From the chapter Rational Numbers, some of the important questions are covered in this question paper. The questions are covers from the Higher Order Thinking Questions and Value Based Questions.

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Questions:

Generic 3

5 x 3 = 15

Which is greater in each of the following?
\(\frac { -3 }{ 4 } ,\frac { 2 }{ -3 } \)

Rewrite the following rational number in simplest form.
\(\frac { 25 }{ 45 } \)

Write four more rational numbers in each of the following patterns:
\(\frac { -3 }{ 5 } ,\frac { -6 }{ 10 } ,\frac { -9 }{ 15 } ,\frac { -12 }{ 20 } ,....\)

If p=m\(\times \)t and q=n\(\times \)t \(\frac { p }{ q } \)=\(\frac { \boxed { } }{ \boxed { } } \)

Express \(\frac { 2 }{ 7 } \) and \(\frac { 5 }{ 3 } \) as equivalent fractions having same numerator.

Generic 2

5 x 2 = 10

Simplify \(\\ \left( \frac { -1 }{ 5 } \times \frac { 2 }{ -3 } \right) +\left( 2\times \frac { 5 }{ 3 } \right) -\left( -\frac { 2 }{ 3 } \times \frac { 5 }{ 6 } \right) \)

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

Express the following rational number with positive denominator \(\frac { 5 }{ -6 } \)

Divide the difference of \(\frac { 2 }{ 5 } \) and \(\frac { 3 }{ 13 } \) by the product \(\frac { 2 }{ 9 } \) and \(\frac { 3 }{ 5 } \)

10.

Product of two rational numbers is 3.If one of them is \(\frac { 5 }{ 8 } \) then find other

Multiple Choice Question

5 x 1 = 5

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.

The subtraction \(6\frac { 4 }{ 5 } \)from \(\frac { 50 }{ 5 } \)

(a)

\(3\frac { 1 }{ 5 } \)

(b)

\(2\frac { 1 }{ 5 } \)

(c)

\(\frac { 31 }{ 95 } \)

(d)

\(\frac { 39 }{ 95 } \)

13.

Which is greater number in the following?

(a)

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

(b)

(c)

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

(d)

-2

14.

-3 can be written in the form of \(\frac { p }{ q } \) as

(a)

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

(b)

\(\frac { -3 }{ 0 } \)

(c)

\(\frac { 0 }{ -3 } \)

(d)

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

15.

Which of the following rational numbers is negative?

(a)

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

(b)

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

(c)

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

(d)

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

Fill up / 1 Marks

5 x 1 = 5

16.

\(4\frac { 4 }{ 5 } \div \frac { 24 }{ 5 } +8\frac { 1 }{ 4 } =\)__________

17.

\(\)\(\frac { -6 }{ 7 } =\frac { \_ \_ \_ \_ }{ 42 } \)

18.

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

19.

The Standard form of \(\frac { 18 }{ -24 } \) is________

20.

1 is a ________ rational number .

True or False

4 x 1 = 4

21.

if \(\frac { p }{ q } \) is rational number and m is non zero integer, then \(\frac { p\times m }{ q\times m } \) is a rational number not equivalent to \(\frac { p }{ q } \) .

(a)

True

(b)

False

22.

\(\frac { 24 }{ 64 } \div \frac { 6 }{ 16 } =\frac { 4 }{ 7 } \)

(a)

True

(b)

False

23.

Every fraction is a rational number

(a)

False

(b)

True

24.

Sum of two rational numbers is always a rational number.

(a)

False

(b)

True

Generic 5

2 x 5 = 10

25.

Taking x\(=\frac { -4 }{ 9 } \), y\(=\frac { 5 }{ 12 } \), and z \(=\frac { 7 }{ 18 } \), Find
( x - y) +z

26.

Find the sum of \(\frac { 4 }{ 7 } +\frac { -8 }{ 9 } +\frac { -5 }{ 21 } +\frac { 1 }{ 3 } \).

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Answers Key:

Generic 3

5 x 3 = 15

Given, \(\frac { -3 }{ 4 } ,\frac { 2 }{ -3 } \)
First, write the rational number with positive denominator, we have \(\frac { 2 }{ -3 } =\frac { 2\times (-1) }{ -3\times (-1) } =\frac { -2 }{ 3 } \)
Thus, the given rational numbers with positive denominators are \(\\ \frac { -3 }{ 4 } \) and \(\frac { -2 }{ 3 } \) .
\(\because \) LCM of the denominators 4 and 3 = 12
\(\\ \therefore \) \(\frac { -3 }{ 4 } =\frac { -3\times 3 }{ 4\times 3 } =\frac { -9 }{ 12 } \) and \(\\ \frac { -2 }{ 3 } =\frac { -2\times 4 }{ 3\times 4 } =\frac { -8 }{ 12 } \)
On comparing the numerators, we get -9 < -8
\(\\ \Rightarrow \frac { -9 }{ 12 } <\frac { -8 }{ 12 } \) or \(\frac { -3 }{ 4 } <\frac { -2 }{ 3 } \)
Hence, \(\\ \frac { -2 }{ 3 } \) is greater than \(\\ \frac { -3 }{ 4 } \).

Given,\(\frac { 25 }{ 45 } \)
\(\because \) 25=5\(\times \)5 and 45=5\(\times \)3\(\times \)3
\(\therefore \) HCF of 25 and 45 = 5
On dividing the numerator and denominator by 5, we get
\(\frac { 25 }{ 45 } =\frac { 25\div 5 }{ 45\div 5 } =\frac { 5 }{ 9 } \)
Hence, the simplest form of \(\frac { 25 }{ 45 } \)is \(\frac { 5 }{ 9 } \).

Given,\(\frac { -3 }{ 5 } ,\frac { -6 }{ 10 } ,\frac { -9 }{ 15 } ,\frac { -12 }{ 20 } ,....\)
Here,\(\frac { -3 }{ 5 } \) is the rational number in standard form.
Now, \(\frac { -3 }{ 5 } =\frac { -3\times 1 }{ 5\times 1 } ,\frac { -6 }{ 10 } =\frac { -3\times 2 }{ 5\times 2 } ,\)
\(\frac { -9 }{ 15 } =\frac { -3\times 3 }{ 5\times 3 } ,\frac { -12 }{ 20 } =\frac { -3\times 4 }{ 5\times 4 } \)
or \(\frac { -3\times 1 }{ 5\times 1 } =\frac { -3 }{ 5 } ,\frac { -3\times 2 }{ 5\times 2 } =\frac { -6 }{ 10 } \)
\(\frac { -3\times 3 }{ 5\times 3 } =\frac { -9 }{ 15 } ,\frac { -3\times 4 }{ 5\times 4 } =\frac { -12 }{ 20 } \)
Thus, we observe a pattern in these numbers. The next four numbers are
\(\frac { -3\times 5 }{ 5\times 5 } =\frac { -15 }{ 25 } ,\frac { -3\times 6 }{ 5\times 6 } =\frac { -18 }{ 30 } \)
\(\\ \frac { -3\times 7 }{ 5\times 7 } =\frac { -21 }{ 35 } ,\frac { -3\times 8 }{ 5\times 8 } =\frac { -24 }{ 40 } \)
Hence, the required four more rational numbers are
\(\frac { -15 }{ 25 } ,\frac { -18 }{ 30 } ,\frac { -21 }{ 35 } \)and \(\frac { -24 }{ 40 } \).

Given p=mand q=n\(\times \)t
\(\therefore \) \(\frac { p }{ q } =\frac { m\times t }{ n\times t } \Rightarrow \frac { p }{ q } =\frac { m }{ n } \)

\(\frac { 10 }{ 35 } \) , \(\frac { 10 }{ 6 } \)

Generic 2

5 x 2 = 10

\(\frac { 181 }{ 45 } \)

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

Given , \(\frac { 5}{ -6 } \)
Rational number with positive denominator is \(\frac { 5}{ 6 } \)

\(\frac { 75 }{ 182 } \)

10.

\(\frac { 24 }{ 5 } \)

Multiple Choice Question

5 x 1 = 5

11.

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

12.

(a)
\(3\frac { 1 }{ 5 } \)

13.

14.

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

15.

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

Fill up / 1 Marks

5 x 1 = 5

16.

\(4\frac { 4 }{ 5 } \div \frac { 24 }{ 5 } +8\frac { 1 }{ 4 } =\frac { (5\times 4)+4 }{ 5 } \div \frac { 24 }{ 5 } +\frac { (8\times 4)+1 }{ 4 } \)
\(\frac { 24 }{ 5 } \div \frac { 24 }{ 5 } +\frac { 33 }{ 4 } \)
Since , the reciprocal of \(\frac { 24 }{ 5 } \) is \(\frac { 5 }{ 24 } \)
\(\\ \therefore \quad \frac { 24 }{ 5 } \times \frac { 5 }{ 24 } +\frac { 33 }{ 4 } =1+\frac { 33 }{ 4 } =\frac { 37 }{ 4 } \)

17.

\(\frac { -6 }{ 7 } =\frac { x }{ 42 } \Rightarrow x=\frac { 42\times (-6) }{ 7 } =6\times (-6)=-36\)

18.

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

19.

Standard form of \(\frac { 18 }{ -24 } =\frac { 18\div 4 }{ -24\div 6 } \) [\(\because \) HCF of 18 and 24 is 6]

20.

1 is a positive rational number [ \(\because \) 1 has positive sign]

True or False

4 x 1 = 4

21.

(b)
False

22.

(b)
False

23.

(a)
False

24.

(a)
False

Generic 5

2 x 5 = 10

25.

We have,( x - y) +z
Put the value of x,y and z
\(=\left( \frac { -4 }{ 9 } -\frac { 5 }{ 12 } \right) +\frac { 7 }{ 18 } \\ \frac { -4\times 4-5\times 3 }{ 36 } +\frac { 7 }{ 18 } =\frac { -16-15 }{ 36 } +\frac { 7 }{ 18 } \\ =\left( \frac { -31 }{ 36 } +\frac { 7 }{ 18 } \right) =\frac { -31+7\times 2 }{ 36 } =\frac { -31+14 }{ 36 } =\frac { -17 }{ 36 } \)

26.

Given,\(\frac { 4 }{ 7 } +\frac { -8 }{ 9 } +\frac { -5 }{ 21 } +\frac { 1 }{ 3 } \)
For same denominator
LCM of 7,9,21 and 3 is 63,\(\)
\(\frac { 4\times 9 }{ 7\times 9 } =\frac { 36 }{ 63 } \),\(\frac { -8\times 7 }{ 9\times 7 } =\frac { -56 }{ 63 } \)
\(\frac { -5\times 3 }{ 21\times 3 } =\frac { -15 }{ 63 } \) , \(\frac { 1\times 21 }{ 3\times 21 } =\frac { 21 }{ 63 } \)
\(\therefore \)\(\frac { 4 }{ 7 } +\frac { -8 }{ 9 } +\frac { -5 }{ 21 } +\frac { 1 }{ 3 } =\frac { 36 }{ 63 } +\frac { -56 }{ 63 } +\frac { -15 }{ 63 } +\frac { 21 }{ 63 } \)
So,\(\frac { 36+(-56)+(-15)+(21) }{ 63 } \)
\(=\frac { 36+21+(-56)+(-15) }{ 63 } =\frac { 57+(-71) }{ 63 } \)
\(=-\frac { 14 }{ 63 } =\frac { -2 }{ 9 } \)

Rational Numbers - Important Questions Model Paper In 7th Maths

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