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

8th Grade > Mathematics

RATIONAL NUMBERS MCQs

Total Questions : 54 | Page 3 of 6 pages

Question 21. Division of the reciprocal of

\frac{5}{11}

\frac{- 55}{18}

results in

\frac{- 18}{25}

True
False
0.01
- 0.01

Discuss Question

Answer: Option A. -> True
:
A
Reciprocal of

\frac{5}{11}

\frac{11}{5}

\frac{11}{5} \div \frac{- 55}{18}

= \frac{11 \times 18}{5 \times (- 55)}

= \frac{- 18}{25}

Question 22. The product of two whole numbers is always a whole number.

True
False

Discuss Question

Answer: Option A. -> True
:
A
If 'a' and 'b' are any two whole numbers, their product will also be a whole number.We know that the multiplication of any two numbers can be expressed as repeatedaddition of one number.So, if weare adding any whole number to itself again and again, then wewill surely get a whole number.
Let's assume

a = 2, b = 3

a \times b = 2 \times 3

which is same asadding '2' three times to itself, which willresult in a whole number.

Question 23.

(59 \div 13) \div 52 = 59 \div (13 \div 52)

True
False
53
63

Discuss Question

Answer: Option B. -> False
:
B
Let's first evaluateLHS.

(\frac{59}{13}) \times \frac{1}{52} = \frac{59}{676}

Now, RHS

59 \times (\frac{52}{13})

= \frac{3068}{13}

We see that both LHS and RHS are not equal.

Question 24. The reciprocal of -10 is

0.1
- 0.1
0.01
- 0.01

Discuss Question

Answer: Option B. -> - 0.1
:
B
The reciprocal of any non-zero number 'a' is

\frac{1}{a}

.
The reciprocal of '-10' =

\frac{1}{(- 10)} = - 0.1

Question 25. By what rational number should we divide

\frac{22}{7}

so as to get the number

\frac{- 11}{14}

- 2
57
127
-4

Discuss Question

Answer: Option D. -> -4
:
D
Let the rational number be

x

\frac{22}{7} \div x

\frac{- 11}{14}

(given)

\Rightarrow \frac{22}{7} = x \times \frac{- 11}{14}

\Rightarrow \frac{22}{7} \div \frac{- 11}{14} = x

\Rightarrow \frac{22}{7} \times \frac{14}{- 11} = x

\Rightarrow x = - 4

Therefore,

\frac{22}{7}

should be divided by -4 to get

\frac{- 11}{14}

Question 26.

The ___ property states that we can add rational numbers in any order.

commutative
associative
closure
distributive

Discuss Question

Answer: Option A. -> commutative
:
A

The addition of rational numbers can be done in any order and the result remains the same. This is called commutative property.
E.g: 2 + 3 = 3 + 2

Question 27.

Choose the rational numbers whose numerator is $(- 5) \times 6$ , and the denominator is $(34 - 23) \times (7 - 5)$ .

$\frac{20}{11}$
$\frac{40}{22}$
$\frac{- 15}{11}$
$\frac{- 30}{22}$

Discuss Question

Answer: Option C. ->

\frac{- 15}{11}

:
C and D

Rational numbers are the numbers which can be expressed in the form of $\frac{p}{q}$ , given $q \neq 0$ , p and q are integers.
$\frac{p}{q} = \frac{- 5 \times 6}{(34 - 23) \times (7 - 5)}$
$= \frac{- 30}{11 \times 2}$
$= \frac{- 30}{22}$
$= \frac{- 15}{11}$

Question 28.

Which of the following pair of rational numbers are smaller than -5?

$\frac{- 12}{2}$ & $\frac{- 20}{2}$
$\frac{- 10}{5}$ & $\frac{- 32}{4}$
$\frac{- 27}{3}$ & $\frac{- 18}{3}$
$\frac{- 100}{5}$ & $\frac{- 200}{5}$

Discuss Question

Answer: Option C. ->

\frac{- 27}{3}

\frac{- 18}{3}

:
A, C, and D
a)

\frac{- 12}{2} = - 6

\frac{- 20}{2} = - 10

-6 and -10 are smaller than -5.
b)

\frac{- 10}{5} = - 2

\frac{- 32}{4} = - 8

-2 is greater than -5.
c)

\frac{- 27}{3} = - 9

\frac{- 18}{3} = - 6

-9 and -6 are smaller than -5.
d)

\frac{- 100}{5} = - 20

\frac{- 200}{5} = - 40

-20 and -40 are smaller than -5.

Question 29.

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

$\frac{1000}{99999}$
$\frac{1000}{99900}$
$\frac{9999}{99999}$
$\frac{1000}{10000}$

Discuss Question

Answer: Option A. ->

\frac{1000}{99999}

:
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 30.

Arrange the following rational numbers in the ascending order
$\frac{5}{4}, \frac{2}{3}, \frac{6}{8}, \frac{8}{5}, \frac{9}{2} .$

$\frac{2}{3} < \frac{6}{8} < \frac{5}{4} < \frac{8}{5} < \frac{9}{2}$
$\frac{5}{4} < \frac{6}{8} < \frac{2}{3} < \frac{8}{5} < \frac{9}{2}$
$\frac{9}{2} < \frac{8}{5} < \frac{5}{4} < \frac{6}{8}$ < $\frac{2}{3}$
$\frac{9}{2} < \frac{2}{3} < \frac{5}{4} < \frac{8}{5} < \frac{6}{8}$

Discuss Question

Answer: Option A. ->

\frac{2}{3} < \frac{6}{8} < \frac{5}{4} < \frac{8}{5} < \frac{9}{2}

:
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

$\frac{5}{4} \times \frac{30}{30} = \frac{150}{120}$

$\frac{2}{3} \times \frac{40}{40} = \frac{80}{120}$

$\frac{6}{8} \times \frac{15}{15} = \frac{90}{120}$

$\frac{8}{5} \times \frac{24}{24} = \frac{192}{120}$

$\frac{9}{2} \times \frac{60}{60} = \frac{540}{120}$
Since the denominator is same in the above equivalent fractions, we can decide the ascending order based on the numerator values.