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Fractions in Disguise: questions with answers

Class 8 Maths, Chapter 8 (NCERT). 15 questions by concept, 15 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Estimating and comparing percentages

Question 1

Between which two percentages does 2/92/9 lie?

A bar split into parts labelled 2 and 7. The whole is labelled 9. The first part occupies two ninths of the bar.27Whole = 9
  1. (a)2% and 3%
  2. (b)20% and 25%
  3. (c)50% and 60%
  4. (d)25% and 30%
Show answer

(b) 20% and 25%

20% of 9 is 1.8, and 25% of 9 is 2.25. Since 2 lies between 1.8 and 2.25, its share lies between 20% and 25%.

Fractions and percentages

Question 2

What percentage is equivalent to 2/52/5?

A bar with 2/5 of its length hatched. The whole is 100%; the marked percentage is unknown.0%100%012/5 of the wholeMarked percentage = ?
  1. (a)5%
  2. (b)60%
  3. (c)40%
  4. (d)2%
Show answer

(c) 40%

Multiply the fraction by 100: 2/5×1002/5 \times 100 equals 40%.

Percentage of a target

Question 3

The sales target is 5000, and sales are 6000. What percentage of the target has been achieved?

Sales of 6000 are hatched on a 0 to 10000 bar. The target 5000 is at the 100% midpoint.Sales: 600005000 target100000%100%200%
  1. (a)1.2%
  2. (b)20%
  3. (c)120%
  4. (d)12%
Show answer

(c) 120%

The target is the whole. The percentage achieved is 60005000×100=120\frac{6000}{5000} \times 100 = 120%.

Percentages and multiples

Question 4

What decimal multiplier represents 250% of a quantity? Write the multiplier to two decimal places.

A bar from 0% to 400%, with whole-number positions 0, 1, 2, 3, 4. The marker is at 250%.0%0100%1200%2300%3400%4Marked position: 250%Each 100% is one whole
  1. (a)0.25
  2. (b)3.50
  3. (c)2.50
  4. (d)1.50
Show answer

(c) 2.50

Divide 250 by 100 to obtain 2.5. Written to two decimal places, the multiplier is 2.50.

Reading and completing bar models

Question 5

The lower question mark was replaced by 20 by copying the percentage label. What quantity should replace it?

A bar divided into equal cells. The whole is 75. Brackets mark 1 of 5 cells on percentage and quantity scales.0%100%75020%?
  1. (a)75
  2. (b)60
  3. (c)15
  4. (d)20
Show answer

(c) 15

One of five equal cells represents 75 divided by 5, or 15. The label 20% is on the percentage scale, not the quantity scale.

Finding a percentage of a quantity

Question 6

The top of the bar runs from 0% to 100% and the bottom from 0 to 120. The hatched part ends at 25%. What is 25% of 120?

A bar marked 0% to 100% above and 0 to 120 below; the part up to 25% is hatched0%100%012025%?
  1. (a)30
  2. (b)300
  3. (c)25
  4. (d)90
Show answer

(a) 30

25% is 25 out of every 100, so it is a quarter. A quarter of 120 is 25100×120=30\frac{25}{100} \times 120 = 30.

Percentage shares sum to100

Question 7

The first three ingredients make up 66%, 20% and 8% of the whole mix. What percentage is left? Give two decimal places.

Four shares of one whole, in table order. Known shares are 66%, 20% and 8%; the last share is unknown.One whole = 100%Sugar66%Milk solids20%Badam powder8%Food chemicals?
  1. (a)94.00%
  2. (b)6.38%
  3. (c)6.00%
  4. (d)80.00%
Show answer

(c) 6.00%

The known shares total 94%, leaving 100% minus 94% = 6%. Dividing the remaining 6 by 94 incorrectly excludes it from the whole.

Ratios as parts of a whole

Question 8

The first part has 10 ratio parts, and the second has the remaining 90. What percentage of the whole is the first part? Give two decimal places.

One whole split into two parts in the ratio 10 to 90. The left part is first.First : second = 10 : 901090Whole = 10 + 90 ratio parts
  1. (a)11.11%
  2. (b)10.00%
  3. (c)90.00%
  4. (d)900.00%
Show answer

(b) 10.00%

The whole contains 100 ratio parts. Ten of them represent 10.00% of the whole.

Compare proportions using percentages

Question 9

The labels show the same ingredient in two mixes. Subtract its percentage in Mix B from its percentage in Mix A. What is the result?

Mix A: 30 g ingredient out of 150 g. Mix B: 64 g ingredient out of 400 g. Each bar represents its own whole.Mix AIngredient: 30 gTotal: 150 gIngredient shareMix BIngredient: 64 gTotal: 400 gIngredient share
  1. (a)-34%
  2. (b)4%
  3. (c)36%
  4. (d)-4%
Show answer

(b) 4%

Mix A contains 20% of the ingredient, while Mix B contains 16%. Their percentages differ by 4%.

Proportions and absolute amounts

Question 10

Either option can be chosen once, and both deposits are affordable. Which option gives the larger net gain in rupees?

One use of one option. Option A; Deposit:₹100; Return:₹300. Option B; Deposit:₹1000; Return:₹1500.One use of one optionOption ADeposit:₹100Return:₹300Option BDeposit:₹1000Return:₹1500
  1. (a)Equal net gains
  2. (b)No net gain under either option
  3. (c)Option B
  4. (d)Option A
Show answer

(c) Option B

Option A gains ₹300 minus ₹100, or ₹200. Option B gains ₹1500 minus ₹1000, or ₹500, despite its lower percentage gain.

Recovering the whole

Question 11

20% of a number is 60. What is the number?

A bar with a marked part of 60. This is 20% of the whole. The whole is unknown.0%100%Known part: 6020% of the wholeWhole = ?
  1. (a)240
  2. (b)12
  3. (c)300
  4. (d)60
Show answer

(c) 300

The whole is 60×100÷2060 \times 100 \div 20, 300. The given part is not the base.

Compounding successive changes

Question 12

Goods cost 16000 rupees. Their price is marked up by 50%, then discounted by 50% of the marked price. What is the final price? Give two decimal places.

Cost is 16000 rupees. Three left-aligned bars represent cost, a 50% mark-up, and a 50% discount on that marked price.Cost: 16000 rupeesAfter 50% mark-upAfter 50% discount
  1. (a)16000.00 rupees
  2. (b)24000.00 rupees
  3. (c)8000.00 rupees
  4. (d)12000.00 rupees
Show answer

(d) 12000.00 rupees

The marked price is 24000 rupees. Half of that is 12000 rupees, so the two changes do not cancel.

Percentage area of a region

Question 13

The square has side 4 units. What percentage of its area is occupied by E?

A square of side 4 units has five labelled regions. The left strip is 2 units wide. Its bottom rectangle is 2 units high and split diagonally into D and E. A is above; B and C are at right.ABCDE4 units
  1. (a)25.000%
  2. (b)20.000%
  3. (c)87.500%
  4. (d)12.500%
Show answer

(d) 12.500%

E has area 2 square units, and the whole square has area 16 square units. Therefore its share is 216×100=12.5\frac{2}{16} \times100=12.5%.

Peaceful Knights

Question 14

Each K marks one of seven knights on this eight-by-eight board. On which square can an eighth knight be placed so that no knight attacks another?

8 by 8 board. Knights at A1, C1, E1, G1, B2, D2, F2.A1B2C3D4E5F6G7H8KKKKKKK
  1. (a)A2
  2. (b)H2
  3. (c)C2
  4. (d)E2
Show answer

(b) H2

Every existing knight and H2 are on the same colour of square. A knight always changes square colour, so these eight knights cannot attack one another.

Grouped bar chart readings

Question 15

Considering females and males separately, which labelled age group has the highest percentage able to use computers for both genders?

Ability to use computer by age and gender, 2023Ability to use computer by age and gender (2023)Female: shadedMale: outlined0%5%10%15%20%25%30%35%40%Children4%Not labelledTeenage24%29%Twenties26%37%Thirties14%25%Forties7%14%Fifties4%9%Seniors2%4%Children: the male percentage is not labelled.
  1. (a)Teenage
  2. (b)Thirties
  3. (c)Twenties
  4. (d)Seniors
Show answer

(c) Twenties

The twenties have the highest labelled female percentage, 26%, and male percentage, 37%. Chart position alone does not establish the highest value.

Common misconception in Fractions in Disguise

Open full misconception guide →

Does a percent already give a count?

Wrong

A 25% discount always means 25 rupees off.

Why it feels right. I read 25% as a fixed amount.

Right

A percentage is a share of a specified whole.

Worked example

25% of ₹20050 rupees
25% of ₹400100 rupees
One quarter is the same fraction of both prices. The higher price has the bigger rupee discount.
  1. One quarter of ₹200 is ₹50.
  2. One quarter of ₹400 is ₹100.
  3. Both discounts are 25%.