Rational Numbers Test

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Rational Numbers Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

Which among the following is/are correct for a rational numbers x and y, where x = and y = - ?
1. x < y
2. x > y
3. x = y

A
Both 1 and 3

B
Both 2 and 3

C
Only 1

D
Only 2

Solution

We have: x = and y = -

So, x > y, as < .

All positive numbers are always greater than any negative number. Here x is positive and y is negative.

Hence, option 4 is correct.
Question 2
1 / -0

Which of the following statements is not true?

A
Multiplication of the numerator and the denominator of a rational number by the same number results in an equivalent rational number.

B
Zero is neither a positive nor a negative rational number.

C
The numerator and the denominator in standard form of a rational number have common factors other than 1.

D
Product of two negative rational numbers results in a positive rational number.

Solution

Statement 1: True

Statement 2: True
Zero is neither a positive nor a negative rational number. It is taken as the reference point on the number line to decide in which direction a negative or a positive rational numbers needs to be written.

Statement 3: False
The numerator and the denominator in standard form of a rational number have common factors other than 1.

In the standard form representation of a rational number, the numerator and the denominator are written as simple numbers, which do not have any common factor other than 1.
For example, the standard form of , where the numerator and the denominator have only 1 as a common factor.

Statement 4: True

Product of two negative rational numbers results in a positive rational number.
Question 3
1 / -0

Find the average of the first and the last rational numbers after arranging the following in descending order:

, , and

A

B

C

D

Solution

LCM of 7, 3, 7 and 7 = 21

So, we have:

Now, descending order =
Or,
Average of first and last terms = = = =
Question 4
1 / -0

The value of x such that and are equivalent rational numbers is ___________.

A
60

B
-60

C
72

D
-72

Solution

We know that if is a rational number and m is a non-zero integer, then is a rational number equivalent to .
=
=
=
x = 60
Question 5
1 / -0

The product of two rational numbers is . If one of the numbers is , then find the other number.

A

B

C

D

Solution

Let the other number be x.

According to the question:

=
Question 6
1 / -0

For the product of rational numbers and , which of the following statements is true?

A
It cannot be represented on a number line.

B
It lies to the right of 0 on the number line.

C
It lies to the left of 0 on the number line.

D
None of the above

Solution

Product of given rational numbers =

So, it lies to the left of 0 on the number line.
Question 7
1 / -0

If a = Every rational number is an integer and b = Every integer is a rational number, then which of the following is correct?

A
a is true, but b is false.

B
a is false, but b is true.

C
Both a and b are true.

D
Both a and b are false.

Solution

A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q 0.

An integer is a whole number (not a fractional number) that can be positive, negative or zero. Example of integer: -5, which can be written as a rational number as shown below:

But, a rational number like cannot be represented as an integer.

Hence, every integer is a rational number but every rational number is not an integer.
Question 8
1 / -0

If , then what is the value of

A

B

C

D

Solution

=
=
=
=
=

Question 9

1 / -0

A rational number is said to be in P if its denominator is a Q. The numerator and the denominator have no common factor other than R.

	P	Q	R
A	equivalent form	negative integer	0
B	equivalent form	positive integer	0
C	standard form	positive integer	1
D	standard form	negative integer	1

A

B

C

D

Solution

A rational number is said to be in standard form if its denominator is a positive integer. The numerator and the denominator have no common factor other than 1.

Question 10
1 / -0

Which of the following sums is in its simplest form?

A

B

C

D

Solution

Let us solve these expressions:

, so this is in its simplest form.
Question 11
1 / -0

Simplify the following expression:

A

B

C

D

Solution

=

=

= = = = = =
Question 12
1 / -0

Which of the following options correctly shows the rational number + on the number line?

A

B

C

D

Solution

+

Option (2) is correct.
Question 13
1 / -0

Which of the following options shows the fractions in correct descending order?

A

B

C

D

Solution

We will make the denominators equal in all fractions:

Or,

Hence, option (1) is correct.
Question 14
1 / -0

Which of the following options does not contain equivalent rational numbers?

A

B

C

D

Solution

We know that if is a rational number and m is a non-zero integer, then is a rational number equivalent to .

Options (1), (3) and (4) satisfy the above condition, but option (2) does not satisfy equivalent rational numbers condition.

This is because is not equal to .
Question 15
1 / -0

Find the product of and .

A

B

C

D

Solution

+ = - = =
and - = =
Therefore, × = =
Question 16
1 / -0

A bucket consists of some apples, each of them weighing kg. If the total weight of the bucket (including apples) is kg, then find the maximum number of apples in the bucket.

A
35

B
37

C
38

D
39

Solution

Weight of one apple = kg

Weight of the bucket = kg
Maximum number of apples in the bucket == = 35
Question 17
1 / -0

Sahib works in a factory. He spends of his income on household needs, on buying groceries, on clothes and saves the rest. What fraction of his income does he save?

A

B

C

D

Solution

Let the total income be denoted by 1.
Now, fraction of income left with him after covering all the expenses = = = .
Question 18
1 / -0

of the participants attending a technical fest are from Punjab, of the participants are from Delhi, of the participants are from Haryana and rest of them are from Mumbai. If there are total 1000 participants in the fest, then find the number of participants from Mumbai.

A
325

B
350

C
425

D
450

Solution

Number of participants from Punjab =

Number of participants from Delhi =

Number of participants from Haryana =

Number of participants from Mumbai = 1000 - (175 + 200 + 300) = 325
Question 19
1 / -0

Four friends - Sahib, Sahil, Ravi and Gautam - buy m of cloth from a shop. How much cloth will each friend get if they divide it equally?

A
m

B
m

C
m

D
m

Solution

Total length of cloth = m
As the cloth is to be divided among four friends equally, so the length of cloth each friend will get is = = m
Question 20
1 / -0

Sahil leaves his office for home. At a point 5 km away of his home, he realises that he has forgotten his mobile at the office. How far is he from the office at this point if the total distance between his home and office is km?

A
km

B
km

C
km

D
km

Solution

Distance from office = - 5 = = km
So, Sahil is km away from his office.

Question 21

1 / -0

Match the following:

Column I	Column II
(1) When we multiply the sum of and by the product of and , the result would be	(A)
(2) Eddy ate of the pizza, while David ate of the pizza. If John ate the rest of the pizza, then John's portion of the pizza was	(B)
(3) If 42 shirts of the same size can be stitched from metres of cloth, then the length (in m) of cloth required for each shirt is	(C)
(4) Two packs of candies cost Rs. and Rs. . The total amount Ram has to pay to buy both of them is Rs.	(D)

1 - A, 2 - C, 3 - D, 4 - B

1 - D, 2 - A, 3 - C, 4 - B

1 - B, 2 - C, 3 - A, 4 - D

1 - D, 2 - C, 3 - A, 4 - B

Solution

(1)
(2)

(3) = =
(4)

Question 22
1 / -0

Which of the following statements is/are true?

(1) To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF, ignoring the negative sign.
(2) When comparing two negative rational numbers, we compare them ignoring their negative signs and then reverse the sign of inequality.
(3) There are unlimited number of rational numbers between any two rational numbers.

A
Statements (1) and (2) only

B
Statement (1) only

C
Statements (2) and (3) only

D
All the given statements

Solution

Statement 1: True

To reduce a rational number to its standard form, we divide its numerator and denominator by their HCF, ignoring the negative sign.

The standard form is the simplest form of the rational number, e.g.

Statement 2: True

When comparing two negative rational numbers, we compare them ignoring their negative signs and then reverse the sign of inequality.

E.g. Let's compare and . We ignore the negative signs and compare these:

and then on reversing the sign of inequality, we get:

Statement 3: True

There are unlimited number of rational numbers between any two rational numbers.
We can find any number of rational numbers between two given rational numbers.
E.g. 0 and 1 have 9 rational numbers between them with denominator 10.
Question 23
1 / -0

Which of the following statements is/are valid in all cases?

I. A rational number will be negative if one out of the numerator and the denominator is negative.
II. When a rational number is multiplied by an integer, the numerator and the denominator both are individually multiplied by the integer.

A
Both statements I and II

B
Only statement II

C
Only statement I

D
Neither statement I nor statement II

Solution

Only statement I holds true in all cases.

Statement I: A rational number will be negative if one out of the numerator and the denominator is negative.

E.g. and are both negative rational numbers.

Statement II is false because when a rational number is multiplied by an integer, only the numerator is multiplied by the integer.

E.g.
Question 24
1 / -0

State 'T' for True and 'F' for false:

(1) 1 is the additive identity of rational numbers.
(2) A rational number is a number which can be written in the form p/q, where p and q are whole numbers.
(3) Rational numbers can be represented on a number line.
(4) Decimals can be expressed as fractions with 10 raised to a certain power as the denominator.

A
(1) - T, (2) - T, (3) - T, (4) - T

B
(1) - F, (2) - T, (3) - F, (4) - F

C
(1) - F, (2) - T, (3) - F, (4) - T

D
(1) - F, (2) - F, (3) - T, (4) - T

Solution

(1) 1 is the additive identity of rational numbers. (False)
0 is the additive identity of rational numbers.
When we add 0 to a rational number, its value does not change: Ex: -2 + 0 = -2

(2) A rational number is a number which can be written in the form , where p and q are whole numbers.(False).

Whole numbers are all the natural numbers including 0. But rational numbers are in the form p/q, where p and q are integers and q ≠ 0.

is not a rational number.

(3) Rational numbers can be represented on a number line. (True).

(4) Decimals can be expressed as fractions with 10 raised to a certain power as the denominator. (True) (As shown on the number line above)

Question 25

1 / -0

Fill in the blanks:

(1) A fraction multiplied by its __________________ equals 1.
(2) To express a fraction as a percentage, first divide the ______________ by the _____________; then multiply the resulting decimal number by 100.
(3) A _______________ fraction has a numerator that is smaller than its denominator and represents a quantity less than the whole.

	(1)	(2)	(3)
A	reciprocal	numerator, denominator	proper
B	inverse	numerator, denominator	improper
C	reciprocal	denominator, numerator	proper
D	inverse	denominator, numerator	improper

A

B

C

D

Solution

(1) A fraction multiplied by its reciprocal equals 1.

E.g.

(2) To express a fraction as a percentage, first divide the numerator by the denominator, then multiply the resulting decimal number by 100.

0.5 × 100 = 50%

(3) A proper fraction has a numerator that is smaller than its denominator and represents a quantity less than the whole.

E.g.

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Rational Numbers Test - 9

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Rational Numbers Test - 9

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Question 1

Both 1 and 3

Both 2 and 3

Only 1

Only 2

Solution

Question 2

Multiplication of the numerator and the denominator of a rational number by the same number results in an equivalent rational number.

Zero is neither a positive nor a negative rational number.

The numerator and the denominator in standard form of a rational number have common factors other than 1.

Product of two negative rational numbers results in a positive rational number.

Solution

Question 3

Solution

Question 4

60

-60

72

-72

Solution

Question 5

Solution

Question 6

It cannot be represented on a number line.

It lies to the right of 0 on the number line.

It lies to the left of 0 on the number line.

None of the above

Solution

Question 7

a is true, but b is false.

a is false, but b is true.

Both a and b are true.

Both a and b are false.

Solution

Question 8

Solution

Question 9

A

B

C

D

Solution

Question 10

Solution

Question 11

Solution

Question 12

Solution

Question 13

Solution

Question 14

Solution

Question 15

Solution

Question 16

35

37

38

39

Solution

Question 17

Solution

Question 18

325

350

425

450

Solution

Question 19

m

m

m