40 practice questions on multiplying-fractions from the Working with Fractions section of the UPSC Prelims syllabus.
40 come with a written explanation.
Try the sample set below - the answer stays hidden until you ask for it.
12 Easy20 Medium8 Hard
Sample questions
Q1
hard
Which of these products is the smallest?
A$24 \times \frac{2}{3}$
B$24 \times \frac{5}{6}$
C$24 \times \frac{3}{4}$
D$24 \times \frac{1}{2}$
Show answer and explanation
Correct answer: D - $24 \times \frac{1}{2}$
The four products are $12$, $16$, $18$ and $20$, so the smallest comes from the smallest fraction, $\frac{1}{2}$. The other three fractions are each closer to $1$, and the nearer a proper fraction is to $1$, the more of the $24$ is kept.
Q2
medium
Multiply $\frac{5}{6}$ by $\frac{3}{10}$ and give the answer in simplest form.
A$\frac{1}{4}$
B$\frac{34}{30}$
C$\frac{25}{9}$
D$\frac{8}{16}$
Show answer and explanation
Correct answer: A - $\frac{1}{4}$
The product is $\frac{15}{60}$, and dividing both parts by $15$ gives $\frac{1}{4}$. The value $\frac{25}{9}$ comes from dividing instead of multiplying, $\frac{8}{16}$ from adding numerators and denominators separately, and $\frac{34}{30}$ from adding the two fractions.
Q3
medium
A rectangle is divided into $2$ equal columns and $5$ equal rows. One column is shaded and one row is shaded. What fraction of the rectangle carries both shadings?
A$\frac{7}{10}$
B$\frac{1}{5}$
C$\frac{1}{10}$
D$\frac{1}{7}$
Show answer and explanation
Correct answer: C - $\frac{1}{10}$
There are $2 \times 5 = 10$ small parts, and the column and the row overlap in just one of them, so the answer is $\frac{1}{10}$, matching $\frac{1}{2} \times \frac{1}{5}$. The value $\frac{1}{7}$ adds $2$ and $5$, $\frac{7}{10}$ adds the two fractions, and $\frac{1}{5}$ is the shaded row on its own.
Q4
hard
Assertion (A): In an area model, the product of two proper fractions is shown by a region larger than either of the two shaded regions. Reason (R): The doubly shaded region is a part of each of the two shaded regions.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: D - A is false, but R is true
A is false, because the overlap is smaller than either shaded region, which is why multiplying two proper fractions gives a smaller answer. R is true, since the doubly shaded region lies inside both shadings. R is exactly what shows the assertion to be wrong.
Q5
medium
Calculate $\frac{3}{5}$ of $45$.
A$27$
B$75$
C$9$
D$18$
Show answer and explanation
Correct answer: A - $27$
One fifth of $45$ is $9$, so three fifths is $9 \times 3 = 27$. The value $18$ is the remaining two fifths, $9$ stops at one fifth, and $75$ comes from multiplying by $\frac{5}{3}$ instead.
Q6
medium
Half of a cake is left after a party. Raju eats $\frac{3}{4}$ of what is left. What fraction of the whole cake does Raju eat?
A$\frac{3}{4}$
B$\frac{1}{8}$
C$\frac{5}{4}$
D$\frac{3}{8}$
Show answer and explanation
Correct answer: D - $\frac{3}{8}$
Raju eats $\frac{3}{4}$ of $\frac{1}{2}$, and $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$ of the whole cake. The value $\frac{3}{4}$ ignores that only half the cake remained, $\frac{1}{8}$ is the part of the whole cake still left, and $\frac{5}{4}$ comes from adding the two fractions.
Q7
hard
Ravi spends $\frac{1}{4}$ of his pocket money on books and then $\frac{1}{3}$ of what is left on food. What fraction of his pocket money goes on food?
A$\frac{1}{3}$
B$\frac{1}{4}$
C$\frac{1}{12}$
D$\frac{7}{12}$
Show answer and explanation
Correct answer: B - $\frac{1}{4}$
After the books, $\frac{3}{4}$ of the money is left, and $\frac{1}{3}$ of $\frac{3}{4}$ is $\frac{3}{12} = \frac{1}{4}$. The value $\frac{1}{3}$ forgets that only part of the money remained, $\frac{1}{12}$ multiplies $\frac{1}{3}$ by $\frac{1}{4}$ instead of by $\frac{3}{4}$, and $\frac{7}{12}$ comes from adding the two fractions.
Q8
hard
In a school, $\frac{2}{5}$ of the students are girls, and $\frac{1}{4}$ of the girls play hockey. What fraction of all the students are girls who play hockey?
A$\frac{13}{20}$
B$\frac{2}{9}$
C$\frac{1}{4}$
D$\frac{1}{10}$
Show answer and explanation
Correct answer: D - $\frac{1}{10}$
The answer is $\frac{1}{4}$ of $\frac{2}{5}$, which is $\frac{2}{20} = \frac{1}{10}$ of all the students. The value $\frac{2}{9}$ comes from adding numerators and denominators separately, $\frac{1}{4}$ is the share of the girls rather than of everybody, and $\frac{13}{20}$ comes from adding the two fractions.
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