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Published on: 03/12/2019
Rational Numbers
Download Tamil Nadu 8th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Simplify \(\frac { 2 }{ 5 } +\frac { 8 }{ 3 } +\frac { -11 }{ 15 } +\frac { 4 }{ 5 } +\frac { -2 }{ 3 } \)
2.
Write the following rational numbers in descending and ascending order.
\(\frac { -3 }{ 5 } ,\frac { 7 }{ -10 } ,\frac { -15 }{ 20 } ,\frac { 14 }{ -30 } ,\frac { -8 }{ 15 } \)
3.
Write the following decimal numbers as rationals.
−5.8
4.
Write the following decimal numbers as rationals.
3.0
5.
Divide the. sum of \(\frac{15}{12}\)and \(\frac{12}{7}\) by their difference.
6.
Find four rational numbers between \(\frac{2}{3}\) and \(\frac{4}{5}\)
7.
Find the rational numbers represented by each of the question marks marked on the following number lines.
8.
Draw the number line and represent the following rational numbers on it.
\(\frac { -17 }{ -5 } \)
9.
Draw the number line and represent the following rational numbers on it.
\(\frac { -8 }{ 3 } \)
10.
Write four rational numbers equivalent to
\(\frac { -7 }{ 6 } \)
11.
Using average, write 3 rational numbers between \(\frac { 14 }{ 5 } \) and \(\frac { 16 }{ 3 } \)
12.
\(\frac { 1 }{ 2 } \times \left( \frac { 2 }{ 3 } +\frac { 6 }{ 4 } \right) =\left( \frac { 1 }{ 2 } +\frac { 2 }{ 3 } \right) +\left( \frac { 1 }{ 2 } \times \_ \_ \right) \)
\(\frac{1}{2}\)
\(\frac{2}{3}\)
\(\frac{4}{6}\)
0
13.
\(\frac{5}{6}\div\frac{6}{2}\) is
\(\frac{5}{2}\)
\(\frac{2}{5}\)
\(\frac{5}{18}\)
\(\frac{30}{12}\)
14.
Closure property is not true for division of rational numbers because of the number
0
-1
0
\(\frac { 1 }{ 2 } \)
15.
\(\frac { 3 }{ 4 } \div \left( \frac { 5 }{ 8 } +\frac { 1 }{ 2 } \right) \) =
\(\frac { 13 }{ 10 } \)
\(\frac { 2 }{ 3 } \)
\(\frac { 3 }{ 2 } \)
\(\frac { 5 }{ 8 } \)
16.
The sum of the digits of the denominator in the simplest form of \(\frac { 112 }{ 528 } \)
4
5
6
7
1.
\(\frac{37}{15}\)
2.
First, make the denominators positive and write the numbers in standard form as \(\frac { -3 }{ 5 } ,\frac { 7 }{ -10 } ,\frac { -15 }{ 20 } ,\frac { 14 }{ -30 } ,\frac { -8 }{ 15 } \) Now, the LCM of 5,10,15,20 and 30 is 60 (How?). Change the given rational numbers to their equivalent form with common denominator 60.
\(\frac { -3 }{ 5 } =\frac { -3 }{ 5 } \times \frac { 12 }{ 12 } =\frac { -36 }{ 60 } \)
\(\frac { 7 }{ -10 } =\frac { -7 }{ 10 } \times \frac { 6 }{ 6 } =\frac { -42 }{ 60 } \)
\(\frac { -15 }{ 20 } =\frac { -15 }{ 20 } \times \frac { 3 }{ 3 } =\frac { -45 }{ 60 } \)
\(\frac { -14 }{ 30 } =\frac { -14 }{ 30 } \times \frac { 2 }{ 2 } =\frac { -28 }{ 60 } \)
\(\frac { -8 }{ 15 } =\frac { -8 }{ 15 } \times \frac { 4 }{ 4 } =\frac { -32 }{ 60 } \)
Now, comparing the numerators − 36, − 42, − 45, − 28 and – 32 we see that
− 28 > − 32 > − 36 > − 42 > − 45
That is, \(\frac { -28 }{ 60 } >\frac { -32 }{ 60 } >\frac { -36 }{ 60 } >\frac { -42 }{ 60 } >\frac { -45 }{ 60 } \)
and so, \(\frac { -14 }{ 30 } >\frac { -8 }{ 15 } >\frac { -3 }{ 5 } >\frac { 7 }{ -10 } >\frac { -15 }{ 20 } \)
Hence, the descending order of the given rational numbers is \(\frac { -14 }{ 30 } ,\frac { -8 }{ 15 } ,\frac { -3 }{ 5 } ,\frac { 7 }{ -10 } ,and\frac { -15 }{ 20 } \) and its reverse order gives the ascending order. Hence the ascending order of the given rational numbers is \(\frac { -15 }{ 20 } ,\frac { 7 }{ -10 } ,\frac { -3 }{ 5 } ,\frac { -8 }{ 15 } ,and\frac { -14 }{ 30 } \)
3.
\(-5.8=\frac { -58 }{ 10 } =\frac { -29 }{ 5 } =-5\frac { 4 }{ 5 } \)
4.
\(3.0=\frac { 30 }{ 10 } =\frac { 3 }{ 1 } \)
5.
\(\frac{599}{311}\)
6.
\(\frac { 41 }{ 60 } ,\frac { 42 }{ 60 } ,\frac { 43 }{ 60 } ,\frac { 44 }{ 60 } \)
7.
The rational number for the point marked on the number line is 1\(\frac{3}{4}=\frac{7}{4}\)
8.
\(\frac { -17 }{ -5 } =3\frac { 2 }{ 5 } \)
\(\frac { -17 }{ -5 }\) lies between 3 and 4
9.
\(\frac { -8 }{ 3 } \) = - 2\(\frac{2}{3}\)
\(\frac { -8 }{ 3 } \) lies between -2 and -3
10.
\(\frac { 7 }{ -6 } =\frac { 7\times 2 }{ -6\times 2 } =\frac { 14 }{ -12 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 3 }{ -6\times 3 } =\frac { 21 }{ -18 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 4 }{ -6\times 4 } =\frac { 28 }{ -24 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 5 }{ -6\times 5 } =\frac { 35 }{ -30 } \)
Four equivalent rational numbers of \(\frac { -7 }{ 6 } \) are \(\frac { 14 }{ -12 } ,\frac { 21 }{ -18 } ,\frac { 28 }{ -24 } ,\frac { 35 }{ -30 } \)
11.
The average of a and b is \(\frac{1}{2}(a+b)\)
The average of \(\frac{14}{5}\) and \(\frac{16}{3}\) is C1=\(\frac { 1 }{ 2 } \left( \frac { 14 }{ 5 } +\frac { 16 }{ 3 } \right) \)
\({ C }_{ 1 }=\frac { 1 }{ 2 } \left( \frac { 42+80 }{ 15 } \right) \)
\({ C }_{ 1 }=\frac { 122 }{ 30 } \)
\({ C }_{ 1 }=\frac { 61 }{ 15 } \)
\(\\ \frac { 14 }{ 5 } <\frac { 61 }{ 15 } <\frac { 16 }{ 3 } \) ..(1)
The average of \(\frac { 14 }{ 5 }\) and \(\frac{61}{15}\)is C2=\(\frac { 1 }{ 2 } \left( \frac { 14 }{ 5 } +\frac { 61 }{ 15 } \right) \)
\(\frac { 1 }{ 2 } \left( \frac { 14 }{ 5 } +\frac { 61 }{ 15 } \right) \)
\({ C }_{ 2 }=\frac { 1 }{ 2 } \times \left( \frac { 42+61 }{ 15 } \right) \)
\({ C }_{ 2 }=\frac { 1 }{ 2 } \times \frac { 103 }{ 15 } \)
\(\frac { 103 }{ 15 } \)
\(\therefore \frac { 14 }{ 5 } <\frac { 103 }{ 30 } <\frac { 61 }{ 15 } \) ..(2)
The average of \(\frac{103}{30}\) and \(\frac{61}{15}\) is C3=\(\frac { 1 }{ 2 } \left( \frac { 103 }{ 30 } +\frac { 61 }{ 15 } \right) \)
\({ C }_{ 3 }=\frac { 1 }{ 2 } \times \left( \frac { 103+122 }{ 30 } \right) \)
\({ C }_{ 3 }=\frac { 1 }{ 2 } \times \frac { 225 }{ 30 } \)
\({ C }_{ 3 }=\frac { 1 }{ 2 } \times \frac { 15 }{ 2 } \)
\(\\ { C }_{ 3 }=\frac { 15 }{ 4 } \)
\(\therefore \frac { 103 }{ 30 } <\frac { 15 }{ 4 } <\frac { 61 }{ 15 } \)...(3)
From (1), (2) and (3) we get,
\(\frac { 14 }{ 5 } <\frac { 103 }{ 30 } <\frac { 15 }{ 4 } <\frac { 61 }{ 15 } <\frac { 16 }{ 3 } \)
12.
(c)
\(\frac{4}{6}\)
13.
(c)
\(\frac{5}{18}\)
14.
(c)
0
15.
(b)
\(\frac { 2 }{ 3 } \)
16.
(c)
6
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Tamilnadu Stateboard 8th Standard Subjects
Tamilnadu Stateboard Standards
