Rational Numbers Test

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Rational Numbers Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

............ is the additive inverse of $$\dfrac {-3}{11}.$$

A
$$\dfrac {-3}{11}$$

B
$$\dfrac {11}{3}$$

C
$$-1$$

D
$$\dfrac {3}{11}$$

Solution

In mathematics, the additive inverse of a number is the number that, when added to a, yields zero.

This number is also known as the opposite (number), sign change, and negation.

For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive.

The given rational number is $$\dfrac {-3}{11}$$ and its negative is $$-\left (\dfrac {-3}{11}\right ) = \dfrac {3}{11}$$. Thus, the additive inverse of $$\dfrac {-3}{11}$$ is $$\dfrac {3}{11}$$.
Question 2
1 / -0

The additive inverse of $$\dfrac {2}{7}$$ is ..........

A
$$\dfrac {2}{7}$$

B
$$\dfrac {-2}{7}$$

C
$$\dfrac {7}{2}$$

D
$$\dfrac {-7}{2}$$

Solution

The additive inverse of a number $$a$$ is the number that, when added to $$a$$, yields zero.

If $$a$$ is an integer, then its negative $$(-a)$$ is called the additive inverse of $$a$$.

The given rational number is $$\dfrac {2}{7}$$ and its negative is $$\dfrac {-2}{7}$$.

Thus, the additive inverse of $$\dfrac {2}{7}$$ is $$\dfrac {-2}{7}$$.
Question 3
1 / -0

There are ....... rational number which when multiplied by $$0$$, gives product as $$1.$$

A
$$0$$

B
$$2$$

C
$$4$$

D
infinite

Solution

There are no rational numbers which when multiplied by $$0$$ gives product as $$1$$ because the product of $$0$$ and any number is always $$0.$$
Question 4
1 / -0

$$1$$ is the multiplicative identity for ........

A
whole numbers

B
integers

C
rational numbers

D
all of the above

Solution

$${\textbf{Step - 1: Defining Multiplicative identity}}$$

$${\text{Multiplicative identity is a number which when multiplied by another number gives}}$$

  $${\text{the another number again as result}}{\text{.}}$$

  $${\text{For example, if x }} \times {\text{ y = x then y is multiplicative identity of x}}$$

$${\textbf{Step - 2: Identifying multiplicative identity}}$$

  $${\text{We know that, any number multiplied by 1 gives the number itself}}{\text{.}}$$

  $$ \Rightarrow {\text{ 1 is the multiplicative identity for any real number}}$$

$${\textbf{Hence correct option is (D) all of the above}}$$
Question 5
1 / -0

$$\dfrac {3x}{y}\times 1 = ..........$$ is stated by multiplicative identity property.

A
$$3x$$

B
$$y$$

C
$$\dfrac {3x}{y}$$

D
$$1$$

Solution

The multiplicative identity property states that when we multiply a number by $$1,$$ then the product is the number itself.
So, $$\dfrac {3x}{y} \times 1 = \dfrac {3x}{y}$$.
Question 6
1 / -0

Find using additive inverse property, what should be added to $$\dfrac {-1}{3}$$, so that the sum is zero ?

A
$$\dfrac {-1}{3}$$

B
$$\dfrac {1}{3}$$

C
$$1$$

D
$$0$$

Solution

We know that the sum of a rational number and its additive inverse is zero.

Since the given rational number is $$\dfrac {-1}{3}$$, its negative is $$-\left (\dfrac {-1}{3}\right ) = \dfrac {1}{3}$$

Now, $$\dfrac {-1}{3} + \dfrac {1}{3} = 0$$. Hence, $$\dfrac {1}{3}$$ should be added to $$\dfrac {-1}{3}$$ to get the sum as $$0$$.
Question 7
1 / -0

The product of ........... and any rational number is the rational number itself.

A
$$1$$

B
$$-1$$

C
$$0$$

D
the given rational number

Solution

The product of $$1$$ and any rational number is the rational number itself because $$1$$ is the multiplicative identity for rational numbers.

Ex: $$\dfrac 3 2$$ when multiplied by $$1$$ gives $$\dfrac 3 2$$ itself, which is a rational number.
Question 8
1 / -0

Which of the following number lines, represents rational numbers?

A

B

C

D
All of the above
Question 9
1 / -0

Which of the following rational number does not have a reciprocal?

A
$$1$$

B
$$-1$$

C
$$0$$

D
none

Solution

If we try to find the reciprocal of 0 then, we get the result which is not defined.
As, $$\dfrac{1}{0}=$$ Not a number
So, we can say that $$0$$ does not have a reciprocal.
Question 10
1 / -0

There exists ....... number of rational numbers between $$\dfrac {2}{5}$$ and $$\dfrac {4}{5}.$$

A
$$0$$

B
$$1$$

C
$$5$$

D
infinite

Solution

There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between $$\dfrac {2}{5}$$ and $$\dfrac {4}{5}$$.

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Rational Numbers Test - 22

Result

Rational Numbers Test - 22

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Question 1

$$\dfrac {-3}{11}$$

$$\dfrac {11}{3}$$

$$-1$$

$$\dfrac {3}{11}$$

Solution

Question 2

$$\dfrac {2}{7}$$

$$\dfrac {-2}{7}$$

$$\dfrac {7}{2}$$

$$\dfrac {-7}{2}$$

Solution

Question 3

$$0$$

$$2$$

$$4$$

infinite

Solution

Question 4

whole numbers

integers

rational numbers

all of the above

Solution

Question 5

$$3x$$

$$y$$

$$\dfrac {3x}{y}$$

$$1$$

Solution

Question 6

$$\dfrac {-1}{3}$$

$$\dfrac {1}{3}$$

$$1$$

$$0$$

Solution

Question 7

$$1$$

$$-1$$

$$0$$

the given rational number

Solution

Question 8

All of the above

Question 9

$$1$$

$$-1$$

$$0$$

none

Solution

Question 10

$$0$$

$$1$$

$$5$$

infinite

Solution

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