Fractions MCQ Quiz - Objective Question with Answer for Fractions - Download Free PDF

Given:

\(\left[{\frac{1}{5} + \left(\frac{9}{15} \times \frac{7}{5} \right) - \left( \frac{4}{5} \times \frac{6}{9}\right) + \frac{3}{4}} \right] \) of \(\frac{2}{3}\)

Concept used:

Follow the BODMAS rule according to the table given below: 

Calculation:

⇒ \(\left[{\frac{1}{5} + \left(\frac{9}{15} \times \frac{7}{5} \right) - \left( \frac{4}{5} \times \frac{6}{9}\right) + \frac{3}{4}} \right] \) of \(\frac{2}{3}\)

⇒ \(\left[{\frac{1}{5} + \left(\frac{21}{25} \right) - \left( \frac{24}{45}\right) + \frac{3}{4}} \right] \)of \(\frac{2}{3}\)

⇒ \(\left[{\frac{60 + 252 - 160 + 225}{300}} \right] \times \frac{2}{3} \)

⇒ \(\left[{\frac{377}{300}} \right] \times \frac{2}{3} \)

⇒ \(\frac{377}{450}\)

∴ \(\left[{\frac{1}{5} + \left(\frac{9}{15} × \frac{7}{5} \right) - \left( \frac{4}{5} × \frac{6}{9}\right) + \frac{3}{4}} \right] × \frac{2}{3} = \frac{377}{450} \)

Given:

\(​\frac{3}{8} + \frac{1}{8} + \frac{5}{16} + \frac{2}{8} - 2\)

Calculation:

\(​\frac{3}{8} + \frac{1}{8} + \frac{5}{16} + \frac{2}{8} - 2\)

⇒ \(​\frac{3 \times 2 + 1 \times 2 + 5 + 2 \times 2 - 2 \times 16}{16}\)

⇒ \(​\frac{6 + 2 + 5 + 4 - 32}{16}\)

⇒ \(​\frac{17 - 32}{16}\)

⇒ \(-\frac{15}{16}\)

The correct answer is Option (4).

Given:

\(\frac{81}{3} \times \frac{27}{3} = ?\)

Calculation:

\(\frac{81}{3} \times \frac{27}{3} = ?\)

⇒ \(\frac{81}{3} = 27\)

⇒ \(\frac{27}{3} = 9\)

⇒ 27 × 9 = 243

∴ The correct answer is: 243

Given:

Expression: \(\frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + \ldots + \frac{2}{45 \times 47} \)

Formula used:

Simplify each term using partial fraction decomposition.

Calculation:

Each term can be written as:

\(\frac{2}{n(n+2)} = \frac{1}{n} - \frac{1}{n+2}\)

Applying this to the given series:

\(\left( \frac{1}{1} - \frac{1}{3} \right) + \left( \frac{1}{3} - \frac{1}{5} \right) + \left( \frac{1}{5} - \frac{1}{7} \right) + \ldots + \left( \frac{1}{45} - \frac{1}{47} \right)\)

All intermediate terms cancel out, and we are left with:

\(1 - \frac{1}{47} = \frac{46}{47}\)

∴ The value of the series is \(\frac{46}{47} \).

Given:

\(\frac{(-2-3) ×(5+3) ÷(-2-3)}{(-6-4) ÷(-7-5)}\)

Formula Used:

Follow the order of operations (PEMDAS/BODMAS)

Calculation:

Calculate the values step by step:

(-2 - 3) = -5

(5 + 3) = 8

(-2 - 3) = -5

(-6 - 4) = -10

(-7 - 5) = -12

Now substitute back into the expression:

\(\left(-5 × 8 ÷ -5\right) ÷ \left(-10 ÷ -12\right)\)

Simplify inside the parentheses first:

-5 × 8 = -40

-40 ÷ -5 = 8

Simplify the second part:

-10 ÷ -12 = \(\frac{10}{12} = \frac{5}{6}\)

Now divide the results:

8 ÷ \(\frac{5}{6}\) = 8 × (6/5)

48/5 = 9.6

The correct answer is option 4, 9.6.

Solution:

\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)

= 25/2 + 37/3 + 73/6

= (75 + 74 + 73)/6

= 222/6

= 37

Shortcut Trick

\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)

= 36 + 1 = 37

Let that fraction be x.

⇒ x + 5/8 = 1

⇒ x = 1 – 5/8

\(\Rightarrow 4\frac{1}{5}-\left[ 3\frac{1}{3}-\left\{ 2\frac{1}{2}-\left( \frac{1}{3}+\frac{1}{6}-\frac{1}{12} \right) \right\} \right]\)

\(\Rightarrow \frac{{21}}{5} - \left[ {\frac{{10}}{3}-\left\{ {\frac{5}{2} - \left( {\frac{{4{\rm{\;}} + {\rm{\;}}2{\rm{\;}}-{\rm{\;}}1}}{{12}}} \right)} \right\}} \right]\)

\(\Rightarrow \frac{{21}}{5} - \left[ {\frac{{10}}{3} - \left\{ {\frac{5}{2} - \frac{5}{{12}}} \right\}} \right]\)

\(\Rightarrow \frac{{21}}{5} - \left[ {\frac{{10}}{3} - \frac{{25}}{{12}}} \right]\)

\(\Rightarrow \frac{{21}}{5} - \frac{{15}}{{12}}\)

\(\Rightarrow \frac{{21}}{5} - \frac{5}{4}\)

\(\Rightarrow \frac{{84 - 25{\rm{\;}}}}{{20}}\)

⇒ 59/20

(7/13) = 0.538

(2/3) = 0.666

(4/11) = 0.3636

(5/9) = 0.5555

Out of 2/3, 7/13, 4/11, 5/9

2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.

Given:

(5x - 2y) ∶ (x - 2y) = 9 ∶ 17

Calculation:

The given ratio can be written as:

(5x - 2y)/(x - 2y) = 9/17

17 × (5x - 2y) = 9 × (x - 2y)

85x - 34y = 9x - 18y

76x = 16y

x/y = 16/76

x/y = 4/19

9 × (4/19)/13 = 36/247

So, 9x/13y = 36/247.

Let the number of people be x and number of the chair be y.

Number of available chair = y × (9/13) = 9y/13

Number of empty chair = y - (9y/13) = 4y/13

Given, Number of empty chairs = 28

According to the question

4y/13 = 28

y = 28 × (13/4) = 91

Total number of chairs = 91

Number of chairs in which people are sitting = 91 - 28 = 63

Number of people who sit = x × (7/9) = 7x/9

According to the question

7x/9 = 63

x = 63 × (9/7) = 81

Total number of people are = 81

Formula used:

a² - b² = (a + b)(a - b)

Calculation

⇒ \(\rm\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2}\)

⇒ [(p + q - r)(p - q + r)]/[(p + q + r)(p - q + r)] + [(p + q - r)(q - p + r)]/[(p + q + r)(p + q - r)] + [(p - q + r)(q  -p + r)]/[(p + q + r)(q - p + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ [(p + q - r)]/[(p + q + r)] + [q - p + r)]/[(p + q + r)] + [(p - q + r)]/[(p + q + r)]

⇒ (p + q + r)/(p + q + r)

⇒ 1.

The value is 1.

Shortcut Trick

Let put p = q = r = 1

So,

\(\rm\frac{p^2-(q-r)^2}{(p+r)^2-q^2}+\frac{q^2-(p-r)^2}{(p+q)^2-r^2}+\frac{r^2-(p-q)^2}{(q+r)^2-p^2}\)

⇒ \(\rm\frac{1^2-(1-1)^2}{(1+1)^2-1^2}+\frac{1^2-(1-1)^2}{(1+1)^2-1^2}+\frac{1^2-(1-1)^2}{(1+1)^2-1^2}\)

⇒ \(\rm\frac{1-0}{(4-1)}+\frac{1-0}{(4-1)}+\frac{1-0}{(4-1)}\)

⇒ 1/3 + 1/3 + 1/3 = 1

Hence, The value is 1.

Given:

\(\frac{{5{\rm{x}}}}{{1{\rm{\;}} + {\rm{\;}}\frac{1}{{1{\rm{\;}} + {\rm{\;}}\frac{{\rm{x}}}{{1{\rm{\;}} - {\rm{\;x}}}}}}}}{\rm{\;}} = {\rm{\;}}1\)

Calculation:

\(\Rightarrow {\rm{\;}}\frac{{5{\rm{x}}}}{{1{\rm{\;}} + {\rm{\;}}\frac{{1 - {\rm{x}}}}{{1 - {\rm{x\;}} + {\rm{\;x}}}}}}{\rm{\;}} = {\rm{\;}}1 \)

\(\Rightarrow {\rm{\;}}\frac{{5{\rm{x}}}}{{1{\rm{\;}} + {\rm{\;}}1 - {\rm{x}}}}{\rm{\;}} = {\rm{\;}}1\)

⇒ 5x/(2 – x) = 1

⇒ 5x = 2 – x

⇒ 6x = 2

⇒ x = 2/6

∴ The required value of x is 1/3.

Given:

The fractions are 13/19, 25/ 31, 28/31, 70/79.

Calculation:

The values are-

13/19 = 0.68

25/31 = 0.80

28/31 = 0.90

70/79 = 0.88

∴ Option C is correct.

Concept Used:

Follow BODMAS rule to solve this question, as per the order given below,

Calculations:

Given expression is,

\(\Rightarrow 5\frac{1}{6} - 3\frac{4}{9} + ? = \frac{7}{3} \times 4\frac{1}{6}\)

\(\Rightarrow {\rm{\;}}\frac{{31}}{6} - \frac{{31}}{9} + ? = \frac{7}{3} \times \frac{{25}}{6}\)

\(\Rightarrow 31\left( {\frac{1}{6} - \frac{1}{9}} \right) + \;? = \left( {\frac{{175}}{{18}}} \right)\)

\(\Rightarrow {\rm{\;}}31(\frac{3}{{54}}) + ? = \frac{{175}}{{18}}\)

\(\Rightarrow {\rm{\;}}\frac{{31}}{{18}} + ? = \frac{{175}}{{18}}\)

⇒ ? = 144/18

⇒ ? = 8