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Published on: 13/08/2019
Rational Numbers
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Questions + Answers key
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1.
The denominator of the rational number - 9 is
-9
9
-1
1
2.
The denominator of the rational number \(\frac{-6}{-5}\) is
6
-6
5
-5
3.
The denominator of the rational number \(\frac{4}{7}\) is
7
4
3
11
4.
rational number \(\frac{p}{q}\)is said to be in its simplest form, when
'p' is a prime number.
'q' is a prime number.
'p' and 'q' both are prime to each other.
all of the above.
5.
Which of the following is equivalent to \(\frac{4}{5}\)?
\(\frac{5}{4}\)
\(\frac{16}{25}\)
\(\frac{16}{20}\)
\(\frac{15}{25}\)
6.
How many rational numbers are there between 2 and 4?
Zero
one
two
uncountable
7.
Which of the following is the standard form \(\frac{36}{-24}\)is
\(\frac{-3}{2}\)
\(\frac{3}{2}\)
\(\frac{2}{3}\)
\(\frac{2}{-3}\)
8.
The subtraction \(6\frac { 4 }{ 5 } \)from \(\frac { 50 }{ 5 } \)
\(3\frac { 1 }{ 5 } \)
\(2\frac { 1 }{ 5 } \)
\(\frac { 31 }{ 95 } \)
\(\frac { 39 }{ 95 } \)
9.
-3 can be written in the form of \(\frac { p }{ q } \) as
\(\frac { -3 }{ -1 } \)
\(\frac { -3 }{ 0 } \)
\(\frac { 0 }{ -3 } \)
\(\frac { -3 }{ 1 } \)
10.
Which of the following rational numbers is postive?
\(\frac { -8 }{ 7 } \)
\(\frac { 19 }{ -13 } \)
\(\frac { -3 }{ -4 } \)
\(\frac { -21 }{ 13 } \)
11.
\(\frac{-16}{24}\)and\(\frac{20}{-16}\) represent____________ rational numbers.
12.
\(\frac{-1}{2}\) is__________than \(\frac{1}{5}\)
13.
\(\frac { -5 }{ 3 } \times \left( \frac { -3 }{ 5 } \right) =\) __________
14.
\(\frac { -5 }{ 6 } +\frac { -1 }{ 6 }\)=_________
15.
Additive inverse of \(\frac { 2 }{ 3 } \) is__________
16.
Arrange the rational numbers \(\frac{-2}{5},\frac{9}{-10}\) and \(\frac{-5}{6}\).
17.
Write four more rational numbers in each of the following patterns:
\(\\ \frac { -1 }{ 6 } ,\frac { 2 }{ -12 } ,\frac { 3 }{ 18 } ,\frac { 4 }{ -24 } ,....\)
18.
Draw the number line and represent the following rational numbers on it .
\(\frac { 3 }{ 4 } \)
19.
Find \(\frac{-4}{7}\times3,\)using both ways. What do you observe?
20.
Taking x \(=\frac { -4 }{ 9 } \),y\(=\frac { 5 }{ 12 } \)and z\(=\frac { 7 }{ 18 } \), Find
The rational number, which when added to x gives y.
21.
Write three rational numbers between \(-\frac{1}{2}\) and \(\frac{1}{2}\).
22.
Write the following rational numbers in their standard form:
\(\frac{36}{-24}\)
23.
What is the standard form of \(\frac{105}{-185}\)?
24.
If product of two rational numbers is \(\frac{-8}{9}\) and one of the number is\(\frac{-10}{3}\) find the other.
25.
'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?
1.
(d)
1
2.
(d)
-5
3.
(a)
7
4.
(c)
'p' and 'q' both are prime to each other.
5.
(c)
\(\frac{16}{20}\)
6.
(b)
one
7.
(a)
\(\frac{-3}{2}\)
8.
(a)
\(3\frac { 1 }{ 5 } \)
9.
(d)
\(\frac { -3 }{ 1 } \)
10.
(c)
\(\frac { -3 }{ -4 } \)
11.
( )
different
12.
( )
less
13.
\(\frac { -5 }{ 3 } \times \left( \frac { -3 }{ 5 } \right) =\frac { 15 }{ 15 } =1\)
14.
\(\frac { -5 }{ 6 } +\frac { -1 }{ 6 } =\frac { -5-1 }{ 6 } =\frac { -6 }{ 6 } =\)-1
15.
Additive inverse of \(\frac { 2 }{ 3 } \) is \(-\frac { 2 }{ 3 } \)
16.
The given rational numbers are: \(\frac{-2}{5},\frac{9}{-10}\) and \(\frac{-5}{6}\).
First let us express the given rational numbers with positive denominators.
\(\therefore\) \(\frac{-2}{5}=\frac{-2\times1}{5\times1}=\frac{-2}{5}\)
\(\frac{9}{-10}=\frac{9\times(-1)}{(-10)\times(-1)}=\frac{-9}{10}\)
\(\frac{-5}{6}=\frac{-5\times1}{6\times1}=\frac{-5}{6}\)
Since, LCM of 5, 10 and 6 is 30.
\(\therefore\)Making the denominators of the given rationals the same, we have
\(\frac{-2}{5}=\frac{-2}{5}\times \frac{6}{6}=\frac{-12}{30}\)
\(\frac{9}{-10}=\frac{-9}{10}\times \frac{3}{3}=\frac{-27}{30}\)
\(\frac{-5}{6}=\frac{-5}{6}\times \frac{5}{5}=\frac{-25}{30}\)
Since, (-27) <(-25) <(-12)
i.e. \(\frac{-27}{30}<\frac{-25}{30}<\frac{-12}{30}\)
Thus, \(\frac{9}{-10}<\frac{-5}{6}<\frac{-2}{5}\)
17.
The required four more rational numbers are
\(\frac { 5 }{ -30 } ,\frac { 6 }{ -36 } ,\frac { 7 }{ -42 }\) and \(\frac { 8 }{ -48 }\)
18.
Representation of rational number \(\frac { 3 }{ 4 } \) on number line .
19.
(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.
20.
Let we add A to x to find y,
A+x=y\(\Rightarrow \) \(A+\left( \frac { -4 }{ 9 } \right) =\left( \frac { 5 }{ 12 } \right) \)
\(A=\frac { 5 }{ 12 } -\left( \frac { -4 }{ 9 } \right) =\frac { 5 }{ 12 } +\frac { 4 }{ 9 } \)
\(=\frac { 5\times 3+4\times 4 }{ 36 } =\frac { 15+16 }{ 36 } =\frac { 31 }{ 36 } \)
21.
( )
\(-\frac{1}{4}\),0,\(\frac{1}{4}\)
22.
( )
\(\frac{-3}{2}\)
23.
( )
-\(\frac{21}{37}\)
24.
( )
Let other number be x
\(x\times \left( \frac { -10 }{ 3 } \right) =\frac { -8 }{ 9 } \)
\(x={8\times3\over10\times9}\)
=\(\frac{4\times1}{5\times3}=\frac{4}{15}\)
25.
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 \(\left(\frac{a+b}{a-b}\right)>\left(\frac{a-b}{a+b}\right)\)
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