Rational Numbers(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

RATIONAL NUMBERS MCQs

Total Questions : 54 | Page 2 of 6 pages

Question 11. Between any two given rational numbers, there are infinite rational numbers.

True
False
2
3

Discuss Question

Answer: Option A. -> True
:
A
There are infiniterational numbers between any two rational numbers. Let's consider an example to understand this better.
Rational numbers between

\frac{- 1}{10}

and

\frac{3}{10}

\frac{0}{10}

\frac{1}{10}

\frac{2}{10}

are the obvious rational numbers between them.
But

\frac{- 1}{10}

can be written as

\frac{- 10000}{100000}

and

\frac{3}{10}

\frac{30000}{100000}

So, rational numbers between

\frac{- 1}{10}

and

\frac{3}{10}

are

\frac{- 9999}{100000}

\frac{- 9998}{100000}

,…..

\frac{29998}{100000}

\frac{29999}{100000}

Thus, we can find infinite rational numbers between any two rational numbers.

Question 12. After reading

\frac{4}{9} t h

of a book, 30 pages are left. How many pages are there in the book?

Discuss Question

Answer: Option A. -> 54
:
A
Let the total number of pages in the book be

x

(\frac{4}{9} \times x) pages are read

Remaining pages = x - \frac{4 x}{9}

= \frac{5 x}{9} = 30

\Rightarrow 5 x = 30 \times 9

x = 54 pages

Question 13. If we subtract

\frac{1}{2}

from a number and multiply the result by

\frac{1}{2}

, we get

\frac{3}{8}

. What is the number?

1
2
1.25
1.5

Discuss Question

Answer: Option C. -> 1.25
:
C
Let the number be

y

(y - \frac{1}{2}) \times (\frac{1}{2}) = (\frac{3}{8})

(y - \frac{1}{2}) = (\frac{3}{4})

y = \frac{3}{4} + \frac{1}{2} = \frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1.25

Question 14. The additive identity for rational numbers is 0.

True
False
2
3

Discuss Question

Answer: Option A. -> True
:
A
Zero is the additive identity forrational numbers, integers and whole numbers,as adding zero to these numbers doesnotaffect its value.

E g : a + 0 = 0 + a = a .

Question 15. Division of whole numbers follows the commutative law.

True
False
2
3

Discuss Question

Answer: Option B. -> False
:
B
An operation is commutative if changing the order of operands does not change the result.
Division of whole numbers is not commutative.

\frac{a}{b} \neq \frac{b}{a}

For example: a = 2, b = 3;

\frac{2}{3} \neq \frac{3}{2}

Question 16. Which of the following statements is incorrect?

Every whole number is a rational number
Every integer is a rational number
Zero is a whole number and it is rational number too
Every rational number is not an integer

Discuss Question

Answer: Option C. -> Zero is a whole number and it is rational number too
:
C
Zero is a whole number as well as the rational number. Zero can be expressed in the form of

\frac{p}{q}

\frac{0}{1}

. Hence zero is a rational number since it satisfies the definition of rational number where p = 0 and q

\neq

Question 17. Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.

100099999
100099900
999999999
100010000

Discuss Question

Answer: Option A. -> 100099999
:
A
The smallest four digit number is 1000 and largest five digit number is 99999.
Therefore, the required rational number is

\frac{smallest four digit number}{largest five digit number} = \frac{1000}{99999}

Question 18.

\frac{- 15}{51}

is a multiplicative inverse of

\frac{- 17}{5}

True
False
7
711

Discuss Question

Answer: Option A. -> True
:
A
Multiplicative inverse of

\frac{a}{b}

\frac{c}{d}

\frac{a}{b} \times \frac{c}{d} = 1

.
Now,

\frac{- 15}{51} \times \frac{- 17}{5} = \frac{3}{3} = 1

Question 19. Arrange the following rational numbers in the ascending order

\frac{5}{4}, \frac{2}{3}, \frac{6}{8}, \frac{8}{5}, \frac{9}{2} .

Discuss Question

Answer: Option A. -> 23
:
A
To compare the rational numbers, we first make the denominators equal.
L.C.M of the denominators 4, 3, 8, 5, 2 is 120.
Equivalent fractions with the denominator 120 are