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MATHS Assertion (A) & Reason (B) MCQ

Fractions · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 6 questions.

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Assertion (A) & Reason (B) MCQ

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6 questions · timed · auto-graded

MCQ 11 Mark
Assertion (A): The reciprocal of the fraction $\frac{8}{5}$ is $\frac{5}{8}$.
Reason (R): The reciprocal of an improper fraction is always a proper fraction.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of
    Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • ✓
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: C.
Assertion (A) is true but Reason (R) is false.
(c): The reciprocal of $\frac{8}{5}$ is $\frac{5}{8}$ since $\frac{8}{5} \times \frac{5}{8}=1 . \quad \therefore$ A is true.
R is false since there exists improper fractions such as $\frac{2}{2}, \frac{3}{3}$, etc., whose reciprocals are improper fractions.
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MCQ 21 Mark
Assertion (A): $\frac{1}{4}$ and $\frac{8}{24}$ are equivalent fractions.
Reason ( R ):If $\frac{a}{b}$ and $\frac{c}{d}$ are two equivalent fractions then $a d=b c$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • ✓
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: D.
Assertion (A) is false but Reason (R) is true.
(d): We have $1 \times 24=24$ and $4 \times 8=32$.
$\therefore \frac{1}{4}$ and $\frac{8}{24}$ are not equivalent fractions. So, $A$ is false.
If $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent fractions then $\frac{a}{b}=\frac{c}{d} \Rightarrow a d=b c$. [by cross multiplication]
$\therefore R$ is true.
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MCQ 31 Mark
Assertion (A): $\frac{6}{11}<\frac{7}{12}$.
Reason (R): $\frac{a}{b}<\frac{c}{d}$ if $b c<a d$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • ✓
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: C.
Assertion (A) is true but Reason (R) is false.
(c): $\frac{6}{11}<\frac{7}{12}$ since $6 \times 12<7 \times 11 . \quad[\because 72<77]$
$\therefore A$ is true. R is false since $\frac{a}{b}<\frac{c}{d}$ if $a d<b c$.
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MCQ 41 Mark
Assertion (A): Aman ate $\frac{4}{7}$ of the pizza and his sister Ramya ate the remaining part. Then, $\frac{3}{7}$ of the pizza was eaten by Ramya.
Reason (R): $\frac{1}{7}+\frac{3}{7}=\frac{4}{7}$
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: B.
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
(b): Aman ate $\frac{4}{7}$ of the pizza. Remaining part of the pizza $=1-\frac{4}{7}=\frac{7-4}{7}=\frac{3}{7}$. Part of the pizza eaten by Ramya $=\frac{3}{7}$.
$\therefore A$ is true.
We have, $\frac{1}{7}+\frac{3}{7}=\frac{1+3}{7}=\frac{4}{7}$.
$\therefore R$ is also true but $R$ is not the correct explanation of $A$.
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MCQ 51 Mark

Assertion (A): The fraction $\frac{4}{9}$ is in its lowest terms.
Reason (R): The LCM of 4 and 9 is 36.

  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: A.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(a): HCF of 4 and 9 is 1 . And so, the fraction $\frac{4}{9}$ is in its lowest terms.
$\therefore A$ is true.
Now, LCM $(4,9)=36=4 \times 9$.
$\therefore \operatorname{HCF}(4,9)=1 \quad[\because \quad$ if $\operatorname{LCM}=$ product of numbers then $HCF =1]$
$\Rightarrow \frac{4}{9}$ is in the lowest terms.
Thus, $R$ is also true and $R$ is the correct explanation of $A$.
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MCQ 61 Mark
Assertion (A): $\frac{4}{11}, \frac{5}{11}$ and $\frac{8}{11}$ are all proper fractions.
Reason $( R )$ : The fractions $\frac{4}{11}, \frac{5}{11}$ and $\frac{8}{11}$ have the same denominator.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • ✓
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
Answer
Correct option: B.
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
(b): $\frac{4}{11}, \frac{5}{11}$ and $\frac{8}{11}$ are all proper fractions because their respective numerators are less than their denominators.
$\therefore A$ is true.
It is also clear that the given fractions have the same denominator and so they are like fractions.
$\therefore R$ is also true but R is not the correct explanation of A .
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Assertion (A) & Reason (B) MCQ - MATHS STD 7 Questions - Vidyadip