Sample QuestionsRational Numbers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Tick $(\checkmark)$ the correct answer the following: What should be subtracted from $\frac{-5}{3}$ to get $\frac{5}{6}$?
- A
$\frac{5}{2}$
- B
$\frac{3}{2}$
- C
$\frac{5}{4}$
- ✓
$\frac{-5}{2}$
Answer: D.
View full solution →Mark $(\checkmark)$ against the correct answer of the following: Reciprocal of $\frac{-7}{9}$ is:
- A
$\frac{9}{7}$
- ✓
$\frac{-9}{7}$
- C
$\frac{7}{9}$
- D
Answer: B.
View full solution →Mark $(\checkmark)$ against the correct answer of the following: $\Big(\frac{-5}{4}\Big)^{-1}=\ ?$
- A
$\frac{4}{5}$
- ✓
$\frac{-4}{5}$
- C
$\frac{5}{4}$
- D
$\frac{3}{5}$
Answer: B.
View full solution →Mark $(\checkmark)$ against the correct answer of the following: The product of two numbers is $\frac{-1}{4}$. If one of them is $\frac{-3}{10}$, then the other is-
- ✓
$\frac{5}{6}$
- B
$\frac{-5}{6}$
- C
$\frac{4}{3}$
- D
$\frac{-8}{5}$
Answer: A.
View full solution →Tick $(\checkmark)$ the correct answer the following: What should be added to $\frac{7}{12}$ to get $\frac{-4}{15}$?
- A
$\frac{17}{20}$
- ✓
$\frac{-17}{20}$
- C
$\frac{7}{20}$
- D
$\frac{-7}{20}$
Answer: B.
View full solution →Assertion (A): There exists a unique rational number whose additive inverse and multiplicative inverse do not exist.
Reason (R) : The additive inverse of 1 is -1 and its multiplicative inverse is 1 .
- 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: D.
View full solution →Assertion (A): Addition and multiplication of rational numbers is both commutative and associative.
Reason (R): The rational numbers may be added or multiplied in any order or by grouping in any order. The sum or product remains the same.
- ✓
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: A.
View full solution →Assertion (A): The product of the additive inverse and multiplicative inverse of a rational number is -1 .
Reason (R): If $a$ is a rational number then its additive inverse is $(-a)$ and its multiplicative inverse is $\frac{1}{a}$.
- ✓
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.
- D
Assertion (A) is false but Reason (R) is true.
Answer: A.
View full solution →Assertion (A): Nonzero rational numbers are closed under addition, subtraction, multiplication and division.
Reason (R): The sum, difference and product of two rational numbers is a rational number but division by 0 is not defined.
- ✓
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: A.
View full solution →Assertion (A): $\frac{2}{3} \times\left(\frac{4}{5}+\frac{6}{7}\right)=\frac{2}{3} \times \frac{4}{5}+\frac{2}{3} \times \frac{6}{7}$.
Reason (R): Multiplication is distributive over addition for rational numbers.
- ✓
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: A.
View full solution →Find the following products: $\frac{5}{-18}\times\frac{-9}{20}$
View full solution →Verify the following: $3+\frac{-7}{12}=\frac{-7}{12}+3$
View full solution →What number should be added to $\frac{-5}{8}$ so as to get $\frac{-3}{2}$?
View full solution →What number should be subtracted from $\frac{-2}{3}$ to get $\frac{-1}{6}$?
View full solution →Verify the following: $\frac{2}{-7}+\frac{12}{-35}=\frac{12}{-35}+\frac{2}{-7}$
View full solution →After reading $\frac{7}{9}$ of a book, $40$ pages are left. How many pages are there in the book$?$
View full solution →Which of the two rational numbers is greater in the given pair$?$
$\frac{2}{3}\ \text{or}\ \frac{3}{4}$
View full solution →Verify whether the given statement is true or false: $\frac{-7}{24}\div\frac{3}{-16}=\frac{3}{-16}\div\frac{-7}{24}$
View full solution →Represent the following numbers on the number line. $-3$
View full solution →If $\frac{3}{5}$ of a number exceeds its $\frac{2}{7}$ by $44,$ find the number.
View full solution →Arrange the following rational numbers in descending order: $\frac{-5}{6},\frac{-7}{12},\frac{-13}{18},\frac{23}{-24}$
View full solution →Arrange the following rational numbers in descending order: $-2,\frac{-13}{6},\frac{8}{-3},\frac{1}{3}$
View full solution →Arrange the following rational numbers in ascending order: $\frac{-3}{4},\frac{5}{-12},\frac{-7}{16},\frac{9}{-24}$
View full solution →Find three rational numbers between $4$ and $5.$
View full solution →Find three rational numbers between $\frac{2}{3}$ and $\frac{3}{4}$.
View full solution →A train starts from station $A$ with a certain number of passengers. At station $B$, the train drops one third of the passengers and takes in 96 more. At the next station $C$ one half of the passengers on board get down while 12 new passengers get on board. At station $D$, a quarter of the passengers get down and 20 new passengers board the train. It then reaches its final destination-station $E$-with 200 passengers.
(1) How many passengers were on board when the train left station $A$ ?
(a) 460$\quad$(b) 520$\quad$(c) 540$\quad$(d) 560
(2) How many passengers were on board when the train left station $B$ ?
(a) 428$\quad$(b) 436$\quad$(c) 444$\quad$(d) 456
(3) How many passengers were on board when the train left station $C$ ?
(a) 228$\quad$(b) 240$\quad$(c) 256$\quad$(d) 264
(4) Had the train started with 720 passengers from station $A$, how many passengers would have got down at station $E$ ?
(a) 228$\quad$(b) 236$\quad$(c) 245$\quad$(d) 256
View full solution →Add the following rational numbers.
$0\ \text{and}\ \frac{-2}{5}$
View full solution →Add the following rational numbers. $\frac{5}{8}\ \text{and}\ \frac{-7}{12}$
View full solution →Can we divide $1$ by $0?$
View full solution →Fill in the blank: The reciprocal of $a,$ where $a ≠ 0,$ is _________.
View full solution →Add the following rational numbers. $\frac{3}{4}\ \text{and}\ \frac{-3}{5}$
View full solution →