Rational Numbers Test

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Rational Numbers Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

Where does a rational number $$\displaystyle\frac{-2}{3}$$ lies on the number line?

A
Lies to the left side of $$0$$ on the number line

B
Lies to the right side of $$0$$ on the number line

C
It is not possible to represent on the number line

D
Cannot be determined on which side the number lies

Solution

$$\dfrac{-2}{3}=-0.667$$
$$-0.667<0$$
Hence it will lie to the left side of $$0$$ on the number line.
Question 2
1 / -0

The given property $$a+b=b+a$$ is known as:

A
Commutative property

B
Distributive Property

C
Associative Property

D
Closure property

Solution

Commutative property says that the numbers can be added in any order, and you will still get the same answer.

$$a+b = b+a$$ is a clear example of commutative property
Question 3
1 / -0

The rational number between the pair of number $$\dfrac{1}{2}$$ and $$\sqrt 1$$ is:

A
$$\dfrac{9}{4}$$

B
$$\dfrac{3}{4}$$

C
$$\dfrac{5}{4}$$

D
$$\dfrac{7}{4}$$

Solution

The rational number between $$\dfrac12$$ and $$\sqrt1$$ :
Since, $$\sqrt1=1$$
So. the rational number between $$\dfrac12$$ and $$1=\dfrac12\times \left(\dfrac12+1\right)$$
$$=\dfrac12 \times \dfrac32$$
$$=\cfrac34$$
So, $$B$$ is the correct option.
Question 4
1 / -0

A: Rational numbers are always closed under division.
R: Division by zero is not defined.

A
A is true and R is the correct explanation of A

B
A is false and R is false

C
A is true and R is false

D
A is false and R is true

Solution

Statement A: False
$$0$$ is a rational number because it can be written as $$\dfrac{0}{1}$$. When we divide any rational number by $$0$$ which is also a rational number, then the resultant number is of the form $$\dfrac{m}{0}$$ where $$m$$ is any rational number.
So, the resultant is not defined and hence rational numbers are not closed under division
Statement R: True
Any Real number divided by $$0$$ is not defined.
Question 5
1 / -0

Find the additive inverse of the following rational numbers:
(i) $$-\dfrac{2}{3}$$

A
$$\dfrac{2}{3}$$

B
$$\dfrac{4}{3}$$

C
$$\dfrac{5}{3}$$

D
$$\dfrac{7}{3}$$

Solution

Additive inverse of $$\dfrac{2}{-3}= -\left ( \dfrac{2}{-3} \right )= \dfrac{2}{3}$$
Question 6
1 / -0

A rational number lie between $$\displaystyle\frac{1}{4}$$ and $$\displaystyle\frac{1}{3}$$ is _________.

A
$$\displaystyle\frac{7}{24}$$

B
$$\displaystyle\frac{15}{48}$$

C
$$\displaystyle\frac{13}{48}$$

D
All of these

Solution

So, a rational number between $$\dfrac {1}{4} $$ and $$ \dfrac {1}{3}$$
$$ = \dfrac {\dfrac {1}{4} + \dfrac {1}{3}}{2} = \dfrac {7}{24} $$

Now, another rational number between $$ \dfrac {1}{4} $$ and $$ \dfrac {7}{24} $$
$$= \dfrac {\dfrac {1}{4} + \dfrac {7}{24}}{2} = \dfrac {13}{48} $$
Now, another rational number between $$ \dfrac {1}{3} $$ and $$ \dfrac {7}{24} $$
$$= \dfrac {\dfrac {1}{3} + \dfrac {7}{24}}{2} = \dfrac {15}{48} $$

Hence, required two rational numbers between $$\dfrac {1}{4} $$ and $$ \dfrac {1}{3} $$ are $$\dfrac {7}{24} ,\dfrac {13}{48}, \dfrac {15}{48}$$
Question 7
1 / -0

Name the property of rational numbers illustrated by the given statement. $$\displaystyle\frac{-3}{2}\times \frac{5}{4}+\frac{-3}{2}\times \frac{-7}{6}=\frac{-3}{2}\times \left(\displaystyle\frac{5}{4}+\frac{-7}{6}\right)$$.

A
Associativity

B
Distributivity

C
Commutativity

D
None of these

Solution

Associative property
$$ (a+b)+c =a+(b+c)$$
or $$(a \times b) \times c = a \times (b \times c)$$

Distributive property
$$a \times (b+c)=a \times b +a \times c $$

Commutative property
$$ a+b=b+a$$
or $$ a \times b =b \times a$$

so the given equation follows:
$$a\times (b+c)=a\times b +a \times c $$
$$a=-\dfrac{3}{2}$$
$$b=\dfrac{5}{4}$$
$$c=-\dfrac{7}{6}$$
Question 8
1 / -0

Which of the following statements is correct?

A
$$0$$ is called the additive identify for rational numbers

B
$$1$$ is called the multiplicative identify for rational numbers

C
The additive inverse of $$0$$ is zero itself

D
All of the above

Solution

1) $$0$$ is called the additive identity for rational numbers - True
2) $$1$$ is called the multiplicative identify for rational numbers -True
3)The additive inverse of $$0$$ is zero itself - True
Hence all the statements are True.
Question 9
1 / -0

Name the property of rational numbers illustrated by the given statement. $$\displaystyle\frac{7}{4}\times \left(\displaystyle\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4}\times \frac{-8}{3}+\frac{7}{4}\times \frac{-13}{12}$$.

A
Commutativity

B
Associativity of multiplication

C
Distributivity of multiplication over addition

D
Distributivity of addition over multiplication

Solution

Distributivity of multiplication over addition
$$a(b+c)=a\times b +b \times c $$
Question 10
1 / -0

(X + Y) + Z = X + (Y + Z) means

A
Operator OR is distributive

B
Operator OR is associative

C
Operator AND is associative

D
None of the above

Solution

associative property means that order of performing an operation does not matter.
OR operator is associative.

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Rational Numbers Test - 24

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Rational Numbers Test - 24

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Question 1

Lies to the left side of $$0$$ on the number line

Lies to the right side of $$0$$ on the number line

It is not possible to represent on the number line

Cannot be determined on which side the number lies

Solution

Question 2

Commutative property

Distributive Property

Associative Property

Closure property

Solution

Question 3

$$\dfrac{9}{4}$$

$$\dfrac{3}{4}$$

$$\dfrac{5}{4}$$

$$\dfrac{7}{4}$$

Solution

Question 4

A is true and R is the correct explanation of A

A is false and R is false

A is true and R is false

A is false and R is true

Solution

Question 5

$$\dfrac{2}{3}$$

$$\dfrac{4}{3}$$

$$\dfrac{5}{3}$$

$$\dfrac{7}{3}$$

Solution

Question 6

$$\displaystyle\frac{7}{24}$$

$$\displaystyle\frac{15}{48}$$

$$\displaystyle\frac{13}{48}$$

All of these

Solution

Question 7

Associativity

Distributivity

Commutativity

None of these

Solution

Question 8

$$0$$ is called the additive identify for rational numbers

$$1$$ is called the multiplicative identify for rational numbers

The additive inverse of $$0$$ is zero itself

All of the above

Solution

Question 9

Commutativity

Associativity of multiplication

Distributivity of multiplication over addition

Distributivity of addition over multiplication

Solution

Question 10

Operator OR is distributive

Operator OR is associative

Operator AND is associative

None of the above

Solution

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