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CBSE 8th Mathematics Rational Numbers Model Questions Papers Study Material - QB365 Set B

Published on: 21/10/2025

Question Set B

CBSE 8th Mathematics Rational Numbers Model Questions Papers Study Material - QB365

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Std: 8th Standard CBSE - Mathematics

chapter: Rational Numbers - Model Questions Papers

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Questions:

Multiple Choice Question

6 x 1 = 6

Which of the following statements is true?

(a)

Natural numbers are associative for addition

(b)

Whole numbers are not associative for addition

(c)

Integers are not associative for addition

(d)

Rational numbers are not associative for addition.

The product of \(\frac { 1 }{ 5 } \) and \(-\frac { 1 }{ 5 } \) is -

(a)

(b)

(c)

\(\frac { 1 }{ 25 } \)

(d)

\(\frac { -1 }{ 25 } \)

What should be added to \(\frac { -3 }{ 4 } \) to get -1?

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { -1 }{ 4 } \)

(c)

(d)

\(\frac { -3 }{ 4 } \)

Multiplicative inverse of a negative rational number is

(a)

(b)

-1

(c)

a negative rational number

(d)

a positive rational number

Zero (0) is

(a)

the identity for addition of rational numbers

(b)

the identity for subtraction of rational numbers

(c)

the identity for multiplication of rational numbers

(d)

the identity for division of rational numbers.

\(\frac{x+y}{2}\) is a rational number

(a)

between x and y

(b)

less than x and y both

(c)

greater than x and y both

(d)

less than x but greater than y

Generic 2

8 x 2 = 16

Find \(\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times\left(\frac{-14}{9}\right)\)

Is 1 the multiplicative identity for integers ? For whole numbers ?

Is (-6) + [(-4) + (-5)] = [(-6) + (-4) + (-5)?

10.

\(\frac{-6}{5} + (\frac{-8}{3}) = \) ______ and \(\frac{-8}{3} + (\frac{-6}{5}) = \) ______
Is \(\frac{-6}{5} + (\frac{-8}{3}) = \)\(\frac{-8}{3} + (\frac{-6}{5})\)?

11.

A farmer has a field of area 49 \({4\over5}\) hec. He wants to divide it equally among his one son and two daughters. Find the area of each one's share. (hec means hectare; 1 hectare = 10000m²)

12.

Write any two pair of rational numbers, which are on the opposite sides of zero on the number line

13.

Multiply \({6\over13}\) by the reciprocal of \({-7\over16}\)

14.

Verify that -(-x) = x,for x = \(-13\over17\)

Generic 3

6 x 3 = 18

15.

Fill in the blanks in the following table:

Number	Closed Under
	Addition	Subtraction	Multuplication	Division
Rational numbers	Yes	Yes	...	No
Integers	...	Yes	...	No
Whole numbers	...	...	Yes	...
Natural numbers	...	No	...	...

16.

On a winter day, the temperature at a place in Jammu and Kashmir was -16^° C. Convert it in degree Fahrenheit (^°F)by using the formula\({c\over5}={F-32\over9}\)

17.

\({4\over7}\) of all the money in Abdul's bank account is Rs.88000. How much money does Abdul have in his bank account?

18.

verify that \({5\over6}\times(-{4\over5}+{-6\over10})=[{5\over6} \times({-4\over5})]+[{5\over6}\times({-6\over10})]\)

19.

Write the rational number for each point labelled with a letter

20.

Multiply the multiplicative inverse of -2 with its reciprocal.

Generic 5

2 x 5 = 10

21.

Find \(\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)\)

22.

Using and associativity of addition of rational numbers, express the following as a rational number.
\({5\over2}+{-3\over7}+{1\over2}+{4\over7}\)

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Answers Key:

Multiple Choice Question

6 x 1 = 6

(a)
Natural numbers are associative for addition

(d)
\(\frac { -1 }{ 25 } \)

(b)
\(\frac { -1 }{ 4 } \)

(a)
the identity for addition of rational numbers

(a)
between x and y

Generic 2

8 x 2 = 16

We have
\(\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times\left(\frac{-14}{9}\right)\)
\(=\left(-\frac{4 \times 3}{5 \times 7}\right) \times\left(\frac{15 \times(-14)}{16 \times 9}\right)\)
\(=\frac{-12}{35} \times\left(\frac{-35}{24}\right)=\frac{-12 \times(-35)}{35 \times 24}=\frac{1}{2}\)
We can also do it as.
\(\frac{-4}{5} \times \frac{3}{7} \times \frac{15}{16} \times\left(\frac{-14}{9}\right)\)
\(=\left(\frac{-4}{5} \times \frac{15}{16}\right) \times\left[\frac{3}{7} \times\left(\frac{-14}{9}\right)\right]\) (Using commutativity and associativity)
\(=\frac{-3}{4} \times\left(\frac{-2}{3}\right)=\frac{1}{2}\)

Yes, 1 is the multiplicative identity for integers as well as for whole numbers.

Yes ; (-6) + [(-4) + (-5)] = [(-6) + (-4) + (-5) = -15.

10.

\(\frac{-6}{5} + (\frac{-8}{3}) = \frac{-58}{15}\)
\(\frac{-8}{3} + (\frac{-6}{5}) = \frac{-58}{15}\)
So, \(\frac{-6}{5} + (\frac{-8}{3}) = \)\(\frac{-8}{3} + (\frac{-6}{5})\).

11.

49 \({4\over5}\) hec = \({249\over5}\) hec
Each share = \({1\over3}\times{249\over5}hec={83\over5}hec=16{3\over5}hec\)

12.

\(-{1\over2}and{1\over4},-{1\over3}and{1\over3}\)

13.

Reciprocal of \({-7\over16}\) is \({-16\over7}\)
According to the question
\({6\over13} \times (Reciprocal \ of {-7\over16})={6\over13} \times [{-16\over 7}] \)
\(\\ ={6\over13} \times{-16\over 7}={6\times(-16)\over 13\times 7}={-96\over91}\)

14.

We have, x = \(-13\over17\)
\(LHS =-(-x)=-\{-({-13\over17})\}=-\{{13\over17}\}\)
=-\({13\over17}\) = x = RHS
So, - (-x) = x is verified for x = \({13\over17}\).

Generic 3

6 x 3 = 18

15.

Using the closure property over addition, subtraction, multiplication and division for rational numbers, integers, whole-numbers and natural numbers, we have:

Number	Closed Under
	Addition	Subtraction	Multuplication	Division
Rational numbers	Yes	Yes	Yes.	No
Integers	Yes	Yes	Yes	No
Whole numbers	Yes	Yes	Yes	No
Natural numbers	Yes	No	Yes	No

16.

3.2F^°

17.

\({4\over7}\) of all the money = Rs.88000
\(\therefore 1 \ or \ whole \ part \ of \ the \ money =88000\div {4\over7}\)
\(\\=88000\times{7\over4}\)
\(\\ =Rs 154000\)

18.

We have
LHS =
\({5\over 6}\times(-{4\over5}+{-6\over10})={5\over6}\times({-8-6\over10}) \)
\(\\={5\over6} \times({-14\over10})={-70\over60}={-7\over6}\)
\(\\ Also, RHS =[{5\over6}\times({-4\over5})]+[{5\over6}\times({-6\over10})] \)
\(\\ ({-20\over30})+({-30\over60})={-20\over30}-{30\over60}\)
\(\\ ={-40-30\over60}={-70\over60}={-7\over6}\)
\(\\ Thus, LHS = RHS\)

19.

We can draw the number line accordingly

20.

\(1\over4\)

Generic 5

2 x 5 = 10

21.

\(\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)\)
\(=\frac{198}{462}+\left(\frac{-252}{462}\right)+\left(\frac{-176}{462}\right)+\left(\frac{105}{462}\right)\) (Note that 462 is the LCM of 7, 11, 21 and 22)
\(=\frac{198-252-176+105}{462}=\frac{-125}{462}\)
We can also solve it as.
\(\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\frac{5}{22}\)
\(=\left[\frac{3}{7}+\left(\frac{-8}{21}\right)\right]+\left[\frac{-6}{11}+\frac{5}{22}\right]\) (by using commutativity and associativity)
\(=\left[\frac{9+(-8)}{21}\right]+\left[\frac{-12+5}{22}\right]\) (LCM of 7 and 21 is 21; LCM of 11 and 22 is 22)
\(=\frac{1}{21}+\left(\frac{-7}{22}\right)=\frac{22-147}{462}=\frac{-125}{462}\)