Rational Numbers Test

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Rational Numbers Test - 8

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Question 1
1 / -0

Directions: Consider the given statements and choose the correct option accordingly.

Statements:
For any rational number,
(i) The mixed number is also a rational number because we can write it as .
(ii) A ratio is a comparison of more than two numbers.

A
(i) is true and (ii) is false.

B
(i) is false and (ii) is true.

C
Both (i) and (ii) are true.

D
Both (i) and (ii) are false.

Solution

(i) The mixed number is also a rational number because we can write it as .

As every fraction is a rational number, statement (i) is true.
(ii) A ratio is a comparison of more than two numbers.
For example: Ratio of 5 to 10 = 5 : 10 = 1 : 2
So, a ratio is a comparison of only two numbers.
Hence, statement (ii) is false.
Question 2
1 / -0

Which of the following statements is incorrect?

A
A rational number can be written as a ratio.

B
Every whole number is a rational number.

C
1.5 is not a rational number.

D
There is no reciprocal of zero.

Solution

A rational number can be written as a ratio, 3/2 is written as 3 : 2.
Every whole number is a rational number. 4 is whole number and it can be written as 4/1.
1.5 is a rational number as it can be written as fraction 3/2.
There is no reciprocal of zero; reciprocal of zero is not defined.
Question 3
1 / -0

Find the average of the first and last terms after arranging the rational numbers and in descending order.

A

B

C

D

Solution

LCM of 7, 3, 7 and 7 = 21

So, and can be written as and , respectively,

So, descending order:

Therefore,
So, average of the first and last terms = = =
Question 4
1 / -0

What will be the value of a if and are equivalent fractions?

A
-36

B
-63

C
-28

D
-53

Solution

a = -63
Question 5
1 / -0

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

A
-

B

C

D
-

Solution

Let the second rational number is x

So,
Question 6
1 / -0

Which of the following statements is correct with respect to ?

A
lies on the left side of 0 on a number line.

B
It is not a rational number.

C
It is less than 2.

D
It is more than 3.

Solution

, which is less than 2 and lies on the right side of 0 on a number line.
Question 7
1 / -0

Directions: Consider the given statements and choose the correct option accordingly.

Statements:
A. Rational numbers can consist of positive numbers, negative numbers, or a zero.
B. Rational numbers can consists of a fraction.

A
A is true and B is false.

B
A is false and B is true.

C
Both A and B are true.

D
Both A and B are false.

Solution

A. Rational numbers can consist of positive numbers, negative numbers, or a zero.
B. Rational numbers can consist of a fraction.
Both A and B are true, as rational numbers can consist of any positive or negative number, a zero, and a fraction.
Question 8
1 / -0

If , then what is the value of ?

A

B

C

D

Solution

(given)

So,
Question 9
1 / -0

A M can be expressed as the quotient of the two N with a denominator that isn't O and it can be expressed as a P .

A
M - whole number, N - additions, O - a fraction, P - decimal number

B
M - rational number, N - integers, O - zero, P - ratio

C
M - ratio, N - zeros, O - a rational number, P - positive number

D
M - rational number, N - fractions, O - one, P - negative number

Solution

A rational number can be expressed as the quotient of the two integers with a denominator that isn't zero and it can be expressed as a ratio.
Question 10
1 / -0

Which of the following subtractions is in the simplest form?

A

B

C

D

Solution

(1) = =

(2) =

(3) = =

(4) = =

So, simplest fraction is of option (1).
Question 11
1 / -0

Simplify:

A
-

B
-

C
-

D
-

Solution

=

=

=

=

=

= = =
Question 12
1 / -0

Which of the following number lines correctly depicts ?

A

B

C

D

Solution

= = ; which is shown in option (3).
Question 13
1 / -0

Which of the following rational numbers are in ascending order?

A

B

C

D

Solution

In option (1),

Taking the LCM of denominators to make the denominators same;

LCM = 3 × 2 × 3 × 1 = 18

So, new fractions = ; which are in ascending order.

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

Which among the following are not equivalent rational numbers?

A
and

B
and

C
and

D
and

Solution

Option 4:

Since both the terms in option 4 are not equivalent, hence option 4 is the correct answer.
Question 15
1 / -0

Multiply the difference between and by sum of and ^.

A

B

C

D

Solution

Difference = = =

Sum = = =

So, their product =
Question 16
1 / -0

The weight of one cupcake is 1/14 kg. If Dony cannot put more than 5/7 kg of weight in a single box, then how many cupcakes can he put in a single box?

A
10

B
12

C
14

D
16

Solution

Weight of 1 cupcake = kg

A maximum weight of kg can be put in a box.

Number of cupcakes in 1 box = divided by cupcakes
Question 17
1 / -0

Ana decorated her house wall using three colours. She painted of the wall in yellow, 3/5 of the wall in pink and remaining portion of the wall in cream. What portion of the wall is painted in cream?

A

B

C

D

Solution

Let the whole wall be represented by 1.
Now, part of wall painted in cream =
So, of the wall is painted in cream.
Question 18
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5/14 of people in a wedding ceremony are wearing a red-coloured outfit, are wearing a blue-coloured outfit, and 9/16 are wearing a green-coloured outfit. If there are total 1680 people in the wedding who wearing red, green, or blue coloured outfit, then how many of them are wearing a blue-coloured outfit?

A
784

B
600

C
945

D
785

Solution

People wearing red outfit = × 1680 = 600

People wearing blue outfit = × 1680 = 784

People wearing green outfit = × 1680 = 945
Question 19
1 / -0

Asha divides a sack of flour weighing kg into 5 smaller bags. What would be the weight of each bag?

A
kg

B
kg

C
kg

D
kg

Solution

Weight of flour sack = kg = kg

Now, Asha divided it into 5 smaller bags.

So, weight of each bag = = = = kg
Question 20
1 / -0

Quintin runs km in the morning from his house to the park. On his way back from the park, he stops at a juice shop after km. How far is the juice shop from his house?

A
km

B
km

C
km

D
km

Solution

Distance between house and park = km
Distance between park and juice shop = km
So, distance between house and juice shop = () km = = = km

Question 21

1 / -0

Match the following:

COLUMN I	COLUMN II
(A) Sum of the product of and and product of and	(M)
(B) Two boxes of apples weigh kg and kg. What is the total weight of the two boxes?	(N)
(C) Ammy had of a pizza, and she ate of it. How much pizza was left?	(O)
(D) If 46 pieces of handkerchiefs can be made from m of cloth, then how much cloth is required to make one handkerchief?	(P)

A - P, B - M, C - O, D - N

A - O, B - P, C - N, D - M

A - O, B - M, C - P, D - N

A - P, B - N, C - O, D - M

Solution

(A) =

=

= =

(B) Sum of weights of boxes =
=

= =

(C) Total pizza =
She ate =
So, pizza left =
= =

(D) Cloth needed for 46 handkerchiefs = m

Cloth required for one handkerchief = = = m

So, A - O, B - M, C - P, D - N is the correct match.

Question 22
1 / -0

Which of the following statements is not true?

(1) Every integer is a rational number since each integer n can be written in the form n/1.
(2) 0 is a rational number.
(3) Rational numbers include integers, terminating decimals, and repeating decimals as well as fractions.
(4) If denominator of a fraction is negative, then its numerator is positive.

A
1

B
2

C
3

D
4

Solution

If the denominator of a fraction is negative, then its numerator is also negative.
Question 23
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Directions: Read the following statements and choose the correct option accordingly.

Statement I: The sum of a rational number and an irrational number is irrational.
Statement II: 10 is not a rational number.

A
Statement I is true, but statement II is false.

B
Statement II is true, but statement I is false.

C
Both statements I and II are true.

D
Both statements I and II are false.

Solution

Statement I: The sum of a rational number and an irrational number is irrational.
This statement holds as the sum of a rational number and an irrational number is irrational.

Statement II: 10 is not a rational number.
This statement does not hold as 10 is a rational number.

Only statement I is true.
Question 24
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State True (T) or False (F) for the following statements:

(1) Every real number is a rational number.
(2) Zero is a rational number.
(3) Between any two integers, there is another integer.
(4) The rational numbers are a subset of the integers.

A

1 2 3 4

F T F F

B

1 2 3 4

T T T F

C

1 2 3 4

F F T F

D

1 2 3 4

T T F F

Solution

(1) Every real number is a rational number. - It is false, as every rational number is a real number, but every real number is not a rational number.
(2) Zero is a rational number. - It is true.
(3) Between any two integers, there is another integer. - It is false.
(4) The rational numbers are a subset of the integers. - It is false, as the integers are a subset of the rational numbers.
Question 25
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Fill in the blanks:

The sum of a ___(A)___ and an irrational number is irrational. A fractional number can be made by dividing two ___(B)___. Rational numbers can be positive, negative or __(C)__, and can be written as a/an __(D)___.

A

A B C D

rational number integers zero fraction

B

A B C D

negative fractions decimal ratio

C

A B C D

whole number decimal numbers zero mixed number

D

A B C D

fraction ratios one irrational number

Solution

The sum of a rational number and an irrational number is irrational. A fractional number can be made by dividing two integers. Rational numbers can be positive, negative or zero, and can be written as a fraction.

A B C D

rational number integers zero fraction

Therefore, option 1 is the correct answer.

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A	B	C	D
rational number	integers	zero	fraction

A	B	C	D
negative	fractions	decimal	ratio

A	B	C	D
whole number	decimal numbers	zero	mixed number

A	B	C	D
fraction	ratios	one	irrational number

Rational Numbers Test - 8

Result

Rational Numbers Test - 8

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Question 1

(i) is true and (ii) is false.

(i) is false and (ii) is true.

Both (i) and (ii) are true.

Both (i) and (ii) are false.

Solution

Question 2

A rational number can be written as a ratio.

Every whole number is a rational number.

1.5 is not a rational number.

There is no reciprocal of zero.

Solution

Question 3

Solution

Question 4

-36

-63

-28

-53

Solution

Question 5

-

-

Solution

Question 6

lies on the left side of 0 on a number line.

It is not a rational number.

It is less than 2.

It is more than 3.

Solution

Question 7

A is true and B is false.

A is false and B is true.

Both A and B are true.

Both A and B are false.

Solution

Question 8

Solution

Question 9

M - whole number, N - additions, O - a fraction, P - decimal number

M - rational number, N - integers, O - zero, P - ratio

M - ratio, N - zeros, O - a rational number, P - positive number

M - rational number, N - fractions, O - one, P - negative number

Solution

Question 10

Solution

Question 11

-

-

-

-

Solution

Question 12

Solution

Question 13

Solution

Question 14

and

and

and

and

Solution

Question 15

Solution

Question 16

10

12

14

16

Solution

Question 17

Solution

1 2 3 4

F T F F

1 2 3 4

T T T F

1 2 3 4

F F T F