dividing-fractions MCQs for UPSC Prelims

35 practice questions on dividing-fractions from the Working with Fractions section of the UPSC Prelims syllabus. 35 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

10 Easy 18 Medium 7 Hard

Sample questions

Q1
medium

How many pieces of size $\frac{2}{3}$ fit into $8$?

  1. A $\frac{3}{16}$
  2. B $12$
  3. C $4$
  4. D $\frac{16}{3}$
Show answer and explanation

Correct answer: B - $12$

Dividing means multiplying by the reciprocal, so $8 \times \frac{3}{2} = \frac{24}{2} = 12$. The value $\frac{16}{3}$ comes from multiplying by $\frac{2}{3}$ instead of dividing, $\frac{3}{16}$ turns that answer over, and $4$ comes from dividing by $2$ and forgetting the $3$.

Q2
medium

Which number has no reciprocal?

  1. A $1$
  2. B $0$
  3. C $\frac{1}{2}$
  4. D $7$
Show answer and explanation

Correct answer: B - $0$

A reciprocal must give $1$ when multiplied by the number, and nothing multiplied by $0$ ever reaches $1$, so $0$ has no reciprocal. The number $1$ is its own reciprocal, $\frac{1}{2}$ has the reciprocal $2$, and $7$ has the reciprocal $\frac{1}{7}$.

Q3
easy

What is the reciprocal of $\frac{3}{5}$?

  1. A $\frac{3}{5}$
  2. B $\frac{5}{3}$
  3. C $\frac{1}{15}$
  4. D $\frac{1}{3}$
Show answer and explanation

Correct answer: B - $\frac{5}{3}$

The reciprocal is found by swapping the numerator and the denominator, so $\frac{3}{5}$ becomes $\frac{5}{3}$, and $\frac{3}{5} \times \frac{5}{3} = 1$. Repeating $\frac{3}{5}$ changes nothing, $\frac{1}{3}$ writes $1$ over the numerator alone, and $\frac{1}{15}$ comes from multiplying the two parts together.

Q4
medium

Without working it out, is $12 \div \frac{3}{4}$ more or less than $12$?

  1. A Less than $12$
  2. B More than $12$
  3. C Exactly $12$
  4. D It cannot be judged without calculating
Show answer and explanation

Correct answer: B - More than $12$

Each whole contains more than one piece of size $\frac{3}{4}$, so more than $12$ such pieces fit into $12$, and the quotient is $16$. A quotient below $12$ would need a divisor greater than $1$, and equality would need a divisor of exactly $1$. The size of $\frac{3}{4}$ alone settles the comparison.

Q5
easy

What is $\frac{3}{4} \div \frac{1}{4}$?

  1. A $3$
  2. B $\frac{1}{3}$
  3. C $1$
  4. D $\frac{3}{16}$
Show answer and explanation

Correct answer: A - $3$

The question asks how many quarters make three quarters, and the answer is $3$. The value $\frac{3}{16}$ comes from multiplying the two fractions instead of dividing, $\frac{1}{3}$ turns the correct answer over, and $1$ would mean the two fractions were equal.

Q6
easy

What is the reciprocal of the whole number $4$?

  1. A $0.4$
  2. B $1$
  3. C $\frac{1}{4}$
  4. D $4$
Show answer and explanation

Correct answer: C - $\frac{1}{4}$

Writing $4$ as $\frac{4}{1}$ and swapping the parts gives $\frac{1}{4}$, and $4 \times \frac{1}{4} = 1$. Choosing $4$ leaves the number unchanged, $0.4$ is $\frac{2}{5}$ and does not give $1$ when multiplied by $4$, and $1$ is the answer to the multiplication rather than the reciprocal itself.

Q7
medium

$\frac{3}{4}\ \text{kg}$ of sweets is shared equally among $3$ children. How much does each child get?

  1. A $\frac{9}{4}\ \text{kg}$
  2. B $\frac{1}{4}\ \text{kg}$
  3. C $4\ \text{kg}$
  4. D $\frac{1}{2}\ \text{kg}$
Show answer and explanation

Correct answer: B - $\frac{1}{4}\ \text{kg}$

Each share is $\frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4}\ \text{kg}$. The value $\frac{9}{4}\ \text{kg}$ comes from multiplying by $3$, which is more than the sweets available, $\frac{1}{2}\ \text{kg}$ from subtracting a quarter instead of dividing, and $4\ \text{kg}$ from turning the answer over.

Q8
medium

Assertion (A): $\frac{2}{5} \div \frac{2}{5} = 0$. Reason (R): Any number other than zero, divided by itself, gives $1$.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: D - A is false, but R is true

Dividing $\frac{2}{5}$ by itself gives $\frac{2}{5} \times \frac{5}{2} = 1$ rather than $0$, so A is false. R states a correct rule for every non-zero number, so R is true. R is the very rule that shows the assertion to be wrong.

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