Rational Numbers Test

Result

Rational Numbers Test - 23

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which of the following rational numbers lies between $$0$$ and $$-1$$?

A
$$0$$

B
$$-1$$

C
$$\dfrac {-1}{4}$$

D
$$\dfrac {1}{4}$$

Solution

Clearly, $$0$$ and $$-1$$ cannot lie between $$0$$ and $$-1$$.
Also,
$$0=\dfrac{0}{4}$$ and $$-1=\dfrac{-4}{4}$$
We can clearly see that $$\dfrac {-1}{4}$$ lies between $$0$$ and $$-1$$.
Question 2
1 / -0

Which of the following rational numbers lies between $$\dfrac {3}{2}$$ and $$4$$ ?

A
$$\dfrac {1}{2}$$

B
$$3$$

C
$$\dfrac {8}{2}$$

D
$$\dfrac {9}{2}$$

Solution

We have to find a rational number between $$\dfrac {3}{2}$$ and $$4$$. The L.C.M. of the denominators of both numbers is $$2$$.
$$\therefore \dfrac {3}{2} = \dfrac {3}{2}$$ and $$4\times \dfrac {2}{2} = \dfrac {8}{2}$$.
$$\therefore$$ From the above given options, only $$\dfrac {6}{2}$$
i.e. $$=3$$ lies between $$\dfrac {3}{2}$$ and $$4$$.
Question 3
1 / -0

The number $$\dfrac {13}{15}$$ is correctly represented on number line

A

B

C

D

Solution

To represent $$\dfrac{13}{15}$$ on a number line, divide the space from $$0$$ to $$1$$ in $$15$$ equal parts
The thirteenth part will represent a rational number $$\dfrac{13}{15}$$.
As we can see, $$\dfrac{11}{15}$$ come after $$\dfrac{10}{15}$$, then $$\dfrac{12}{15}$$ and then $$\dfrac{13}{15}$$.
Hence, the above line is the correct representation of $$\dfrac{13}{15}$$
Question 4
1 / -0

The sum of two rational numbers is $$-5$$. If one of the numbers is $$\dfrac {-3}{5}$$, find the other number

A
$$-4\dfrac {2}{5}$$

B
$$4\dfrac {8}{5}$$

C
$$\dfrac {-6}{5}$$

D
$$4\dfrac {6}{5}$$

Solution

$$Let\quad other\quad will\quad be\quad x\\ then\quad x+\dfrac { -3 }{ 5 } =-5\\ x=-5+\dfrac { 3 }{ 5 } =\dfrac { -22 }{ 5 } =-4\dfrac { 2 }{ 5 } $$
So correct answer will be option A
Question 5
1 / -0

Which are three rational numbers between $$-2$$ and $$-1$$?

A
$$\dfrac { -1 }{ 2 } ,\dfrac { -1 }{ 3 } ,\dfrac { -1 }{ 5 } $$

B
$$\dfrac { -3 }{ 2 } ,\dfrac { -7 }{ 4 } ,\dfrac { -5 }{ 4 } $$

C
$$\dfrac { -12 }{ 5 } ,\dfrac { -22 }{ 5 } ,\dfrac { 12 }{ 5 } $$

D
$$\dfrac { 3 }{ 2 } ,\dfrac { 7 }{ 4 } ,\dfrac { 5 }{ 4 } $$

Solution

Mean $$= \dfrac {(-2) + (-1)}{2} = \dfrac {-1 -2}{2} = \dfrac {-3}{2}$$.
$$\frac{(-2)+\dfrac{-3}{2}}{2}$$ =$$\dfrac {-7}{4}$$
$$\frac{(-1)+\dfrac{-3}{2}}{2}$$ =$$\dfrac {-5}{4}$$
Mean of numbers lies between the two numbers.
So, answer is option $$B.$$
Question 6
1 / -0

How many rational numbers exist between any two distinct rational numbers?

A
$$2$$

B
$$3$$

C
$$10$$

D
Infinite

Solution

Rational numbers are those numbers which can be expressed in the form of $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are integers. Hence between two rational numbers there can be infinite rational numbers

So correct answer is option D
Question 7
1 / -0

Out of the following numbers, which can be represented on a number line?
$$0, \dfrac56, 1, \dfrac24$$

A
$$0$$

B
$$\dfrac56$$

C
$$1$$

D
All of these

Solution

Given numbers are $$0,\dfrac{5}{6} ,1,\dfrac{2}{4}$$
$$0,1$$ are integers and $$\dfrac{5}{6}, \dfrac{2}{4}$$ are rational numbers.
As, rationals and integers are subset of reals.
Thus, all the above numbers are real.
Hence, we can represent all above numbers on a number line.
Question 8
1 / -0

While representing $$\dfrac23$$ on a number line, between which two integers does the point lie?

A
$$1$$ and $$2$$

B
$$0$$ and $$1$$

C
$$2$$ and $$3$$

D
$$1$$ and $$3$$

Solution

$$\dfrac{2}{3}=0.67$$
It is clear that 0.67 lies between 0 and 1
So correct answer will be option B
Question 9
1 / -0

The multiplicative inverse of $$-7$$ is _____

A
$$7$$

B
$$\dfrac {1}{7}$$

C
$$-7$$

D
$$\dfrac {-1}{7}$$

Solution

Multiplicative inverse means the same thing as reciprocal.
And the product of a number and its multiplicative inverse is 1.
So $$-7\times \frac{-1}{7}=1$$
Hence multiplicative inverse of -7 is $$\frac{-1}{7}$$
Question 10
1 / -0

The additive inverse of $$\dfrac {-3}{5}$$ is ________

A
$$\dfrac {-3}{5}$$

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

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

D
$$\dfrac {-5}{3}$$

Solution

We know that for any real number $$a$$, the additive number inverse is given by $$-a$$ such that $$ a+( -a) =0.$$

As, $$\dfrac{-3}{5}+\dfrac{3}{5}=0$$
Then additive inverse of $$\dfrac{-3}{5}$$ is $$\dfrac{3}{5}$$.

Hence, option $$C$$ is correct.