 7/24 < 33.3%
So the answer lies between 25% and 33%, nearer the top → estimate about 29%
(the exact value is 700/24 = 29.17%)

Why it happens: Landmarks like 1/2, 1/3, 1/4 and 1/10 of the denominator are quick to compute, and each one you check cuts the range of possible answers. Two or three checks narrow the estimate to within a couple of per cent — enough to win a five-second round.

Tip: Keep score over the 10 rounds and, afterwards, work out the exact percentages. Compare how far off each estimate was; you will find your estimates tighten as you play.

Was this helpful? Report an error