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MATHS M.C.Q. [1 Marks Each]

Operations On Rational Numbers · Gujarat Board (GSEB) STD 7 (GSEB - English Medium). 30 questions.

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M.C.Q. [1 Marks Each]

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30 questions · auto-graded multiple-choice test.

MCQ 11 Mark
$\frac{-7}{13}-\Big(\frac{-8}{15}\Big)=$
  • A
    $-\frac{239}{195}$
  • B
    $\frac{29}{195}$
  • C
    $\frac{-29}{195}$
  • ✓
    None of these.
Answer
Correct option: D.
None of these.
$\frac{-7}{13}-\Big(\frac{-8}{15}\Big)$
$=​​\frac{-7}{13}+\frac{8}{15}$ $\Big[-\Big(\frac{-8}{15}\Big)=\frac{8}{15}\Big]$
$=\frac{-7\times15+8\times13}{195}$ $(LCM$ of $13$ and $15 = 195)$
$=\frac{-105+104}{195}$
$=\frac{-1}{195}$
Hence, the correct answer is option $(d)$.
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MCQ 21 Mark
$1\div\frac{1}{3}=$
  • A
    $\frac{1}{3}$
  • ✓
    $3$
  • C
    $1\frac{1}{3}$
  • D
    $3\frac{1}{3}$
Answer
Correct option: B.
$3$
$1\div\frac{1}{3}$
$=1\times3$ $\Big(\text{x}\div\text{y}=\text{x}\times\frac{1}{\text{y}}\Big)$
$=3$
Hence, the correct answer is option $(b)$.
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MCQ 31 Mark
What should be added to $\frac{-7}{9}$ to get?
  • A
    $\frac{11}{9}$
  • B
    $\frac{-11}{9}$
  • C
    $\frac{25}{9}$
  • ✓
    $\frac{-25}{9}$
Answer
Correct option: D.
$\frac{-25}{9}$
Sum of the given number and the required number $= 2$
Given number $=\frac{-7}{9}$
$\therefore$ Required number = Sum of the numbers - Given number
$=2-\Big(\frac{-7}{9}\Big)$
$=\frac{2}{1}+\frac{7}{9}$
$=\frac{2\times9+7\times1}{9}$
$=\frac{18+7}{9}$
$=\frac{25}{9}$
Hence, the correct answer is option $(d)$.
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MCQ 41 Mark
If $\frac{\text{x}}{3}+\frac{1}{3}=1,$ then $x = ?$
  • A
    $\frac{3}{4}$
  • ✓
    $\frac{4}{3}$
  • C
    $-\frac{3}{4}$
  • D
    $\frac{-4}{3}$
Answer
Correct option: B.
$\frac{4}{3}$
$​​\frac{\text{x}}{2}+\frac{1}{3}=1$
$\Rightarrow\frac{\text{x}}{2}=1-\frac{1}{3}$
$\Rightarrow\frac{\text{x}}{2}=\frac{3\times1-1}{3}$
$\Rightarrow\frac{\text{x}}{2}=\frac{3-1}{3}$
$\Rightarrow\frac{\text{x}}{2}=\frac{2}{3}$
$\Rightarrow\frac{2\text{x}}{2}=\frac{2\times2}{3}$ (Multiplying both sides by $2$)
$\Rightarrow\text{x}=\frac{4}{3}$
Hence, the correct answer is option $(b)$.
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MCQ 51 Mark
The product $3\times\frac{1}{7}\times1\frac{5}{6}\times1\frac{2}{5}\times1\frac{1}{11}$is equal to:
  • A
    $5\frac{5}{8}$
  • B
    $5\frac{4}{5}$
  • ✓
    $8\frac{4}{5}$
  • D
    $7\frac{4}{5}$
Answer
Correct option: C.
$8\frac{4}{5}$
$3\frac{1}{7}\times1\frac{5}{6}\times1\frac{2}{5}\times1\frac{1}{11}$
$=\frac{22}{7}\times\frac{11}{6}\times\frac{7}5{}\times\frac{12}{11}$
$=\frac{22\times11\times7\times2}{7\times6\times5\times11}$ $\Big(\frac{\text{a}}{\text{b}}\times\frac{\text{c}}{\text{d}}=\frac{\text{a}\times\text{c}}{\text{b}\times\text{d}}\Big)$
$=\frac{44}{5}$
$=\frac{8\times5+4}{5}$
$=8\frac{4}{5}$
Hence, the correct answer is option $(c)$.
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MCQ 61 Mark
$1\div\frac{-5}{7}=$
  • A
    $\frac{2}{7}$
  • B
    $\frac{5}{7}$
  • C
    $-\frac{2}{7}$
  • ✓
    $\frac{-7}{5}$
Answer
Correct option: D.
$\frac{-7}{5}$
$1\div​​\frac{-5}{7}$
$=1\times\frac{7}{-5}$ $\Big(\text{x}\div\text{y}=\text{x}\times\frac{1}{\text{y}}\Big)$
$=\frac{7}{-5}$
$=\frac{7\times(-1)}{-5\times(-1)}$
$=\frac{-7}{5}$
Hence, the correct answer is option $(d)$.
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MCQ 71 Mark
If the product of two non-zero rational numbers is $1$, Then they are:
  • A
    Additve inverse of each other.
  • B
    Multiplicative inverse of each other.
  • C
    Reciprocal of each other.
  • ✓
    Both (b) and (c)
Answer
Correct option: D.
Both (b) and (c)
For every non-zero rational number $\frac{\text{a}}{\text{b}}$ there exists a rational number $\frac{\text{b}}{\text{a}}$ such that:
$\frac{\text{a}}{\text{b}}\times\frac{\text{b}}{\text{a}}=1$
Here, the rational number $\frac{\text{b}}{\text{a}}$ is called the multiplicative inverse or reciprocal of $\frac{\text{a}}{\text{b}}$
Thus, if the product of two non-zero rational numbers is $1$, then they are multiplicative inverse or reciprocal of each other.
Hence, the correct answer is option $(d)$.
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MCQ 81 Mark
$-2\frac{3}{7}+4=?$
  • A
    $\frac{-11}{7}$
  • ✓
    $\frac{11}{7}$
  • C
    $\frac{-45}{7}$
  • D
    $\frac{45}{7}$
Answer
Correct option: B.
$\frac{11}{7}$
$?=-2​​\frac{3}{7}+4$
$\Rightarrow?=-\frac{17}{7}+\frac{4}{1}$
$\Rightarrow?=\frac{-17\times1+4\times7}{7}$
$\Rightarrow=\frac{-17+28}{7}$
$\Rightarrow?=\frac{11}{7}$
Hence, the correct answer is option $(b)$.
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MCQ 91 Mark
$(-2)\div\Big(-\frac{5}{3}\Big)=$
  • A
    $\frac{5}{6}$
  • B
    $-\frac{5}{6}$
  • ✓
    $\frac{6}{5}$
  • D
    $\frac{-6}{5}$
Answer
Correct option: C.
$\frac{6}{5}$
$(-2)\div\Big(​​-\frac{5}{3}\Big)$
$=-2\times\Big(-\frac{3}{5}\Big)$ $\text{x}\div\text{y}=\text{x}\times\frac{1}{\text{y}}$
$=\frac{-2}{1}\times\frac{(-3)}{5}$
$=\frac{-2\times(-3)}{1\times5}$ $\Big(\frac{\text{a}}{\text{b}}\times\frac{\text{c}}{\text{d}}=\frac{\text{a}\times\text{c}}{\text{b}\times\text{d}}\Big)$
$=\frac{6}{5}$
Hence, the correct answer is option $(c)$.
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MCQ 101 Mark
$\frac{-5}{13}+?=-1$
  • A
    $\frac{8}{13}$
  • ✓
    $\frac{-8}{13}$
  • C
    $\frac{-18}{13}$
  • D
    $\frac{18}{13}$
Answer
Correct option: B.
$\frac{-8}{13}$
$\frac{-5}{13}+?=-1$
$\Rightarrow?=-1-\Big(\frac{-5}{13}\Big)$
$\Rightarrow?=-1+\frac{5}{13}$ $\Big[-\Big(\frac{-5}{13}=\frac{5}{13}\Big)\Big]$
$\Rightarrow?=\frac{-1\times13+5}{13}$
$\Rightarrow\frac{-13+5}{13}$
$\Rightarrow=\frac{-8}{13}$
Hence, the correct answer is option $(b)$.
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MCQ 111 Mark
What should be subtracted from $\frac{-2}{3}$ to get$\frac{4}{5}?$
  • A
    $\frac{22}{15}$
  • ✓
    $\frac{-22}{15}$
  • C
    $\frac{15}{22}$
  • D
    $\frac{-15}{22}$
Answer
Correct option: B.
$\frac{-22}{15}$
Difference of the given number and required number $=\frac{4}{5}$
Given number $=\frac{-2}{3}$
$\therefore$ Required number = Given number - Difference of the numbers
$=\frac{-2}{3}-\frac{4}{5}$
$=\frac{-2}{3}+\Big(\frac{-4}{5}\Big)$
$=\frac{-2\times5+(-4)\times3}{15}$
$=\frac{-10+(-12)}{15}$
$=\frac{-22}{15}$
Hence, the correct answer is option $(b)$.
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MCQ 121 Mark
The multiplicative inverse of $\frac{4}{-5}$ of:
  • A
    $-\frac{4}{5}$
  • B
    $\frac{5}{4}$
  • ✓
    $\frac{5}{-4}$
  • D
    $​​\frac{-5}{-4}$
Answer
Correct option: C.
$\frac{5}{-4}$
We know that the multiplicative inverse of the rational number $\frac{\text{a}}{\text{b}}\text{ is }\frac{\text{b}}{\text{a}}$
$\therefore$ Multiplicative inverse of $\frac{4}{-5}=\frac{-5}{4}=\frac{5}{-4}$
Hence, the correct answer is option $(c)$.
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MCQ 131 Mark
$0\div\frac{3}{5}=$
  • ✓
    $0$
  • B
    $\frac{5}{3}$
  • C
    $\frac{3}{5}$
  • D
    $-\frac{3}{5}$
Answer
Correct option: A.
$0$
We know that $0$ divided by any non-zero rational number is always $0$.
$\therefore0\div\frac{3}{5}=0$
$\Big(0\div\frac{\text{a}}{\text{b}}=0\Big)$
Hence, the correct answer is option $(a)$.
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MCQ 141 Mark
Reciprocal of $\frac{-3}{4}$ is:
  • A
    $\frac{3}{4}$
  • B
    $\frac{4}{3}$
  • ✓
    $\frac{-4}{3}$
  • D
    None of these.
Answer
Correct option: C.
$\frac{-4}{3}$
We know that the reciprocal of the rational number $\frac{\text{a}}{\text{b}}\text{ is }\Big(\frac{\text{a}}{\text{b}}\Big)^{-1}=\frac{\text{b}}{\text{a}}$
$\therefore$ Reciprocal of $\frac{-3}{4}$
$=\Big(\frac{-3}{4}\Big)^{-1}$
$=\frac{4}{-3}$
$=\frac{4\times(-1)}{-3\times(-1)}$
$=\frac{-4}{3}$
Hence, the correct answer is option $(c)$.
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MCQ 151 Mark
$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=$
  • ✓
    $\frac{3}{4}$
  • B
    $-\frac{3}{4}$
  • C
    $\frac{-7}{12}$
  • D
    $\frac{7}{12}$
Answer
Correct option: A.
$\frac{3}{4}$
$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
$=\frac{5}{4}+\Big(\frac{-7}{6}\Big)+\frac{2}{3}$ $\Big[-\Big(\frac{-2}{3}\Big)=\frac{2}{3}\Big]$
$=\frac{5\times3+(-7)\times2+2\times4}{12}$ $(LCM$ of $3, 4$ and $6 = 12)$
$=\frac{15-14+8}{12}$
$=\frac{9}{12}$
$=\frac{9\div3}{12\div3}$ $($Dividing numerator and denominator by $3)$
$=\frac{3}{4}$
Hence, the correct answer is option $(a)$.
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MCQ 161 Mark
$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=$
  • ✓
    $\frac{3}{4}$
  • B
    $-\frac{3}{4}$
  • C
    $\frac{-7}{12}$
  • D
    $\frac{7}{12}$
Answer
Correct option: A.
$\frac{3}{4}$
A
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MCQ 171 Mark
If $\frac{x}{2}+\frac{1}{3}=1$, then $x=$
  • A
    $\frac{3}{4}$
  • ✓
    $\frac{4}{3}$
  • C
    $-\frac{3}{4}$
  • D
    $\frac{-4}{3}$
Answer
Correct option: B.
$\frac{4}{3}$
B
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MCQ 181 Mark
$(-2) \div\left(-\frac{5}{3}\right)=$
  • A
    $\frac{5}{6}$
  • B
    $-\frac{5}{6}$
  • ✓
    $\frac{6}{5}$
  • D
    $\frac{-6}{5}$
Answer
Correct option: C.
$\frac{6}{5}$
C
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MCQ 201 Mark
$\frac{-7}{13}-\left(\frac{-8}{15}\right)=$
  • A
    $-\frac{239}{195}$
  • B
    $\frac{29}{195}$
  • C
    $\frac{-29}{195}$
  • ✓
    none of these
Answer
Correct option: D.
none of these
D
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MCQ 211 Mark
The product $3 \frac{1}{7} \times 1 \frac{5}{6} \times 1 \frac{2}{5} \times 1 \frac{1}{11}$ is equal to
  • A
    $5 \frac{8}{5}$
  • B
    $5 \frac{4}{5}$
  • ✓
    $8 \frac{4}{5}$
  • D
    $7 \frac{4}{5}$
Answer
Correct option: C.
$8 \frac{4}{5}$
C
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MCQ 231 Mark
$-2 \frac{3}{7}+4=$ ?
  • A
    $\frac{-11}{7}$
  • ✓
    $\frac{11}{7}$
  • C
    $\frac{-45}{7}$
  • D
    $\frac{45}{7}$
Answer
Correct option: B.
$\frac{11}{7}$
B
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MCQ 251 Mark
$\frac{-5}{13}+?=-1$
  • A
    $\frac{8}{13}$
  • ✓
    $\frac{-8}{13}$
  • C
    $\frac{-18}{13}$
  • D
    $\frac{18}{13}$
Answer
Correct option: B.
$\frac{-8}{13}$
B
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MCQ 261 Mark
$1 \div \frac{-5}{7}=$
  • A
    $\frac{2}{7}$
  • B
    $\frac{5}{7}$
  • C
    $-\frac{2}{7}$
  • ✓
    $\frac{-7}{5}$
Answer
Correct option: D.
$\frac{-7}{5}$
D
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MCQ 271 Mark
The multiplicative inverse ot $\frac{2}{-5}$ is
  • A
    $-\frac{4}{5}$
  • B
    $\frac{5}{4}$
  • ✓
    $\frac{5}{-4}$
  • D
    $\frac{-5}{-4}$
Answer
Correct option: C.
$\frac{5}{-4}$
C
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MCQ 281 Mark
Reciprocal of $\frac{-3}{4}$ is
  • A
    $\frac{3}{4}$
  • B
    $\frac{4}{3}$
  • ✓
    $\frac{-4}{3}$
  • D
    none of these
Answer
Correct option: C.
$\frac{-4}{3}$
C
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MCQ 291 Mark
What should be subtracted from $\frac{-2}{3}$ to get $\frac{4}{5}$ ?
  • A
    $\frac{22}{15}$
  • ✓
    $\frac{-22}{15}$
  • C
    $\frac{15}{22}$
  • D
    $\frac{-15}{22}$
Answer
Correct option: B.
$\frac{-22}{15}$
B
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MCQ 301 Mark
What should be added to $\frac{-7}{9}$ to get 2 ?
  • A
    $\frac{11}{9}$
  • B
    $\frac{-11}{9}$
  • C
    $\frac{-25}{9}$
  • ✓
    $\frac{25}{9}$
Answer
Correct option: D.
$\frac{25}{9}$
D
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