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CBSE 7th Standard Mathematics Rational Numbers Sample Question Papers Study Material - QB365 Set D

Published on: 31/10/2025

Question Set D

CBSE 7th Standard Mathematics Rational Numbers Sample Question Papers Study Material - QB365

Download CBSE Class 7th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 7th Standard CBSE Mathematics

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Std: 7th Standard CBSE - Mathematics

chapter: Rational Numbers - Sample Question Papers

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Questions:

Generic 2

5 x 2 = 10

'a' and 'b' are two different numbers taken from the numbers 1-50. What is the largest value that \(\frac{a-b}{a+b}\) can have? What is the largest value that \(\frac{a+b}{a-b}\) can have?

What will be the additive inverse of \(\frac { -3 }{ 9 } \)

What number should be added to \(\frac { -3 }{ 5 } ,\)so as to get \(\frac { 1 }{ 3 } \) ?

Express \(\frac { -36 }{ 48 } \) as a rational number with denominator 4

Find the product \(\frac { 7 }{ 2 } \times \frac { 9 }{ 4 } \times 1\frac { 1 }{ 4 } \)

Multiple Choice Question

10 x 1 = 10

The denominator of the rational number \(\frac{4}{7}\) is

(a)

(b)

(c)

(d)

The multiplicative inverse of \(\frac{-5}{3}\) is:

(a)

\(\frac{3}{5}\)

(b)

\(\frac{-3}{5}\)

(c)

\(\frac{3}{2}\)

(d)

\(\frac{-1}{3}\)

The reciprocal of \(\frac{1}{2}\)is

(a)

(b)

(c)

-1

(d)

The value of -\(\frac{4}{3}\)-\(\frac{-1}{3}\) is

(a)

-2

(b)

-3

(c)

(d)

-1

10.

How many rational numbers are there between 2 and 4?

(a)

Zero

(b)

one

(c)

two

(d)

uncountable

11.

The simplified value of \(2\frac { 1 }{ 2 } \times 2\frac { 1 }{ 4 } \div 4\frac { 1 }{ 2 } \) is

(a)

\(1\frac { 1 }{ 7 } \)

(b)

\(1\frac { 1 }{ 8 } \)

(c)

\(\frac { 9 }{ 11 } \)

(d)

\(\frac { 13 }{ 15 } \)

12.

Which is greater number in the following?

(a)

\(\frac { -1 }{ 2 } \)

(b)

(c)

\(\frac { 1 }{ 2 } \)

(d)

-2

13.

How many rational numbers are there between two rational numbers?

(a)

(b)

(c)

unlimited

(d)

100

14.

Which of the following rational numbers is negative?

(a)

\(-\left( \frac { -3 }{ 7 } \right) \)

(b)

\(\frac { -5 }{ -8 } \)

(c)

\(\frac { 9 }{ 8 } \)

(d)

\(\frac { 3 }{ -7 } \)

15.

Which of the following rational numbers is postive?

(a)

\(\frac { -8 }{ 7 } \)

(b)

\(\frac { 19 }{ -13 } \)

(c)

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

(d)

\(\frac { -21 }{ 13 } \)

Fill up / 1 Marks

10 x 1 = 10

16.

\(\frac{-3}{7}\) is ______________ than \(\frac{3}{7}\).

17.

The sum of \((-\frac{1}{2})\) and _____________ is 0.

18.

\(\frac{7}{-8}\)◻️\(\frac{8}{9}\)

19.

\(\frac{-3}{7}\)+\(\frac{-7}{3}\)=____________.

20.

\(\frac{-16}{24}\)and\(\frac{20}{-16}\) represent____________ rational numbers.

21.

\(\frac { 1 }{ 2 } =\frac { 6 }{ \_ \_ \_ \_ \_ } \)

22.

\(\frac { 3 }{ 4 } \times \left( \frac { -2 }{ 3 } \right) =\) ___________

23.

\(\frac { -5 }{ 6 } +\frac { -1 }{ 6 }\)=_________

24.

Additive inverse of \(\frac { 2 }{ 3 } \) is__________

25.

On number line \(\frac { 4 }{ 3 } \) is to the _________ of zero (0)

Generic 3

5 x 3 = 15

26.

Which is greater \(-\frac{2}{3}\ or\ (-\frac{3}{4})?\)

27.

Divide the sum of \(\frac{12}{5}\) and \(\frac{21}{25}\) by their difference.

28.

What should be added to \(\left( \frac { -3 }{ 4 } +\frac { -13 }{ 8 } \right) \) to get 2?

29.

Find five rational number between \(\frac { -5 }{ 7 } \) and \(\frac { -3 }{ 8 } \)

30.

Convert the following rational numbers to have same denominator \(\frac { -3 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 5 }{ 6 } ,\frac { 2 }{ -8 } \)

Generic 5

3 x 5 = 15

31.

Find \(\frac{-4}{7}\times3,\)using both ways. What do you observe?

32.

Can you list five rational numbers between \(-\frac{5}{3}\ and-\frac{8}{7}?\)

33.

Write each of the following numbers in the form of \(\frac { p }{ q } \), Where p and q are integers.
Three and half

1 Marks

5 x 1 = 5

34.

Find:
\(\frac{4}{13}\div(\frac{-4}{65})\)

35.

Multiply:
\(\frac{3}{5}\) by -2

36.

Write the following rational numbers in ascending order: \(\frac{3}{4}\), \(\frac{-1}{2}\), \(\frac{-4}{5}\), \(\frac{-1}{-4}\)

37.

The sum of two rational numbers is -5. If one of the rational number is\(\frac{-17}{6}\), then find the other:

38.

What should be added to \(\frac{-3}{4}\) to get 0?

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Answers Key:

Generic 2

5 x 2 = 10

Since, a and b are two different numbers.
Let a = 15 and b = 10.
\(\therefore\) \(\frac{a-b}{a+b}\)=\(\frac{15-10}{15+10}\)=\(\frac{5}{25}=\frac{1}{5}\)
and \(\frac{a+b}{a-b}\)=\(\frac{15+10}{15-10}=\frac{25}{5}\)=5
So, (a + b) always greater than (a - b) when denominator is less number is greater,
then \(\left(\frac{a+b}{a-b}\right)>\left(\frac{a-b}{a+b}\right)\)

The additive inverse of =\(\frac { -3 }{ 9 } =-\left( \frac { -3 }{ 9 } \right) =\frac { 3 }{ 9 } \)

\(\frac { 14 }{ 15 } \)

Given \(\frac { -36 }{ 48 } \)as a rational number with denomiantor 4.
\(\because \) HCF of 36 and 48 is 12.
So, \(\frac { -36\div 12 }{ 48\div 12 } =\frac { -3 }{ 4 } \)

\(9\frac { 27 }{ 32 } \)

Multiple Choice Question

10 x 1 = 10

(a)
7

(b)
\(\frac{-3}{5}\)

(b)
2

(d)
-1

10.

(b)
one

11.

(b)
\(1\frac { 1 }{ 8 } \)

12.

13.

14.

(d)
\(\frac { 3 }{ -7 } \)

15.

Fill up / 1 Marks

10 x 1 = 10

16.

()
less

17.

()
\(\frac{1}{2}\)

18.

()
<

19.

()
\(\frac{9}{49}\)

20.

()
different

21.

\(\frac { 1 }{ 2 } =\frac { 6 }{ 12 }=\frac { 1 }{ 2 } =\frac { 6 }{ x } \Rightarrow x=12\)

22.

\(\frac { 3 }{ 4 } \times \left( \frac { -2 }{ 3 } \right) =\frac { 3\times (-2) }{ 4\times (3) } =\frac { -6 }{ 12 } =\)\(-\frac { 1 }{ 2 } \)

23.

\(\frac { -5 }{ 6 } +\frac { -1 }{ 6 } =\frac { -5-1 }{ 6 } =\frac { -6 }{ 6 } =\)-1

24.

Additive inverse of \(\frac { 2 }{ 3 } \) is \(-\frac { 2 }{ 3 } \)

25.

On number line \(\frac { 4 }{ 3 } \) is to the right of zero (0)

Generic 3

5 x 3 = 15

26.

We have
\(\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}\)
\(\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}\)
\(\frac{8}{12}<\frac{9}{12}\)
\(\Rightarrow \frac{2}{3}<\frac{3}{4}\Rightarrow-\frac{2}{3}>(-\frac{3}{4})\)

27.

Sum of \(\frac{12}{5}\) and \(\frac{21}{25}\)=\(\frac{12}{5}+\frac{21}{25}\)
=\(\frac{5(12)-21(1)}{25}=\frac{60-21}{25}=\frac{81}{25}\)
[\(\because\)LCM of 5 and 25 is 25.]
Difference of \(\frac{12}{5}\) and \(\frac{21}{25}\)=\(\frac{12}{5}-\frac{21}{25}\)
=\(\frac{5(12)-21(1)}{25}=\frac{60+21}{25}=\frac{39}{25}\)
Now, \(\left[ \frac { 12 }{ 5 } +\frac { 21 }{ 25 } \right] +\left[ \frac { 12 }{ 5 } -\frac { 21 }{ 25 } \right] =\left[ \frac { 81 }{ 25 } \right] \div \left[ \frac { 39 }{ 25 } \right] \)
=\(\frac{81}{25}\times\frac{25}{39}=\frac{81}{39}=\frac{27}{13}\)

28.

\(\because \) \(\frac{-3}{4}+\frac{-13}{8}\)=\(\frac{-3(2)+(-13)(1)}{8}\)
[\(\because \)LCM of 4 and 8 is 8.]
=\(\frac{-6-13}{8}=\frac{-19}{8}\)
\(\therefore\) \(2-(\frac{-19}{8})=\frac{2}{1}+\frac{19}{8}=\frac{2(8)+19(1)}{8}\)
=\(\frac{16+19}{8}=\frac{35}{8}\)
Thus, \(\frac{35}{8}\)is to be added to\((\frac{-3}{4}+\frac{-13}{8})\) to get 2.

29.

Given,\(\frac { -5 }{ 7 } \) and \(\frac { -3 }{ 8 } \)
Here.LCM of 7 and 8=7\(\times \)8=56
\(\therefore \) \(\frac { -5 }{ 7 } =\frac { -5\times 8 }{ 7\times 8 } =\frac { -40 }{ 56 } \) and \(\frac { -3 }{ 8 } =\frac { -3\times 7 }{ 8\times 7 } =\frac { -21 }{ 56 } \)
we have, \(\frac { -40 }{ 56 } <\frac { -39 }{ 56 } <\frac { -38 }{ 56 } <\frac { -37 }{ 56 } <\frac { -36 }{ 56 } <\frac { -35 }{ 56 } <\frac { -21 }{ 56 } \)
or \(\frac { -5 }{ 7 } <\frac { -39 }{ 56 } <\frac { -38 }{ 56 } <\frac { -37 }{ 56 } <\frac { -36 }{ 56 } <\frac { -35 }{ 56 } <\frac { -3 }{ 8 } \)
Thus, the five rational number between \(\frac { -5 }{ 7 } \) and \(\frac { -3 }{ 8 } \) are
\(\frac { -39 }{ 56 } ,\frac { -38 }{ 56 } ,\frac { -37 }{ 56 } ,\frac { -36 }{ 56 } \) and \(\frac { -35 }{ 56 } \)
\(\\ i.e. \frac { -39 }{ 56 } ,\frac { -19 }{ 56 } ,\frac { -37 }{ 56 } ,\frac { -9 }{ 14 } \) and \(\frac { -5 }{ 8 } \).

30.

For same /common denominators, LCM of 4,3,6,8 is 24,
\(\frac { -3\times 6 }{ 4\times 6 } ,\frac { 2\times 8 }{ 3\times 8 } ,\frac { 5\times 4 }{ 6\times 4 } ,\frac { 7\times 3 }{ (-8)\times 3 } \)
So, \(\\ \frac { -18 }{ 24 } ,\frac { 16 }{ 24 } ,\frac { 20 }{ 24 } ,\frac { -21 }{ 24 } \)

Generic 5

3 x 5 = 15

31.

(a) On the number line, it will mean three jumps of \(\frac{4}{7}\) to the left from zero. We reach at \(\frac{-12}{7}.\)

So, \(\frac{-4}{7}\times3=\frac{-12}{7}\)
(b) \(\frac{-4}{7}\times3=\frac{-4\times3}{7}=\frac{-12}{7}\)
We observe that we arrive at the same rational number.

32.

\(-\frac{5}{3}=-\frac{5\times7}{3\times7}=-\frac{35}{21}\)
\(-\frac{8}{7}=-\frac{8\times3}{7\times3}=-\frac{24}{21}\)
Five rational numbers:
\(-\frac{35}{21}<-\frac{33}{21}<-\frac{32}{21}<-\frac{31}{21}<-\frac{30}{21}<\frac{-29}{21}<\frac{-24}{21}\)
\(\Rightarrow -\frac{5}{3}<(-\frac{33}{21})<(-\frac{32}{21})<(-\frac{31}{21})<(-\frac{30}{21})<(-\frac{29}{21})<\frac{-8}{7}\)
So, five rational numbers between \(-\frac{5}{3}\ and-\frac{8}{7}\)
\(-\frac{33}{21},-\frac{32}{21},\frac{-31}{21},\frac{-30}{21}\ and -\frac{29}{21}\)

33.

Three and half =\(3\frac { 1 }{ 2 } =\frac { 3\times 2+1 }{ 2 } =\frac { 7 }{ 2 } \)

1 Marks

5 x 1 = 5

34.