Rational Numbers Test

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Rational Numbers Test - 13

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Weekly Quiz Competition

Question 1
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 2
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 3
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 4
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 5
1 / -0

The value of X such that $$-\displaystyle\frac{3}{8}$$ and $$\displaystyle\frac{X}{-24}$$ are equivalent rational numbers is __________.

A
$$64$$

B
$$-64$$

C
$$-9$$

D
$$9$$

Solution

$$-\dfrac{3}{8}=\dfrac{X}{-24}$$
$$X=\dfrac{-3\times-24}{8}$$
$$X=9$$
Hence the correct answer is option D.
Question 6
1 / -0

For any two rational numbers x and y which of the following are correct, if x is positive and y is negative?
$$(1)$$ x $$<$$ y
$$(2)$$ x $$=$$ y
$$(3)$$ x $$>$$ y.

A
Only $$1$$ and $$2$$ are correct

B
Only $$2$$ and $$3$$ are correct

C
Only $$3$$ is correct

D
All $$1, 2$$ and $$3$$ are correct

Solution

If x is positive and y is negative, then the value of x will always be greater than value of y
$$\therefore$$ $$x>y$$
Hence the correct answer is option C.
Question 7
1 / -0

State which of the following statements is/are true?
I. Numerator and denominator of a positive rational number need not to have like signs.
II. Numerator and denominator of a negative rational number should have like signs.

A
Only I

B
Only II

C
Both I and II

D
Neither I nor II

Solution

If both the numerator and denominator has same sign, then the fraction is a positive rational number.
If the numerator and denominator have different signs, then the fraction is a negative rational number.
Question 8
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 9
1 / -0

Which of the following rational numbers is positive?

A
$$\dfrac{-7}{9}$$

B
$$\dfrac{-8}{2}$$

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

D
$$\dfrac{3}{-2}$$

Solution

A rational number is positive only when both its numerator and denominator are positive.
We can see that only $$\dfrac{6}{5}$$ has positive numerator and denominator. Rest all the given options have either negative numerator or negative denominator.
Therefore, only $$\dfrac{6}{5}$$ is a positive rational number.
Hence, option C is correct.
Question 10
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.

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Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 13

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Rational Numbers Test - 13

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SHARING IS CARING

Question 1

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

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

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

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

Solution

Question 2

$$0$$

$$\dfrac56$$

$$1$$

All of these

Solution

Question 3

$$1$$ and $$2$$

$$0$$ and $$1$$

$$2$$ and $$3$$

$$1$$ and $$3$$

Solution

Question 4

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

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

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

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

Solution

Question 5

$$64$$

$$-64$$

$$-9$$

$$9$$

Solution

Question 6

Only $$1$$ and $$2$$ are correct

Only $$2$$ and $$3$$ are correct

Only $$3$$ is correct

All $$1, 2$$ and $$3$$ are correct

Solution

Question 7

Only I

Only II

Both I and II

Neither I nor II

Solution

Question 8

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

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

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

All of these

Solution

Question 9

$$\dfrac{-7}{9}$$

$$\dfrac{-8}{2}$$

$$\dfrac{6}{5}$$

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

Solution

Question 10

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

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