Rational Numbers Test

Result

Rational Numbers Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

Directions: Divide the sum of the given fractions by their difference.

and

A

B

C

D

Solution

Fractions = and
Sum = +
=
=
=
Difference = -
=
=
According to the question,

x =
Question 2
1 / -0

Directions: Find the sum of the additive inverse and the multiplicative inverse of the given fraction.

A

B

C

D

Solution

Additive inverse of =
Multiplicative inverse =
Sum = + =
Question 3
1 / -0

If the product of two rational numbers is and one number is , then what is the second number?

A

B

C

D

Solution

Let two numbers be m and n and
m =

It is given that
m x n =
x n =
n = x
=
Question 4
1 / -0

If a = 5, then find the value of .

A

B

C

D

Solution

=
=
=
Question 5
1 / -0

Which of the following statements is correct?

A
It is a rational number, if in a fraction, the denominator is 0.

B
An irrational number can be written as a decimal, but not as a fraction.

C
Π is a rational number.

D
Reciprocal of is 1.

Solution

π = 3.1415926535897932384626433832795... (and more)
We cannot write down a simple fraction that equals Pi.

The popular approximation of = 3.1428571428571... is close, but not accurate.
Question 6
1 / -0

Directions: Find the multiplicative inverse of the given fraction.

A

B

C

D

Solution

Multiplicative inverse of a number is a number which, when multiplied by the original number, gives result 1.
For example: × = 1
Therefore, is a multiplicative inverse of .
Question 7
1 / -0

Which of the following properties of rational numbers is shown below?

A
Closure property

B
Associative property

C
Commutative property

D
Distributive property

Solution

When a, b, c, d, e and f are any natural numbers, then associative property can be explained as follows:
+ = +
In this question, the given mathematical expression is:
; which is an example of associative property.
Question 8
1 / -0

If x = , then what is the value of |x|?

A

B

C

D

Solution

X =
= =
|x| =
Question 9
1 / -0

Which of the following is correct?

A
< < <

B
< < <

C
< < <

D
< < <

Solution

We can make the denominators equal in each.
, = , = ,
So, the order is < < < .
Question 10
1 / -0

The rational number which does not lie between and is

A

B

C

D

Solution

Given, and
We need to make the denominators equal.
So, =
does not lie between .
Question 11
1 / -0

Directions: Simplify the given equation.

+ -

A

B

C

D

Solution

+ -
=
=
Question 12
1 / -0

Which of the following numbers should be subtracted from to get ?

A

B

C

D

Solution

Let the number be X.
- X =
- X =
X = =
Question 13
1 / -0

Directions: Simplify the given equation.

A

B

C

D

Solution

= =
Question 14
1 / -0

If x = and y =, then find the value of (2x + y) + (4x + 3y).

A
6

B
5

C
4

D
3

Solution

x = , y =
2x + y = =
4x + 3y = =
2x + y + 4x + 3y =
= = 4
Question 15
1 / -0

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

A

B

C

D

Solution

x = and |x| =
Numbers between and will be numbers which are greater than and less than .
From the given options, only lies between and .
So, option 1 is the correct answer.
Question 16
1 / -0

There are 70 pupils in a lab. Out of these, of the boys and of the girls have prepared the presentation. The total number of boys and girls who all have prepared the presentation is 46. How many boys are there in the lab?

A
30

B
35

C
25

D
29

Solution

Let the number of boys in the lab be x.
So, number of girls in the lab = 70 – x
According to the question,

x + (70 - x) = 46
x^- x + 42 = 46

= 4

4x = 140
x = 35
So, number of boys = 35
Question 17
1 / -0

Ms. Archie earns Rs. 13,000 per month and spends of that amount on cosmetics and of that amount on clothing. Find out the amount that she saves every month.

A
Rs. 2,828.32

B
Rs. 2,528.02

C
Rs. 2,228.82

D
Rs. 2,128.52

Solution

Savings = Earnings - Expenditures
= 13,000 - + x 13,000
= 13,000 - x13,000
= 13,000 - x13,000
= 13,000 - 10,771.18
= Rs. 2,228.82
Question 18
1 / -0

One recipe of a pie requires cup of sugar. Another recipe of the same pie requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to of a cup, then how much more sugar does the first recipe require?

A
cup

B
cup

C
cup

D
cup

Solution

Given,
1 tablespoon = cup
2 tablespoons = cup
So, the amount of sugar required in the second recipe of pie is cup.
Also, the amount of sugar required in the first recipe is cup.
So, difference = - = cup

Question 19

1 / -0

Directions: Study the information given below and answer the question that follows.

Ingredients required to make a cake.

Ingredients	Amount
Flour	cups
Sugar	cups
Baking soda	cups

How many less cups of flour are needed than cups of baking soda?

Solution

Flour = cups
Baking soda = cups

-

= =

Question 20
1 / -0

Some parents attended a parent teacher meeting. If of the parents in the meeting are fathers and there are 50 more mothers than fathers, then how many mothers are there in the meeting?

A
225

B
175

C
150

D
125

Solution

Let the total parents in the meeting be .
The number of fathers =
The number of mothers = [+ 50]
According to the question,
+ [ + 50] =
- = 50
= 50
2 = 600
= 300
Number of fathers = =125
Number of mothers = 125 + 50 = 175
Question 21
1 / -0

Which of the following options is incorrect?

A
If a/b and c/d are any two rational numbers, then (a/b) + (c/d) is also a rational number.

B
If a/b, c/d and e/f are any three rational numbers, then a/b + (c/d + e/f) = (a/b + c/d) + e/f.

C
If a/b is any rational number then a/b × b/a = 1.

D
If a/b, c/d and e/f are any three rational numbers,then a/b - (c/d - e/f) = (a/b - c/d) - e/f.

Solution

If a/b, c/d and e/f are any three rational numbers, then
a/b - (c/d - e/f) = a/b - c/d + e/f ≠ (a/b - c/d) - e/f

Question 22

1 / -0

Match the following.

Column A	Column B
A) Addition of two rational numbers gives	1. -(3/5)
B) The additive inverse of (3/5) is	2. 1/2
C) The sum of a rational number and its additive inverse is	3. a rational number
D)	4. 0

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

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

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

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

Solution

Column A	Column B
A) Addition of two rational numbers gives	3. a rational number
B) The additive inverse of (3/5) is	1. -(3/5)
C) The sum of a rational number and its additive inverse is	4. 0
D)	2. 1/2

D)

=

=

=

Question 23
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Directions: Fill in the blanks.

1. The reciprocal of 1/3 is __(a)__.
2. (2/3) ÷ (1/3) = (2/3) × (3/1) = __(b)__.
3. (5/9) × (2/9) = 10/81 is a __(c)__ number.
4. Multiplication of rational numbers is distributive over __(d)__.

A
a - 1, b -0, c - negative, d - division

B
a - 3, b - 2, c - rational, d - addition

C
a- 3, b - 1, c - natural, d - division

D
a- 1, b - 0, c - positive, d -subtraction

Solution

1. The reciprocal of 1/3 is 3.
2. (2/3) ÷ (1/3) = (2/3) × (3/1) = 2.
3. (5/9) × (2/9) = 10/81 is a rational number.
4. Multiplication of rational numbers is distributive over addition.
Question 24
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Which of the following statements is/are true?

Statement 1: If , and are any three rational numbers, then = .
Statement 2: + 0 = 0 + =

A
Both are true.

B
Only 1 is true.

C
Only 2 is true.

D
None of the statements is true.

Solution

Statement 1: If , and are any three rational numbers, then = . This is a distributive property of rational numbers.

Statement 2: + 0 = 0 + = . This is also true as its following commutative property and showing additive identity i.e. zero (0) for rational numbers.
Question 25
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Directions: State T for true and F for false.

1. Two rational numbers can be added in any order.
2. While adding three rational numbers, they cannot be grouped in any order.
3. The reciprocal of 0 is undefined.
4. Every rational number multiplied with 0 gives 1.

A
1 - F, 2 - F, 3 - T, 4 - F

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

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

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

Solution

1. Two rational numbers can be added in any order.
2. While adding three rational numbers, they can be grouped in any order.
3. The reciprocal of 0 is undefined.
4. Every rational number multiplied with 0 gives 0.