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Published on: 25/09/2019
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 \(=\frac { -12 }{ 10 } +\left( \frac { -90 }{ 15 } \right) -\left( \frac { 3 }{ 8 } \right) \)
2.
Arrange the following rational numbers in ascending and descending order
\(\frac { -17 }{ 10 } ,\frac { -7 }{ 5 } ,0,\frac { -2 }{ 4 } ,\frac { -19 }{ 20 } \)
3.
Find \(\frac { -5 }{ 8 } \times 7\)
4.
Write the following decimal numbers as rationals.
1.15
5.
The multiplicative inverse of -1 is ________.
6.
If \(x\times \frac { -55 }{ 63 } =\frac { -55 }{ 63 } \times x=1\) then x is called the _______________ of \(\frac { 55 }{ 63 } \)
7.
If -3 x \(\frac { -6 }{ 11 } \) = \(\frac { -6 }{ 11 } \times x\) is _______________
8.
The value of \(\frac { -5 }{ 12 } +\frac { 7 }{ 15 } \) = ________________
9.
\(\frac { -19 }{ 5 } \) lies between the integers ______________ and ________________
10.
The multiplicative inverse exists for all rational numbers
11.
The additive inverse of \(\frac { -11 }{ -17 } \) is \(\frac { 11 }{ 17 } \)
12.
The rational numbers that are equal to their additive inverses are 0 and –1.
13.
The rational number that does not have a reciprocal is 0.
14.
0 is the smallest rational number
15.
Explain why the statements are true?
0.4>0.386
16.
Show that \(\left( \frac { \frac { 7 }{ 9 } -5 }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =-2\)
17.
A piece of wire is \(\frac { 4 }{ 5 } \) m long. If it is cut into 8 pieces of equal length, how long will each piece be?
18.
In a constituency, \(\frac { 19 }{ 25 } \) of the voters had voted for candidate A whereas \(\frac { 7 }{ 50 } \) had voted for candidate B. Find the rational number of the voters who had voted for others.
19.
Divide: -2 by \(\frac { -6 }{ 15 } \)
20.
Evaluate: \(\frac{9}{132} \times \frac{-11}{3}\)
21.
Draw the number line and represent the following rational numbers on it.
\(\frac { -8 }{ 3 } \)
22.
List five rational numbers between
–2 and 0
23.
Simplify \(\frac { 5 }{ 12 } +\frac { -5 }{ 18 } -\frac { 7 }{ 24 } \)
24.
Using average, write 3 rational numbers between \(\frac { 14 }{ 5 } \) and \(\frac { 16 }{ 3 } \)
25.
\(\frac { 1 }{ 2 } -\left( \frac { 3 }{ 4 } -\frac { 5 }{ 6 } \right) \neq \left( \frac { 1 }{ 2 } -\frac { 3 }{ 4 } \right) -\frac { 5 }{ 6 } \) illustrates that subtraction does not satisfy the ________ property for rational numbers.
commutative
closure
distributive
associative
26.
\(\frac { 3 }{ 4 } \div \left( \frac { 5 }{ 8 } +\frac { 1 }{ 2 } \right) \) =
\(\frac { 13 }{ 10 } \)
\(\frac { 2 }{ 3 } \)
\(\frac { 3 }{ 2 } \)
\(\frac { 5 }{ 8 } \)
27.
The sum of the digits of the denominator in the simplest form of \(\frac { 112 }{ 528 } \)
4
5
6
7
28.
The number which is subtracted from \(\frac { -6 }{ 11 } \) to get \(\frac { 8 }{ 9 } \) is
\(\frac { 34 }{ 99 } \)
\(\frac { -142 }{ 99 } \)
\(\frac { 142 }{ 99 } \)
\(\frac { -34 }{ 99 } \)
1.
\(=\frac { (-12\times 12)+(-90\times 8)-(3\times 15) }{ 120 } \)
\(=\frac { -144+(-720)-45 }{ 120 } =\frac { -864-45 }{ 120 } \)
\(=\frac { -864+(-45) }{ 120 } =\frac { -909 }{ 120 } =\frac { -303 }{ 40 } \\ \)
2.
\(\frac { -17 }{ 10 } ,\frac { -7 }{ 5 } ,0,\frac { -2 }{ 4 } ,\frac { -19 }{ 20 } \)
LCM of 10, 5, 4, 20 is 5 x 2 x 2 = 20
\(\frac { -17 }{ 10 } =\frac { -17\times 2 }{ 10\times 2 } =\frac { -34 }{ 20 } \)
\(\frac { -7 }{ 5 } =\frac { -7\times 4 }{ 5\times 4 } =\frac { -28 }{ 20 } \)
\(\frac { -2 }{ 4 } =\frac { -2\times 5 }{ 4\times 5 } =\frac { -10 }{ 20 } \)
\(\frac { -19 }{ 20 } =\frac { -19 }{ 20 } \)
Negative numbers are less then zero.
∴ Arranging the numerators we get
-34 < - 28< -19 < -10 < 0
Ascending Order: \(\frac { -17 }{ 10 } ,\frac { -7 }{ 5 } ,\frac { -19 }{ 20 } ,\frac { -2 }{ 4 } ,0\)
Descending Order: \(0,\frac { -2 }{ 4 } ,\frac { -19 }{ 20 } ,\frac { -7 }{ 5 } ,\frac { -17 }{ 10 } \)
3.
\(\frac { -5 }{ 8 } \times 7=\frac { -5 }{ 8 } \times \frac { 7 }{ 1 } =\frac { -5\times 7 }{ 8\times 1 } =\frac { -35 }{ 8 } \)
4.
\(1.15=\frac { 115 }{ 100 } =\frac { 23 }{ 10 } =1\frac { 3 }{ 20 } \)
5.
( )
-1
6.
( )
Multiplicative Inverse
7.
( )
-3
8.
( )
\(\frac { 1 }{ 20 } \)
9.
( )
-4 and -3
10.
(b)
11.
(b)
12.
(b)
13.
(a)
14.
(b)
15.
\(0.4=\frac { 4 }{ 10 } =\frac { 400 }{ 1000 } \)
\(\\ 0.386=\frac { 386 }{ 1000 } \)
\(\frac { 400 }{ 1000 } >\frac { 386 }{ 1000 } \)
0.4>0.386
16.
\(LHS=\left( \frac { \frac { 7 }{ 9 } -5 }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =\left( \frac { \frac { 7-(5\times 9) }{ 9 } }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } \)
\(=\left( \frac { \frac { 7 }{ 9 } -5 }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =\left( \frac { \frac { -38 }{ 9 } }{ \frac { 4 }{ 3 } } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } \)
\(=\left( \frac { -38 }{ 9 } \times \frac { 3 }{ 4 } \right) \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =\frac { -19 }{ 6 } \div \frac { 3 }{ 2 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } \)
\(=\frac { -19 }{ 6 } \times \frac { 2 }{ 3 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =\frac { -19 }{ 9 } +\frac { 4 }{ 9 } -\frac { 1 }{ 3 } =\frac { -19+4-(1\times 3) }{ 9 } \)
\(=\frac { -15-3 }{ 9 } =\frac { -18 }{ 9 } =-2=RHS\)
17.
Length of the wire = \(\frac{4}{5}m\)
\(=\frac { 4\times 100 }{ 5 } cm=80cm\)
Number of equal pieces made from it = 80 \(\div\) 8 = 10 cm
∴ Length of each small pieces = 10 cm
18.
Voters voted for A \(=\frac{19}{25}\) of the total
Voters voted for B \(=\frac{7}{50}\) of the total
∴ Total voters voted for A or B =\(\frac{19}{25}+\frac{7}{50}\)
\(=\frac { (19\times 2)+(7\times 1) }{ 50 } =\frac { 38+7 }{ 50 } =\frac { 45 }{ 50 } \)
Let the total voters be 1.
∴ Remaining voters = 1-\(\frac{45}{50}\)
\(\\ =\frac { (1\times 50)-(45\times 1) }{ 50 } =\frac { 50-45 }{ 50 } =\frac { 5 }{ 50 } =\frac { 1 }{ 10 } \)
∴ \(\frac{1}{10}\) of total voters voted for others.
19.
\(=-2 \times \frac{15}{-6}
\)
\(=1 \times \frac{15}{3}=5
\)
20.
\(\frac{9}{132} \times \frac{-11}{3}=\frac{3}{12} \times \frac{-1}{1}=\frac{-1}{4} \)
21.
\(\frac { -8 }{ 3 } \) = - 2\(\frac{2}{3}\)
\(\frac { -8 }{ 3 } \) lies between -2 and -3
22.
-2 and 0
i,e. \(\frac{-2}{1}\) and \(\frac{0}{1}\)
\(\frac { -2 }{ 1 } =\frac { -2\times 10 }{ 1\times 10 } =\frac { -20 }{ 10 } \)
\(\frac { 0 }{ 1 } =\frac { 0\times 10 }{ 1\times 10 } =\frac { 0 }{ 10 } \)
∴ Five rational numbers between \(\frac{-20}{10}\) ( = -2) and \(\frac{0}{10}\)( = 0)are
\(\frac { -20 }{ 10 } ,\frac { -19 }{ 10 } ,\frac { -18 }{ 10 } ,\frac { -7 }{ 10 } ,\frac { -6 }{ 10 } ,\frac { -5 }{ 10 } ,\frac { 0 }{ 10 } (=0)\)
23.
\(\frac { 5 }{ 12 } +\frac { -5 }{ 18 } -\frac { 7 }{ 24 } =\frac { (5\times 6)+(-5\times 4)-(7\times 3) }{ 72 } \)
\(=\frac { 30+(-20)-(21) }{ 72 } =\frac { 10-21 }{ 72 } \)
\(=\frac { -11 }{ 72 } \)
Hint:
= 2 x 3 x 2 x 3 x 2
= 72
24.
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,
\(\frac { 14 }{ 5 } <\frac { 103 }{ 30 } <\frac { 15 }{ 4 } <\frac { 61 }{ 15 } <\frac { 16 }{ 3 } \)
25.
(d)
associative
26.
(b)
\(\frac { 2 }{ 3 } \)
27.
(c)
6
28.
(b)
\(\frac { -142 }{ 99 } \)
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Tamilnadu Stateboard 8th Standard Subjects
Tamilnadu Stateboard Standards
