8th Standard Maths Rational Numbers Important Questions | QB365

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8th Standard Maths Rational Numbers Important Questions

Published on: 19/07/2019

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.

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Std: 8th Standard - Maths

chapter: - Model Question paper

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Questions:

Generic 3

6 x 3 = 18

Reduce to the standard form
\(\frac { 48 }{ -84 } \)

Write the following decimal numbers as rationals.
1.15

Write the following decimal numbers as rationals.
−5.8

Write the following decimal numbers as rationals.
0.666…

Write the following decimal numbers as rationals.
0.25

Write the following decimal numbers as rationals.
3.0

Fill in the blanks

5 x 1 = 5

If distributive property is true for \(\left( \frac { 3 }{ 5 } \times \frac { -4 }{ 9 } \right) +\left( x\times \frac { 15 }{ 17 } \right) =\frac { 3 }{ 5 } \times (y+z)\) then x, y, z are ________ , ________ and ________.

If -3 x \(\frac { -6 }{ 11 } \) = \(\frac { -6 }{ 11 } \times x\) is _______________

The multiplicative inverse of \(2\frac { 3 }{ 5 } \) is _____________

10.

The value of \(\left( \frac { -15 }{ 23 } \right) \div \left( \frac { +30 }{ -46 } \right) \) is _____________

11.

The value of \(\frac { -5 }{ 12 } +\frac { 7 }{ 15 } \) = ________________

True or False

5 x 1 = 5

12.

The rational numbers that are equal to their additive inverses are 0 and –1.

(a)

True

(b)

False

13.

The rational number which is its own reciprocal is –1.

(a)

True

(b)

False

14.

The rational number that does not have a reciprocal is 0.

(a)

True

(b)

False

15.

There are an unlimited rationals between 0 and 1

(a)

True

(b)

False

16.

0 is the smallest rational number

(a)

True

(b)

False

Generic 2

6 x 2 = 12

17.

If p + 2q = 18 and pq = 40, find \(\frac { 2 }{ p } +\frac { 1 }{ q } \)

18.

Write four rational numbers equivalent to
\(\frac { 8 }{ 9 } \)

19.

Write four rational numbers equivalent to
\(\frac { -7 }{ 6 } \)

20.

Write four rational numbers equivalent to
\(\frac { -3 }{ 5 } \)

21.

List five rational numbers between
–1.2 and -2.3

22.

List five rational numbers between
0.25 and 0.35

Multiple Choice Question

5 x 1 = 5

23.

\(\frac { 1 }{ 2 } -\left( \frac { 3 }{ 4 } -\frac { 5 }{ 6 } \right) \neq \left( \frac { 1 }{ 2 } -\frac { 3 }{ 4 } \right) -\frac { 5 }{ 6 } \) illustrates that subtraction does not satisfy the ________ property for rational numbers.

(a)

commutative

(b)

closure

(c)

distributive

(d)

associative

24.

Closure property is not true for division of rational numbers because of the number

(a)

(b)

-1

(c)

(d)

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

25.

Which of the following pairs is equivalent?

(a)

\(\frac { -20 }{ 12 } ,\frac { 5 }{ 3 } \)

(b)

\(\frac { 16 }{ -30 } ,\frac { -8 }{ 15 } \)

(c)

\(\frac { -18 }{ 36 } ,\frac { -20 }{ 44 } \)

(d)

\(\frac { 7 }{ -5 } ,\frac { -5 }{ 7 } \)

26.

Which of the following rational numbers is the greatest?

(a)

\(\frac { -17 }{ 24 } \)

(b)

\(\frac { -13 }{ 16 } \)

(c)

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

(d)

\(\frac { -31 }{ 32 } \)

27.

The number which is subtracted from \(\frac { -6 }{ 11 } \) to get \(\frac { 8 }{ 9 } \) is

(a)

\(\frac { 34 }{ 99 } \)

(b)

\(\frac { -142 }{ 99 } \)

(c)

\(\frac { 142 }{ 99 } \)

(d)

\(\frac { -34 }{ 99 } \)

Match the following

5 x 1 = 5

28.

\(\frac { 22 }{ 7 } \)

29.

\(\frac { 1 }{ 0 } \)

30.

\(\frac { -4 }{ 9 } \times \frac { 9 }{ -4 } =\frac { 9 }{ -4 } \times \frac { -4 }{ 9 } =1\)

31.

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

32.

\(\left( \frac { 5 }{ 6 } +-1 \right) +\frac { -3 }{ 4 } =\frac { 5 }{ 6 } +\left( -1+\frac { -3 }{ 4 } \right) \)

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Answers Key:

Generic 3

6 x 3 = 18

Method 1:
\(\frac { 48 }{ -84 } =\frac { 48\div (-2) }{ -84\div (-2) } =\frac { -24\div 2 }{ 42\div 2 } =\frac { -12\div 3 }{ 21\div 3 } =\frac { -4 }{ 7 } \) (dividing by –2, 2 and 3 successively)
Method 2:
The HCF of 48 and 84 is 12 (Find it). Thus, we can get its standard form by dividing it by -12.
\(=\frac { 48\div (-12) }{ -84\div (-12) } =\frac { -4 }{ 7 } \)

\(1.15=\frac { 115 }{ 100 } =\frac { 23 }{ 10 } =1\frac { 3 }{ 20 } \)

\(-5.8=\frac { -58 }{ 10 } =\frac { -29 }{ 5 } =-5\frac { 4 }{ 5 } \)

\(0.666...=\frac { 2 }{ 3 } \)

\(0.25=\frac { 25 }{ 100 } =\frac { 1 }{ 4 } \)

\(3.0=\frac { 30 }{ 10 } =\frac { 3 }{ 1 } \)

Fill in the blanks

5 x 1 = 5

()
\(\frac { 3 }{ 5 } \), \(\frac { -4 }{ 9 } \) and \(\frac { 15 }{ 17 } \)

()
-3

()
\(\frac { 5 }{ 13 } \)

10.

()
1

11.

()
\(\frac { 1 }{ 20 } \)

True or False

5 x 1 = 5

12.

(b)
False

13.

(b)
False

14.

(a)
True

15.

(a)
True

16.

(b)
False

Generic 2

6 x 2 = 12

17.

Given p + 2q = 18 ...(1)
pq = 40 ...(2)
\(\frac { 2 }{ p } +\frac { 1 }{ q } =\frac { (2\times q)+(1\times p) }{ pq } =\frac { 2q+p }{ pq } =\frac { 18 }{ 40 } \) [∵ from (1) and (2)]
\(\\ \frac { 2 }{ p } +\frac { 1 }{ q } =\frac { 9 }{ 20 } \)

18.

\(\frac { 8 }{ 9 } =\frac { 8\times 2 }{ 9\times 2 } =\frac { 16 }{ 18 } \)
\(\frac { 8 }{ 9 } =\frac { 8\times 3 }{ 9\times 3 } =\frac { 24 }{ 27 } \)
\(\frac { 8 }{ 9 } =\frac { 8\times 4 }{ 9\times 4 } =\frac { 32 }{ 36 } \)
\(\frac { 8 }{ 9 } =\frac { 8\times 5 }{ 9\times 5 } =\frac { 40 }{ 45 } \)
Four equivalent rational numbers of \(\frac { 8 }{ 9 } \) are \( \frac { 16 }{ 18 } ,\frac { 24 }{ 27 } ,\frac { 32 }{ 36 } ,\frac { 40 }{ 45 } \)

19.

\(\frac { 7 }{ -6 } =\frac { 7\times 2 }{ -6\times 2 } =\frac { 14 }{ -12 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 3 }{ -6\times 3 } =\frac { 21 }{ -18 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 4 }{ -6\times 4 } =\frac { 28 }{ -24 } \)
\(\frac { 7 }{ -6 } =\frac { 7\times 5 }{ -6\times 5 } =\frac { 35 }{ -30 } \)
Four equivalent rational numbers of \(\frac { -7 }{ 6 } \) are \(\frac { 14 }{ -12 } ,\frac { 21 }{ -18 } ,\frac { 28 }{ -24 } ,\frac { 35 }{ -30 } \)

20.

\(\frac { -3 }{ 5 } =\frac { -3\times 2 }{ 5\times 2 } =\frac { -6 }{ 10 } \)
\(\frac { -3 }{ 5 } =\frac { -3\times 3 }{ 5\times 3 } =\frac { -9 }{ 15 } \)
\(\frac { -3 }{ 5 } =\frac { -3\times 4 }{ 5\times 4 } =\frac { -12 }{ 20 } \)
\(\frac { -3 }{ 5 } =\frac { -3\times 5 }{ 5\times 5 } =\frac { -15 }{ 25 } \)
Four equivalent rational numbers of \(\frac { -3 }{ 5 } \)are \(\frac { -6 }{ 10 } ,\frac { -9 }{ 15 } ,\frac { -12 }{ 20 } ,\frac { -15 }{ 25 } \)

21.

–1.2 and -2.3
\(-1.2=\frac { -1.2\times 10 }{ 1\times 10 } =\frac { -12 }{ 10 } \)
\(-2.3=\frac { -2.3\times 10 }{ 1\times 10 } =\frac { -23 }{ 10 } \)
∴ Five rational numbers between -1.2\(\\ \\ (=\frac { -12 }{ 10 } )\) and -2.3 \((=\frac { -23 }{ 10 } )\) are \(\frac { -21 }{ 10 } ,\frac { -20 }{ 10 } ,\frac { -15 }{ 10 } ,\frac { -14 }{ 10 } ,\frac { -13 }{ 10 } \)

22.

0.25 and 0.35
\(0.25=\frac { 0.25\times 100 }{ 1\times 100 } =\frac { 25 }{ 100 } \)
\(0.35=\frac { 0.35\times 100 }{ 1\times 100 } =\frac { 35 }{ 100 } \)
∴ Five rational numbers between 0.25\((=\frac { 25 }{ 100 } )\) and 0.35 \((=\frac { 35 }{ 100 } )\) are \(\frac { 26 }{ 100 } ,\frac { 27 }{ 100 } ,\frac { 30 }{ 100 } ,\frac { 32 }{ 100 } ,\frac { 33 }{ 100 } \)

Multiple Choice Question

5 x 1 = 5

23.