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

Rational Numbers · CBSE STD 7 (CBSE - English Medium). 30 questions.

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M.C.Q. [1 Marks Each]

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30 questions · timed · auto-graded

MCQ 11 Mark
What is the additive identity element in the set of whole numbers?
  • ✓
    $0$
  • B
    $1$
  • C
    $-1$
  • D
    None of these.
Answer
Correct option: A.
$0$
If a is a whole number then $a + 0 = a = 0 + a.$
Therefore, $0$ is the additive identity element for addition of whole number because it does not change the identity or value of the whole number during the operation of addition.
Hence, the correct answer is option $(a).$
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MCQ 21 Mark
$\frac{44}{-77}$ is standard form is:
  • A
    $\frac{4}{-7}$
  • ✓
    $-\frac{4}{7}$
  • C
    $-\frac{44}{77}$
  • D
    None of these
Answer
Correct option: B.
$-\frac{4}{7}$
The denominator of $\frac{44}{-77}$ is nagative.
Hence, the correct answer is option $(b).$
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MCQ 31 Mark
If $\frac{27}{-45}$ is expressed as a rational number with denominator $5$, then the numerator is:
  • A
    $3$
  • ✓
    $-3$
  • C
    $6$
  • D
    $-6$
Answer
Correct option: B.
$-3$
In order to express $\frac{27}{-45}$ as a rational number with denominator $5$, firstly find a number which gives $5$ when $-45$ is divided by it.
This number is $-45\div5=-9$
Dividing the numerator and denominator of $\frac{27}{-45}$ by -9,
We have:
$\frac{27}{-45}=\frac{27\div(-9)}{-45\div(-9)}=\frac{-3}{5}$
Thus, the numerator is $-3.$
Hence, the correct answer is option $(b).$
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MCQ 41 Mark
If the rational numbers $\frac{-2}{3}\text{ and }\frac{4}{\text{x}}$ represent a pair of equivalent rational numbers, then $x$:
  • A
    $6$
  • ✓
    $-6$
  • C
    $3$
  • D
    $-3$
Answer
Correct option: B.
$-6$
It is given that the rational numbers $\frac{-2}{3}\text{ and }\frac{4}{\text{x}}$ represent a pair of equivalent rational numbers.
We know that the values of two equivalent rational numbers is equal.
$\therefore\frac{-2}{3}=\frac{4}{\text{x}}$
$\Rightarrow-2\times\text{x}=4\times3$ $\Big(\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\Rightarrow\text{ad}=\text{bc}\Big)$
$\Rightarrow-2\text{x}=12$
$\Rightarrow\frac{-2\text{x}}{-2}=\frac{12}{-2}$ (Dividing both sides by $-2$)
$\Rightarrow\text{x}=-6$
Hence, the correct answer is option $(b)$.
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MCQ 51 Mark
If $-\frac{3}{8}\text{ and }\frac{\text{x}}{-24}$ are equivalent rational numbers, then $x =?$
  • A
    $3$
  • B
    $6$
  • ✓
    $9$
  • D
    $12$
Answer
Correct option: C.
$9$
It is given that the rational numbers $-\frac{3}{8}\text{ and }\frac{\text{x}}{-24}$ are equivalent rational numbers.
We know that the values of two equivalent rational numbers is equal.
$\therefore\frac{\text{x}}{-24}=-\frac{3}{8}$
$\Rightarrow\text{x}\times8=-3\times(-24)$ $\Big(\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\Rightarrow\text{ad}=\text{bc}\Big)$
$\Rightarrow8\text{x}=72$
$\Rightarrow\frac{8\text{x}}{8}=\frac{72}{8}$
(Dividing both sides by $8$)
$\Rightarrow\text{x}=9 $
Hence, the correct answer is option $(c)$.
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MCQ 61 Mark
If $\frac{-3}{7}=\frac{\text{x}}{35}\text{ then }\text{x}=?$
  • A
    $15$
  • B
    $21$
  • ✓
    $-15$
  • D
    $-21$
Answer
Correct option: C.
$-15$
Firstly, write $\frac{-3}{7}$ as a rational number with denominator $35$.
Multiplying the numerator and denominator of $\frac{-3}{7}$ by $5$,
We have:
$\frac{-3}{7}=\frac{-3\times5}{7\times5}=\frac{-15}{35}$
$\therefore\frac{-3}{7}=\frac{\text{x}}{35}$
$\Rightarrow\frac{-15}{35}=\frac{\text{x}}{35}$
$\Rightarrow\text{x}=-15$
Hence, the correct answer is option $(c)$.
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MCQ 71 Mark
A rational number equal to $\frac{-2}{3}$ is:
  • A
    $\frac{-10}{25}$
  • ✓
    $\frac{10}{-15}$
  • C
    $\frac{-9}{6}$
  • D
    None of these.
Answer
Correct option: B.
$\frac{10}{-15}$
We know that two rational numbers are equal if they have the same standard form.
The rational number $\frac{-2}{3}$ is in its standard form.
Consider the rational number $\frac{10}{-15}$
This rational numbner can be expressed in standerd form as follows:
$\frac{10}{-15}=\frac{10\times(-1)}{-15\times(-1)}=\frac{-10}{15}$ (Multiplying numerator and denominator by $-1$ to make denominator positive)
$HCF$ of $10$ and $15 = 5$
Dividing the numeator and denominator of $\frac{-10}{15}$ by $5$,
We have:
$\frac{-10}{15}=\frac{-10\div5}{15\div5}=\frac{-2}{3}$
Thus, the standard form of $\frac{-10}{15}$ is $\frac{-2}{3},$ which is same as the given rational number.
So, the rational number equal to $\frac{-2}{3}$ is $\frac{-10}{15}$
Let us check why options $(a)$ and $(c)$ are not correct.
The standard form of $\frac{-10}{25}\text{ is }\frac{-2}{5}$
$HCF$ of $10$ and $25 = 5$
Dividing the numerator and denominator of $=\frac{-10}{25}$ by 5,
We have:
$\frac{-10}{25}=\frac{-10\div5}{25\div5}=\frac{-2}{5}$
The standard form of $\frac{-9}{6}\text{ is }\frac{-3}{2}$
$HCF$ of $6$ and $9 = 3$
Dividing the numerator and denominator of $\frac{-9}{3}$by $3$,
We have:
$\frac{-9}{6}=\frac{-9\div3}{6\div2}=\frac{-3}{2}$
Hence, the correct answer is option $(b)$
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MCQ 81 Mark
Which of the following pairs of rational numbers are on the opposite side of the zero on the number line?
  • A
    $\frac{3}{7}\text{ and }\frac{5}{12}$
  • B
    $-\frac{3}{7}\text{ and }\frac{-5}{12}$
  • ✓
    $\frac{3}{7}\text{ and }\frac{-5}{12}$
  • D
    None of these.
Answer
Correct option: C.
$\frac{3}{7}\text{ and }\frac{-5}{12}$
The rational numbers $\frac{3}{7}\text{ and }\frac{5}{12}$ are positive rational numbers. We know that every positive rational number is greater than $0$, so both the rational numbers $\frac{3}{7}\text{ and }\frac{5}{12}$ are represented by points on the right of the zero on the number line.
The rational numbers $-\frac{3}{7}\text{ and }\frac{-5}{12}$ are negative rational numbers. We know that every negative rational number is less than $0$, so both the rational numbers $\frac{3}{7}\text{ and }\frac{5}{12}$ are represented by points on the left of the zero on the number line.
The rational numbers $\frac{3}{7}$ is a positive rational number whereas the rational number $\frac{-5}{12}$ is a negative rational numbers. We know that every negative rational number is less than $0$ and every positive rational number is greater than $0$, so the rational number $\frac{3}{7}$ is represented by point on the right of the zero and $\frac{-5}{12}$ is represented by point on the left of the zero on the number line.
Thus, the rational numbers $-\frac{3}{7}\text{ and }\frac{-5}{12}$ are on the opposite side of the zero on the number line.
Hence, the correct answer is option $(c)$.
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MCQ 91 Mark
The rational number equal to $\frac{2}{-3}$ is:
  • A
    $\frac{14}{-18}$
  • ✓
    $\frac{-6}{9}$
  • C
    $\frac{-8}{-12}$
  • D
    $\frac{3}{-2}$
Answer
Correct option: B.
$\frac{-6}{9}$
We know that two rational numbers are equal if they have the same standard form.
$\frac{2}{-3}=\frac{2\times(-1)}{-3\times(-1)}=\frac{-2}{3}$
The standard form of $\frac{2}{-3}\text{ is }\frac{-2}{3}$
Consider the rational number $\frac{-6}{9}$
$HCF$ of $6$ and $9 = 3$
Dividing the numerator and denominator of $\frac{-6}{9}$ by $3$,
We have:
$\frac{-6}{9}=\frac{-6\div3}{9\div3}=\frac{-2}{3}$
So, the rational number $\frac{-6}{9}$ is equal to $\frac{2}{-3}$
It can be checked that:
Standard form of $\frac{14}{-18}=\frac{-7}{9}$
Standard form of $\frac{3}{-2}=\frac{-3}{2}$
Hence, the correct answer is option $(b)$.
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MCQ 101 Mark
Which of the following is correct?
  • ✓
    $\frac{5}{9}>\frac{-3}{8}$
  • B
    $\frac{5}{9}<\frac{-3}{-8}$
  • C
    $\frac{2}{-3}<\frac{-8}{7}$
  • D
    $\frac{4}{-3}>\frac{-8}{7}$
Answer
Correct option: A.
$\frac{5}{9}>\frac{-3}{8}$
Consider the rational numbers $\frac{5}{9}\text{ and } \frac{-3}{-8}$
We write the rational number $\frac{-3}{-8}$ with positive denominator.
$\frac{-3}{-8}=\frac{-3\times(-1)}{-8\times(-1)}=\frac{3}{8}$
Now, we write the rational numbers so that they have a common denominator.
$LCM$ of $8$ and $9 = 72$
So, $\frac{5}{9}=\frac{5\times8}{9\times8}=\frac{40}{72}$ and $\frac{3}{8}=\frac{3\times9}{8\times9}=\frac{27}{72}$
Now,
$40>27$
$\Rightarrow\frac{40}{72}>\frac{27}{72}$
$\Rightarrow\frac{5}{9}>\frac{3}{8}$
$\Rightarrow\frac{5}{9}>\frac{-3}{-8}$
Hence the correct option is $(a)$.
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MCQ 111 Mark
The whole number nearest to $457$ and divisible by $11$ is:
  • A
    $450$
  • B
    $451$
  • C
    $460$
  • ✓
    $462$
Answer
Correct option: D.
$462$
The numbers $450$ and $460$ are not divisible by $11$.
Now, both the numbers $451$ and $462$ are divisible by $11$.
Distance between $457$ and $451$ on the number line $= 457 - 451 = 6$
Distance between $457$ and $462$ on the number line $= 462 - 457 = 5$
Thus, the whole number nearest to $457$ and divisible by $11$ is $462$.
Hence, the correct answer is option $(d)$.
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MCQ 121 Mark
If $-\frac{3}{4}=\frac{6}{\text{x}},$ then $x =$
  • ✓
    $-8$
  • B
    $4$
  • C
    $-4$
  • D
    $8$
Answer
Correct option: A.
$-8$
$-\frac{3}{4}=\frac{6}{\text{x}}$
$\Rightarrow-3\times\text{x}=6\times4$ $\Big(\frac{\text{a}}{\text{b}}=\frac{\text{c}}{\text{d}}\Rightarrow\text{ad}=\text{bc}\Big)$
$\Rightarrow-3\text{x}=24$
$\Rightarrow\frac{-3\text{x}}{-3}=\frac{24}{-3}$ (Dividing both sides by $-3$)
$\Rightarrow\text{x}=-8$
Hence, the correct answer is option $(a)$.
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MCQ 131 Mark
Which of the following is not zero?
  • A
    $0\times0$
  • B
    $\frac{0}{3}$
  • C
    $\frac{7-7}{3}$
  • ✓
    $9\div0$
Answer
Correct option: D.
$9\div0$
If any number is multiplied by $0$, the product is $0$.
$\therefore0\times0=0$
If $0$ is divided by any number $(\neq0),$ the quotient is always $0$.
$\therefore\frac{0}{3}\text{ and }\frac{7-7}{3}=\frac{0}{3}=0$
Division of any number by $0$ is meaningless and is not defined.
$\therefore9\div0$ is not defined.
Hence, the correct answer is option $(d)$.
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MCQ 141 Mark
What is the multiplicative identity element in the set of whole numbers?
  • A
    $0$
  • ✓
    $1$
  • C
    $-1$
  • D
    None of these.
Answer
Correct option: B.
$1$
We know that if a is a whole number, then $a \times 1 = a = 1 \times a.$
Therefore, $1$ is the multiplicative identity element for multiplication of whole numbers because it does not change the identity or value of the whole number during the operation of multiplication.
Hence, the correct answer is option $(b)$.
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MCQ 151 Mark
$-\frac{102}{119}$ is standard form is:
  • ✓
    $-\frac{6}{7}$
  • B
    $\frac{6}{7}$
  • C
    $-\frac{6}{17}$
  • D
    None of these
Answer
Correct option: A.
$-\frac{6}{7}$
The denominator of the rational number $-\frac{102}{119}$ is positivr.
In order to write the rational number in standerd form, divide its numerator and denominator by the $HCF$ of $102$ and $119$.
$HCF$ of $102$ and $119 = 17$
Dividing the numerator and denominator of $-\frac{102}{119}$ by $17$,
We have:
$-\frac{102}{119}=-\frac{102\div17}{119\div17}=-\frac{6}{7}$
Thus the standard form of $-\frac{102}{119}\text{ is }-\frac{6}{7}$
Hence, the correct answer is option $(a)$.
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MCQ 171 Mark
The rational number equal to $\frac{2}{-3}$ is
  • A
    $\frac{14}{-18}$
  • ✓
    $\frac{-6}{9}$
  • C
    $\frac{-8}{-12}$
  • D
    $\frac{3}{-2}$
Answer
Correct option: B.
$\frac{-6}{9}$
B
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MCQ 181 Mark
Which of the following pairs of rational numbers are on the opposite sides of the zero on the number line?
  • A
    $\frac{3}{7}$ and $\frac{5}{12}$
  • B
    $-\frac{3}{7}$ and $\frac{-5}{12}$
  • ✓
    $\frac{3}{7}$ and $\frac{-5}{12}$
  • D
    none of these
Answer
Correct option: C.
$\frac{3}{7}$ and $\frac{-5}{12}$
C
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MCQ 191 Mark
If $\frac{27}{-45}$ is expressed as a rational number with denominator 5 , then the numerator is
  • A
    3
  • ✓
    -3
  • C
    6
  • D
    -6
Answer
Correct option: B.
-3
B
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MCQ 201 Mark
If $-\frac{3}{8}$ and $\frac{x}{-24}$ are equivalent rational numbers, then $x=$
  • A
    3
  • B
    6
  • ✓
    9
  • D
    12
Answer
Correct option: C.
9
C
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MCQ 221 Mark
Wach of the following is not zero?
  • A
    $0 \times 0$
  • B
    $\frac{0}{3}$
  • C
    $\frac{7-7}{3}$
  • ✓
    $9+0$
Answer
Correct option: D.
$9+0$
D
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MCQ 231 Mark
What is the multiplicative identity element in the set of whole numbers?
  • A
    0
  • ✓
    1
  • C
    -1
  • D
    none of these
Answer
Correct option: B.
1
B
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MCQ 241 Mark
What is the additive identity element in the set of whole numbers?
  • ✓
    0
  • B
    1
  • C
    -1
  • D
    none of these
Answer
Correct option: A.
0
A
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MCQ 251 Mark
If the rational numbers $\frac{-2}{3}$ and $\frac{4}{x}$ represent a pair of equivalent rational numbers, then $x=$
  • A
    6
  • ✓
    -6
  • C
    3
  • D
    -3
Answer
Correct option: B.
-6
B
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MCQ 261 Mark
Which of the following is correct?
  • ✓
    $\frac{5}{9}>\frac{-3}{-8}$
  • B
    $\frac{5}{9}<\frac{-3}{-8}$
  • C
    $\frac{2}{-3}<\frac{-8}{7}$
  • D
    $\frac{4}{-3}>\frac{-8}{7}$
Answer
Correct option: A.
$\frac{5}{9}>\frac{-3}{-8}$
A
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MCQ 281 Mark
A rational number equal to $\frac{-2}{3}$ is
  • A
    $\frac{-10}{25}$
  • ✓
    $\frac{10}{-15}$
  • C
    $\frac{-9}{6}$
  • D
    none of these
Answer
Correct option: B.
$\frac{10}{-15}$
B
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MCQ 291 Mark
$-\frac{102}{119}$ in standard form is
  • ✓
    $-\frac{6}{7}$
  • B
    $\frac{6}{7}$
  • C
    $-\frac{6}{17}$
  • D
    none of these
Answer
Correct option: A.
$-\frac{6}{7}$
A
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MCQ 301 Mark
$\frac{44}{-77}$ in standard form is
  • A
    $\frac{4}{-7}$
  • ✓
    $-\frac{4}{7}$
  • C
    $-\frac{44}{77}$
  • D
    none of these
Answer
Correct option: B.
$-\frac{4}{7}$
B
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