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Maths MCQ

Fractions · Maharashtra Board STD 6 (MSBSHSE - Semi English Medium). 25 questions.

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25 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Mark the correct alternative of the following:Which of the following is a proper fraction?
  • ✓
    $\frac{3}{5}$
  • B
    $\frac{5}{3}$
  • C
    $1\frac{2}{3}$
  • D
    None of these.
Answer
Correct option: A.
$\frac{3}{5}$
A fraction whose numerator is less than the denominator is called a proper fraction.
Here, $\frac{3}{5}$ is a proper fraction.
Hence, the correct option is $(a).$
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MCQ 21 Mark
Mark the correct alternative of the following: A fraction equivalent to $\frac{30}{45}$ is:
  • A
    $\frac{3}{4}$
  • B
    $\frac{3}{2}$
  • ✓
    $\frac{2}{3}$
  • D
    None of these.
Answer
Correct option: C.
$\frac{2}{3}$
Fraction equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non$-$zero number.
Therefore, the fraction equivalent to $\frac{30}{45}$ is $\frac{30\div15}{45\div15}=\frac{2}{3}.$
Hence, the correct option is $(c).$
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MCQ 31 Mark
Mark the correct alternative of the following:$\frac{34}{13}$ is an example of:
  • A
    A proper fraction.
  • ✓
    An improper fraction.
  • C
    A mixed fraction.
  • D
    None of these.
Answer
Correct option: B.
An improper fraction.
A fraction whose numerator is less than the denominator is called a proper fraction, otherwise it is called an improper fraction.
Here, $\frac{34}{13}$ is an example of an improper fraction.
Hence, the correct option is $(b).$
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MCQ 41 Mark
Mark the correct alternative of the following:Which of the following is an improper fraction?
  • A
    $\frac{1}{2}$
  • B
    $\frac{3}{7}$
  • ✓
    $\frac{7}{3}$
  • D
    $\frac{3}{15}$
Answer
Correct option: C.
$\frac{7}{3}$
$\frac{7}{3},$ because in an improper fraction, the numerator is more than the denominator.
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MCQ 51 Mark
Mark the correct alternative of the following:If $\frac{\text{a}}{\text{b}}=\frac{4}{3},$ then the value of $\frac{6\text{a}+4\text{b}}{6\text{a}-5\text{b}}$ is:
  • A
    $-1$
  • B
    $3$
  • ✓
    $4$
  • D
    $5$
Answer
Correct option: C.
$4$
$\frac{\text{a}}{\text{b}}=\frac{4}{3}$
$\Rightarrow\text{a}=\frac{4\text{b}}{3}$
On putting the value of $\text{a}=\frac{4\text{b}}{3}$ in $\frac{6\text{a}+\text{4b}}{6\text{a}-5\text{b}},$ we get:
$\frac{6\text{a}+4\text{b}}{6\text{a}-5\text{b}}=\frac{6\Big(\frac{4\text{b}}{3}\Big)+4\text{b}}{6\Big(\frac{4\text{b}}{3}\Big)-5\text{b}}=\frac{\frac{24\text{b}}{3}+4\text{b}}{\frac{24\text{b}}{3}-5\text{b}}$
$\ce{LCM}$ of $3$ and $1$ is $3.$
$\frac{\frac{24\text{b}}{3}+\frac{4\text{b}\times3}{1\times3}}{\frac{24\text{b}}{3}-\frac{5\text{b}\times3}{1\times3}}$
$=\frac{\frac{24\text{b}}{3}+\frac{12\text{b}}{3}}{\frac{24\text{b}}{3}-\frac{15\text{b}}{3}}$
$=\frac{\frac{24\text{b}+12\text{b}}{3}}{\frac{24\text{b}-15\text{b}}{3}}$
$=\frac{\frac{36\text{b}}{3}}{\frac{9\text{b}}{3}}$
$=\frac{36}{9}$
On dividing the numerator denominator by the $\ce{HCF}$ of $36 9,$ we get:
$\frac{36\div9}{9\div9}=4$
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MCQ 61 Mark
Mark the correct alternative of the following:The smallest of the fractions $\frac{3}{5},\frac{2}{3},\frac{5}{6},\frac{7}{10}$ is:
  • A
    $\frac{2}{3}$
  • ✓
    $\frac{3}{5}$
  • C
    $\frac{5}{6}$
  • D
    $\frac{7}{10}$
Answer
Correct option: B.
$\frac{3}{5}$
Fractions can be compared by converting them into like fractions and then arranging them in ascending or descending order.
$\frac{3}{5}=\frac{3}{5}\times\frac{6}{6}=\frac{18}{30}$
$\frac{2}{3}=\frac{2}{3}\times\frac{10}{10}=\frac{20}{30}$
$\frac{5}{6}=\frac{5}{6}\times\frac{5}{5}=\frac{25}{30}$
$\frac{7}{10}=\frac{7}{10}\times\frac{3}{3}=\frac{21}{30}$
We know,
$18 < 20 < 21 < 25$
$\Rightarrow\frac{18}{30}<\frac{20}{30}<\frac{21}{30}<\frac{25}{30}$
$\Rightarrow\frac{3}{5}<\frac{2}{3}<\frac{7}{10}<\frac{5}{6}$
$\therefore$ the smallest fraction is $\frac{3}{5}.$
Hence, the correct option is $(b).$
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MCQ 71 Mark
Mark the correct alternative of the following:A fraction equivalent to $\frac{8}{12}$ is:
  • A
    $\frac{8+4}{12+4}$
  • ✓
    $\frac{8\div4}{12\div4}$
  • C
    $\frac{8-4}{12-4}$
  • D
    None of these.
Answer
Correct option: B.
$\frac{8\div4}{12\div4}$
Fraction equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non$-$zero number.
Therefore, the fraction equivalent to $\frac{8}{12}$ is $\frac{8-4}{12-4}.$
Hence, the correct option is $(b).$
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MCQ 81 Mark
Mark the correct alternative of the following:If $\frac{5}{12}$ is equivalent of $\frac{\text{x}}{3},$ then $x =$
  • ✓
    $\frac{5}{4}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{5}{3}$
  • D
    $\frac{3}{5}$
Answer
Correct option: A.
$\frac{5}{4}$
$\frac{5}{12}=\frac{\text{x}}{3}$
On cross$-$multiplying, we get:
$5\times3=\text{x}\times12$
$\Rightarrow\text{x}=\frac{5\times3}{12}$
$\Rightarrow\text{x}=\frac{15}{12}$
$\text{x}=\frac{5}{4}$
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MCQ 91 Mark
Mark the correct alternative of the following: A fraction equivalent to $\frac{2}{3}$ is:
  • A
    $\frac{2+3}{3+3}$
  • B
    $\frac{2-1}{3-1}$
  • ✓
    $\frac{2\times5}{3\times5}$
  • D
    $\frac{2+5}{3+5}$
Answer
Correct option: C.
$\frac{2\times5}{3\times5}$
Fraction equivalent to a given fraction can be obtained by multiplying or dividing its numerator and denominator by a non$-$zero number.
Therefore, the fraction equivalent to $\frac{2}{3}$ is $\frac{2\times5}{3\times5}.$
Hence, the correct option is $(c).$
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MCQ 101 Mark
Mark the correct alternative of the following:Which of the following fractions is the smallest? $\frac{1}{2},\frac{3}{7},\frac{3}{5},\frac{4}{9}$
  • A
    $\frac{4}{9}$
  • B
    $\frac{3}{5}$
  • ✓
    $\frac{3}{7}$
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
$\frac{3}{7}$
The $\ce{LCM}$ of numerators is $12,$ so we can convert each fraction into an equivalent fraction with numerator $12.$
$\frac{1}{2}=\frac{1}{2}\times\frac{12}{12}=\frac{12}{24}$
$\frac{3}{7}=\frac{3}{7}\times\frac{4}{4}=\frac{12}{28}$
$\frac{3}{5}=\frac{3}{5}\times\frac{4}{4}=\frac{12}{20}$
$\frac{4}{9}=\frac{4}{9}\times\frac{3}{3}=\frac{12}{27}$
When numerator is the same, the fraction with greater denominator is the smallest.
Thus, $\frac{3}{7}$ is the smallest fraction.
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MCQ 111 Mark
Mark the correct alternative of the following:If $\frac{1}{2}+\frac{1}{\text{x}}=2,$ then $x =$
  • A
    $\frac{2}{5}$
  • B
    $\frac{5}{2}$
  • C
    $\frac{3}{2}$
  • ✓
    $\frac{2}{3}$
Answer
Correct option: D.
$\frac{2}{3}$
$\frac{1}{2}+\frac{1}{\text{x}}=2$
$\Rightarrow\frac{1}{\text{x}}=2-\frac{1}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{2\times2}{1\times2}-\frac{1\times1}{2\times1}$
$\Rightarrow\frac{1}{\text{x}}=\frac{4}{2}-\frac{1}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{4-1}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{3}{2}$
$\text{x}=\frac{2}{3}$
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MCQ 121 Mark
Mark the correct alternative of the following:A fraction equivalent to $\frac{3}{5}$ is:
  • A
    $\frac{3+2}{5+2}$
  • B
    $\frac{3-2}{5-2}$
  • ✓
    $\frac{3\times2}{5\times2}$
  • D
    None of these.
Answer
Correct option: C.
$\frac{3\times2}{5\times2}$
On dividing the numerator $\&$ denominator by $2,$ we get $\frac{3}{5}.$
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MCQ 131 Mark
Mark the correct alternative of the following:Which of the following fractions is the smallest? $\frac{5}{9},\frac{4}{9},\frac{2}{9},\frac{11}{9}$
  • A
    $\frac{11}{9}$
  • B
    $\frac{4}{9}$
  • C
    $\frac{5}{9}$
  • ✓
    $\frac{2}{9}$
Answer
Correct option: D.
$\frac{2}{9}$
$2 < 4 < 5 < 11$
$\Rightarrow\frac{2}{9}<\frac{4}{9}<\frac{5}{9}<\frac{11}{9}$
$\therefore$ the smallest fraction is $\frac{2}{9}.$
Hence, the correct option is $(d).$
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MCQ 141 Mark
Mark the correct alternative of the following:If $\frac{11}{7}=\frac{77}{\text{x}},$ then $x =$
  • ✓
    $28$
  • B
    $\frac{77}{28}$
  • C
    $44$
  • D
    $308$
Answer
Correct option: A.
$28$
$\frac{11}{7}=\frac{77}{\text{x}}$
On cross$-$multiplying, we get:
$11\times\text{x}=77\times4$
$\Rightarrow\text{x}=\frac{77\times4}{11}$
$\Rightarrow\text{x}=\frac{7\times11\times4}{11}$
$\text{x}=28$
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MCQ 151 Mark
Mark the correct alternative of the following:$\frac{1}{2\frac{1}{3}}+\frac{1}{1\frac{3}{4}}$ is equal to:
  • A
    $\frac{7}{14}$
  • B
    $\frac{12}{49}$
  • C
    $4\frac{1}{2}$
  • ✓
    None of these.
Answer
Correct option: D.
None of these.
$\frac{1}{2\frac{1}{3}}+\frac{1}{1\frac{3}{4}}$
$=\frac{1}{\frac{2\times3+1}{3}}+\frac{1}{\frac{1\times4+3}{4}}$
$=\frac{1}{\frac{7}{3}}+\frac{1}{\frac{7}{4}}$
$=\frac{3}{7}+\frac{4}{7}$
$=\frac{3+4}{7}$
$=\frac{7}{7}$
$=1$
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MCQ 161 Mark
Mark the correct alternative of the following:If $\frac{45}{60}$ is equivalent to $\frac{3}{\text{x}},$ then the value of $x$ is:
  • A
    $3$
  • B
    $6$
  • ✓
    $4$
  • D
    $9$
Answer
Correct option: C.
$4$
$\frac{45}{60}=\frac{3}{\text{x}}$
$\Rightarrow\frac{45\div15}{60\div15}=\frac{3}{\text{x}}$
$\Rightarrow\frac{3}{4}=\frac{3}{\text{x}}$
$\text{x}=4$
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MCQ 171 Mark
Mark the correct alternative of the following:Which of the following fractions is the greatest of all?
$\frac{7}{8},\frac{6}{7},\frac{4}{5},\frac{5}{6}$
  • A
    $\frac{6}{7}$
  • B
    $\frac{4}{5}$
  • C
    $\frac{5}{6}$
  • ✓
    $\frac{7}{8}$
Answer
Correct option: D.
$\frac{7}{8}$
The $\text{LCM}$ of $8, 7, 6$ and $5$ is $840,$ so we can convert each fraction into an equivalent fraction with denominator $840$.
$\frac{7}{8}=\frac{7}{8}\times\frac{105}{105}=\frac{735}{840}$
$\frac{6}{7}=\frac{6}{7}\times\frac{120}{120}=\frac{720}{840}$
$\frac{4}{5}=\frac{4}{5}\times\frac{168}{168}=\frac{672}{840}$
$\frac{5}{6}=\frac{5}{6}\times\frac{140}{140}=\frac{700}{840}$
When denominator is the same, the fraction with the largest numerator is the greatest.
Thus, $\frac{7}{8}$ is the greatest fraction among all.
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MCQ 181 Mark
Mark the correct alternative of the following:Which of the following are like fractions?
  • A
    $\frac{3}{5},\frac{3}{7},\frac{3}{11},\frac{3}{16}$
  • ✓
    $\frac{5}{11},\frac{7}{11},\frac{15}{11},\frac{2}{11}$
  • C
    $\frac{2}{3},\frac{3}{4},\frac{4}{5},\frac{6}{7}$
  • D
    None of these.
Answer
Correct option: B.
$\frac{5}{11},\frac{7}{11},\frac{15}{11},\frac{2}{11}$
Because like fractions are the fractions with the same denominator.
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MCQ 191 Mark
Mark the correct alternative of the following:Which of the following is a proper fraction?
  • A
    $\frac{4}{3}$
  • ✓
    $\frac{3}{4}$
  • C
    $1\frac{3}{4}$
  • D
    $2\frac{1}{5}$
Answer
Correct option: B.
$\frac{3}{4}$
$\frac{3}{4},$ because in a proper fraction, the numerator is less than the denominator.
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MCQ 201 Mark
Mark the correct alternative of the following : What is the value of $\frac{\text{a}+\text{b}}{\text{a}-\text{b}},$ if $\frac{\text{a}}{\text{b}}=4?$
  • A
    $\frac{3}{5}$
  • ✓
    $\frac{5}{3}$
  • C
    $\frac{4}{5}$
  • D
    $\frac{5}{4}$
Answer
Correct option: B.
$\frac{5}{3}$
$\frac{\text{a}}{\text{b}}=4$
$\Rightarrow\text{a}=4\text{b}$
On putting the value of a in $\frac{\text{a}+\text{b}}{\text{a}-\text{b}},$ we get:
$\frac{\text{a}+\text{b}}{\text{a}-\text{b}}=\frac{4\text{b}+\text{b}}{4\text{b}-\text{b}}=\frac{5\text{b}}{3\text{b}}$
On dividing the numerator denominator by $b,$ we get $\frac{5}{3}.$
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MCQ 211 Mark
Mark the correct alternative of the following:If $\frac{1}{3}+\frac{1}{2}+\frac{1}{\text{x}}=4,$ then $x = ?$
  • A
    $\frac{5}{18}$
  • ✓
    $\frac{6}{19}$
  • C
    $\frac{18}{5}$
  • D
    $\frac{24}{11}$
Answer
Correct option: B.
$\frac{6}{19}$
$\frac{1}{3}+\frac{1}{2}+\frac{1}{\text{x}}=4$
$\Rightarrow\frac{1}{\text{x}}=4-\frac{1}{3}-\frac{1}{2}$
$\Rightarrow\frac{1}{\text{x}}=\frac{4\times6}{1\times6}-\frac{1\times2}{3\times2}-\frac{1\times3}{2\times3}$
$\Rightarrow\frac{1}{\text{x}}=\frac{24}{6}-\frac{2}{6}-\frac{3}{6}$
$\Rightarrow\frac{1}{\text{x}}=\frac{24-2-3}{6}$
$\Rightarrow\frac{1}{\text{x}}=\frac{19}{6}$
$\text{x}=\frac{6}{19}$
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MCQ 221 Mark
Mark the correct alternative of the following:If $\frac{1}{5}-\frac{1}{6}=\frac{4}{\text{x}},$ then $x =$
  • A
    $-120$
  • B
    $-100$
  • C
    $100$
  • ✓
    $120$
Answer
Correct option: D.
$120$
$\frac{1}{5}-\frac{1}{6}=\frac{4}{\text{x}}$
$\Rightarrow\frac{1\times6}{5\times6}-\frac{1\times5}{6\times5}=\frac{4}{\text{x}}$
$\Rightarrow\frac{6}{30}-\frac{5}{30}=\frac{4}{\text{x}}$
$\Rightarrow\frac{6-5}{30}=\frac{4}{\text{x}}$
$\Rightarrow\frac{1}{30}=\frac{4}{\text{x}}$
$\Rightarrow1\times\text{x}=4\times30$
$\text{x}=120$
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MCQ 231 Mark
Mark the correct alternative of the following:$\frac{1}{3}+\text{x}=3,$ then $x =$
  • A
    $\frac{7}{3}$
  • B
    $\frac{2}{3}$
  • C
    $\frac{4}{3}$
  • ✓
    $\frac{8}{3}$
Answer
Correct option: D.
$\frac{8}{3}$
$\frac{1}{3}+\text{x}=3$
$\Rightarrow\frac{1}{3}+\text{x}-\frac{1}{3}=3-\frac{1}{3}$
$\Rightarrow\text{x}=3-\frac{1}{3}$
$\Rightarrow\text{x}=\frac{3\times3}{1\times3}-\frac{1}{3}$
$\Rightarrow\text{x}=\frac{9}{3}-\frac{1}{3}$
$\Rightarrow\text{x}=\frac{9-1}{3}$
$\text{x}=\frac{8}{3}$
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MCQ 241 Mark
Mark the correct alternative of the following:If $\frac{1}{4}$ is equivalent to $\frac{\text{x}}{28},$ then the value of $x$ is:
  • A
    $6$
  • ✓
    $7$
  • C
    $8$
  • D
    $9$
Answer
Correct option: B.
$7$
$\frac{1}{4}=\frac{\text{x}}{28}$
$\Rightarrow\frac{1\times7}{4\times7}=\frac{\text{x}}{28}$
$\Rightarrow\frac{7}{28}=\frac{\text{x}}{28}$
$\text{x}=7$
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MCQ 251 Mark
Mark the correct alternative of the following : $\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$ is equal to:
  • A
    $\frac{15}{24}$
  • B
    $\frac{17}{24}$
  • ✓
    $\frac{19}{24}$
  • D
    $\frac{21}{24}$
Answer
Correct option: C.
$\frac{19}{24}$
$\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$
$\text{LCM}$ of $8, 4$ and $12$ is $24$.
$\Rightarrow\frac{5\times3}{8\times3}+\frac{3\times6}{4\times6}-\frac{7\times2}{12\times2}$
$\Rightarrow\frac{15}{24}+\frac{18}{24}-\frac{14}{24}$
$\Rightarrow\frac{15+18-14}{24}=\frac{19}{24}$
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