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QUESTION: 1

Which of the following is correct?

Solution:

Let us consider a fraction 3/5 and a rational number = 14/7

By definition, 3/5 is a rational number. So, p is true. By definition, -4/7 is not a fraction, since, −4 is not a natural number. So, q is false.

QUESTION: 2

Which of the following is not a rational number(s)?

Solution:

√2/3 is not a rational number.

QUESTION: 3

Which of the following statements is correct?

Solution:

Since, every integer having a denominator 1 can be expressed in P/q form, p is true. Since, a rational number with denominator other than 1 is not an integer (e.g., 3/5), q is false.

QUESTION: 4

What type of a number is −3/0 ?

Solution:

Since, denominator is 0, it is not a rational number.

QUESTION: 5

Which among the following is a rational number equivalent to 5/3?

Solution:

QUESTION: 6

What type of a numerator does 0/7 have?

Solution:

QUESTION: 7

Which of the following statements is true?

Solution:

QUESTION: 8

If −4/7 = −32/x, what is the value of x?

Solution:

QUESTION: 9

Which is the greatest?

Solution:

QUESTION: 10

Which is the correct descending order of −2,4/−5,−11/20,3/4?

Solution:

L.C.M. of 5, 4 and 20 is 20.

4/−5 × 4/4 = 16/−20;3/4 = 3×5/4×5 = 15/20

−2 < 4/−5 < −11/20 < 3/4

or

3/4 > −11/20 > 4/−5 > −2

is the required descending order.

Rewrite equivalent fractions of the given fractions and then compare then.

Arrange them in descending order.

QUESTION: 11

What is the average of the two middle rational numbers if 4/7,1/3,2/5 and 5/9 are arranged in ascending order?

Solution:

The ascending order of 4/7,1/3, 2/5 and 5/9 is 1/3<2/5<5/9<4/7. The two middle numbers are 2/5 and 5/9.

∴ Average = = 43/90

QUESTION: 12

What is the percentage of the least number in the greatest number of 3/5,9/5,1/5 and 7/5 ?

Solution:

The given numbers can be arranged in ascending order as1/5 < 3/5 < 7/5 < 9/5

The greatest number = 9/5;

The least number = 1/5

We have, 9/5 × x/100 = 1/5

⇒ x = 10/09 =

QUESTION: 13

What is the difference between the greatest and least numbers of 5/9,1/9 and 11/9 ?

Solution:

The ascending order of given numbers is 1/9,5/9,11/9.

∴ Required difference = 11/9 −1/9 = 10/9

QUESTION: 14

Which of the following pairs represent the same rational number?

Solution:

−24/15 is the equivalent rational number of −8/5.

QUESTION: 15

P: The quotient of two integers is always a rational number.

Q : 1/0 is not rational. Which of the following statements is true?

Solution:

Since, 1/0 is not rational, the quotient of two integers is not always rational.

QUESTION: 16

What is the result of 2 − 11/39 + 5/26?

Solution:

QUESTION: 17

Which is the equivalent of −143/21?

Solution:

QUESTION: 18

Of which property is −7/5 + (2/−11 + −13/25) = (−7/5 + 2/−11) + −13/25 an example?

Solution:

QUESTION: 19

Which of the following statements is correct?

Solution:

All the given statements are correct. Consider

4/5 [a] Since 4/5 + 0 = 4/5,, 1 is the additive identity of rational numbers. [b] Since

4/5 × 1= 4/5, is the multiplicative identity of rational numbers. [c] Since 0+0=0,

0 is the additive inverse of 0.

QUESTION: 20

The sum of two rational numbers is −3. If one of the numbers is −7/5, find the other number.

Solution:

Let x be the required number. So,

x+(−7/5) = −3

⇒ x = −3+7/5 = −1/5 + 7/5 = −8/5

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