Rational Numbers Test

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Rational Numbers Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Multiply the difference between and by their sum.

A

B

C

D

Solution

The difference between and =
Sum of and =
Now, product of their difference and their sum =
Question 2
1 / -0

The difference between additive inverse and multiplicative inverse of 6 is

A

B

C

D

Solution

The additive inverse of 6 is -6 and the multiplicative inverse of 6 is .
So, required difference =
Question 3
1 / -0

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

A

B

C

D

Solution

Suppose that the other rational number is y. Then, according to the question:

y x =

y =

y =
Question 4
1 / -0

If b = 6, then what is the value of ?

A

B

C

D

Solution

By putting the value of b = 6 in the given expression, we get
Question 5
1 / -0

Which of the following statements is true?

1. The additive inverse of a is .

2. The multiplicative inverse of a is - a.
3. The sum of multiplicative inverse and additive inverse of a is .
4. The reciprocal of a is - a.

A
1

B
3

C
4

D
2

Solution

Additive inverse of a is -a.
Multiplicative inverse of a is (1/a).

Sum =
The reciprocal of a is (1/a).
Question 6
1 / -0

The multiplicative inverse of is

A

B

C

D
p - q

Solution

Let y be the multiplicative inverse of .

Note: Two numbers are called multiplicative inverses of each other if their product is 1.
So,
Question 7
1 / -0

Which property of rational numbers is indicated below?

× = ×

A
Commutativity of addition

B
Associativity of multiplication

C
Distributivity of multiplication

D
Commutativity of multiplication

Solution

Commutativity of multiplication has been indicated in the given equation.
Commutative property of multiplication tells us that the order in which you multiply numbers doesn't matter. This is given as: a b = b a.
Hence, option (4) is correct.
Question 8
1 / -0

If p = , then |-p| is equal to

A

B

C

D

Solution

p = =
-p =
|-p| =
Question 9
1 / -0

Which of the following options is true?

A
<<<

B
< < <

C
< < <

D
< < <

Solution

We have the following four fractions:

^, ^, ^,

L.C.M. of 5, 7, 13, 17 = 7735

So,

= =

= =

= =

= =

Therefore,

< < <
So, the correct order is: < < <
Question 10
1 / -0

Which among the following is the rational number which does not lie between and ^?

A

B

C

D

Solution

Let us convert the two given fractions into decimal numbers:
= 0.35(Approx)
= 0.75
We also convert the given options into decimal numbers.
Now,= 0.80, which clearly does not lie between 0.35 and 0.75.
Hence, option (3) is the correct answer.
Question 11
1 / -0

Simplify the following expression:

A

B

C

D

Solution
Question 12
1 / -0

What should be added toto get ?

A

B

C

D

Solution

Let the required number be y.

Then,
+ y =

+ y =
+ y =
y = -
y =
y =
Question 13
1 / -0

Simplify:

A

B

C

D

Solution

=
=
=
Question 14
1 / -0

If a = and b =, find the value of (a - b) ÷ (a + b).

A

B

C

D

Solution

a - b = =

a + b = =

(a - b) ÷ (a + b)
= = =
Question 15
1 / -0

If x = , then which of the following rational numbers lies between x and |x|?

A

B

C

D

Solution

x =
|x| =
So, the numbers between andare:
,,, …,,

Hence, option (4) is correct.
Question 16
1 / -0

In a certain company, there are 58 employees in the IT department. of males and of females come to office by their own vehicles. The total of 32 employees come to office by their own vehicles. Find the number of males in the IT department.

A
61

B
46

C
31

D
22

Solution

Let the number of males in the IT department be y.
Then, number of females in the IT department = 58 - y
According to the question,
y + (58 - y) = 32
= 32 -

y = 46
Therefore, number of males = 46
Question 17
1 / -0

Sahil's monthly income is Rs. 24,000. He gives of the amount to Raman and of the amount to Akshay. How much amount is left with Sahil?

A
Rs. 12,000

B
Rs. 10,000

C
Rs. 8,000

D
Rs. 9,000

Solution

Total income = Rs. 24,000
Amount given to Raman =
Amount given to Akshay =
Amount left with Sahil = 24,000 - (8,000 + 6,000) = 24,000 - 14,000 = Rs. 10,000
Question 18
1 / -0

One bowl of pulses requires cup of salt. Another recipe for the same bowl of pulses requires 2 tablespoons of salt. If 1 tablespoon is equal to cup, how much more salt does the first recipe require than the second recipe?

A
cup

B
cup

C
cup

D
cup

Solution

According to the question,

1 tablespoon of salt = cup of salt

So, tablespoon of salt = x cup of salt
= cup of salt
That is second recipe requires ^. cup of salt.

So, Difference = cup of salt.
That is, first recipe requires more cup of salt than second recipe.

Question 19

1 / -0

The following table shows the heights of different people in a certain city:

Names	Govind	Arsh	Preet	Sahib
Height	feet	5 feet	feet	6 feet

What is the difference between the heights of Govind and Sahib?

feet

Solution

Sahib's height = 6 feet
According to the question,

Difference = 6 - = = = feet.

Question 20
1 / -0

In a technical festival, there were males and females. If of them were females and there were 45 more males than females, then how many people were there in the festival?

A
100

B
75

C
150

D
175

Solution

Let the total number of people be x.

Then, number of females = Number of males =
According to the question,
Question 21
1 / -0

Which of the following statements is incorrect?

A
The sum of any two rational numbers is not always a rational number. This is called closure property of addition of rational numbers.

B
Addition of two rational numbers is commutative.

C
is the negative or additive inverse of .

D
The product of two rational numbers is always a rational number. Hence, Q is closed under multiplication.

Solution

1. The sum of any two rational numbers is always a rational number. This is called closure property of addition of rational numbers. Thus, Q is closed under addition.

2. If and are any two rational numbers, then + is also a rational number.

Addition of two rational numbers is commutative.

If and are any two rational numbers, then + = + .

3. is the negative or additive inverse of .

If is a rational number, then there exists a rational number such that + = + = 0.

4. The product of two rational numbers is always a rational number. Hence, Q is closed under multiplication.

If and are any two rational numbers, then x = is also a rational number.

Hence, option (1) is correct.

Question 22

1 / -0

Match the columns:

Column I	Column II
(P) Two numbers are called reciprocal to each other if their product is	(A)
(Q) If , then x is equal to	(B)
(R) The additive inverse of is	(C) a rational number
(S) The sum of two rational numbers is always	(D) 1

P - D, Q - A, R - B, S - C

P - D, Q - B, R - A, S - C

P - C, Q - A, R - B, S - D

P - D, Q - C, R - B, S - A

Solution

P) Two numbers are called reciprocal to each other if their product is 1.
Q)
x =

R) The additive inverse of

.
S) The sum of two rational numbers is always a rational number.

Question 23

1 / -0

Fill in the blanks.
i) Zero has P reciprocal.
ii) The numbers Q and R are their own reciprocals.
iii) The reciprocal of a positive rational number is S .

Options	P	Q	R	S
(A)	no	-1	2	positive
(B)	no	-1	1	positive
(C)	1	-1	1	positive
(D)	no	-1	1	negative

(A)

(B)

(C)

(D)

Solution

Zero has no reciprocal.
The numbers -1 and 1 are their own reciprocals.
The reciprocal of a positive rational number is positive.

Question 24
1 / -0

Which of the following options is true for the given statements?

Statement I: If x + 0 = 0 + x = x, which is a rational number, then 0 is called the identity for the addition of rational numbers.
Statement II:

A
Only statement I is true.

B
Only statement II is true.

C
Both statement I and statement II are true.

D
None of the statements are true.

Solution

Statement I: We know that the sum of any rational number and zero is the rational number itself.
So, if x + 0 = 0 + x = x, which is a rational number, then 0 is called the identity for the addition of rational numbers.

Statement II: Hence, both statement I and statement II are true.
Question 25
1 / -0

State T for True and F for False.

(i) The rational numbers and are on the opposite side of zero on the number line.
(ii) The difference between any two rational numbers is always a rational number.
(iii) Subtraction of two rational numbers is commutative.
(iv) Subtraction of rational numbers is not associative.

A
(i) - T, (ii) - T, (iii) - F, (iv) - T

B
(i) - F, (ii) - T, (iii) - F, (iv) - T

C
(i) - T, (ii) - T, (iii) - F, (iv) - F

D
(i) - T, (ii) - F, (iii) - F, (iv) - T

Solution

Statement (i) is true as one value is negative and the other is positive.

Statement (ii) is true. The difference between any two rational numbers is always a rational number.

If and are any two rational numbers, then is also a rational number.

Statement (iii) is false. Subtraction of two rational numbers is not commutative.

If and are any two rational numbers, then

Statement (iv) is true. Subtraction of rational numbers is not associative.

If , and are any three rational numbers, then