Rational Numbers Test

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Rational Numbers Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

Express $$\dfrac{-125}{625}$$ as a rational number with smallest positive denominator equal to

A
$$25$$

B
$$5$$

C
$$625$$

D
$$125$$

Solution

$$\cfrac{-125}{625} = \cfrac{-1}{5} \; \left\{ \because 125 \times 5 = 625 \right\}$$
Question 2
1 / -0

Express $$\dfrac{126}{-196}$$ as a rational number with denominator equal to $$14$$ then value of numerator will be

A
$$63$$

B
$$-9$$

C
$$-126$$

D
None of these

Solution

$$\cfrac{126}{-196} =-\cfrac{126}{196}$$

$$ = -\cfrac{9 \times 14}{14 \times 14}$$

$$ = \cfrac{-9}{14}$$
Question 3
1 / -0

$$\dfrac {p}{q}$$ is a rational number when

A
$$p=0,q\neq0$$

B
$$p=0,q=0$$

C
$$p\ne 0,q=0$$

D
$$p=1,q=0$$

Solution

By the definition of rational number, $$\dfrac{p}{q}$$ is rational where $$p$$ and $$q$$ are integers and $$q$$ is not equal to zero.
In all three options except A, $$q=0$$.
Hence, $$p=0, q\ne 0$$ is true.
Question 4
1 / -0

In the number line, the rational numbers represented by $$'A'$$ is

A
$$\dfrac {2}{8}$$

B
$$\dfrac {3}{8}$$

C
$$\dfrac {1}{8}$$

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

Solution

Consider the given figure,
Distance between $$0$$ to $$3$$ is divided in equal $$8$$ part

So, each part is equal to $$=\dfrac{3}{8}$$

Hence, point $$A$$ is at $$=\dfrac{3}{8}$$unit

Hence, this is the answer.
Question 5
1 / -0

Between two rational numbers, there exists-

A
No rational number

B
Only one rational number

C
Infinite numbers of rational numbers

D
No irrational number

Solution

Between two rational numbers there are infinitely many rational number for example between $$4$$ and $$5$$ there are $$4.1, 4.2, .4.22, 4.223 .....$$
Hence, $$(C)$$ is the correct answer.
Question 6
1 / -0

A rational number is defined as a number that can be expressed in the form $$\dfrac{p}{q}$$ where $$p$$ and $$q$$ are integers and

A
$$q=0$$

B
$$q=1$$

C
$$q\neq 1$$

D
$$q\neq 0$$

Solution

According to the definition of a rational number, it can be expressed in the form of $$\dfrac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q\neq$$0
Question 7
1 / -0

How many rational numbers are there between two rational numbers?

A
$$1$$

B
$$0$$

C
unlimited

D
$$100$$

Solution

Consider $$a\,\&\,b$$ as rational numbers
Then a rational number $$n_1$$ can be find in between $$a\,\&\,b$$ such that $$a<n_1<b$$
using the formula $$n_1=\dfrac{a+b}{2}$$

similarly, again we can find a rational number between $$a\,\&\,n_1$$ and $$n_1\,\&\,b$$
and so on...

Hence, between any two distinct rational numbers there are infinitely many rational numbers.
Question 8
1 / -0

Reciprocal of the fraction $$\dfrac{2}{3}$$is:

A
2

B
3

C
$$\frac{2}{3}$$

D
$$\frac{3}{2}$$

Solution
Question 9
1 / -0

In the standard form of a rational number, the common factor of numerator and denominator is always:

A
$$0$$

B
$$1$$

C
$$-2$$

D
$$2$$

Solution

According to the definition, the common factor of numerator and denominator is always $$1$$.
Question 10
1 / -0

Which of the following numbers is the greatest?

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

B
$$0$$

C
$$\dfrac{1}{2}$$

D
$$-2$$

Solution

The given numbers are $$\dfrac{-1}{2},\ 0,\ \dfrac{1}{2},\text{ and } -2$$

We can write $$0$$ and $$-2$$ as $$\dfrac{0}{1}$$ and $$\dfrac{-2}{1}$$ respectively.

For comparing all the $$4$$ rational numbers, we have to make their denominators same.

Hence, multiplying $$\dfrac{2}{2}$$ with $$\dfrac{0}{1}\ and\ \dfrac{-2}{1}$$.

Now, the numbers will be:
$$\dfrac{-1}{2},\ \dfrac{0}{2},\ \dfrac{1}{2}\ and\ \dfrac{-4}{2}$$

Comparing the numerators, we get:
$$-4<-1<0<1$$

Hence, the rational number with numerator $$1$$ is the greatest.

Hence, $$\dfrac{1}{2}$$ is the greatest of all the given numbers.

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Re-Attempt Weekly Quiz Competition

Rational Numbers Test - 14

Result

Rational Numbers Test - 14

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SHARING IS CARING

Question 1

$$25$$

$$5$$

$$625$$

$$125$$

Solution

Question 2

$$63$$

$$-9$$

$$-126$$

None of these

Solution

Question 3

$$p=0,q\neq0$$

$$p=0,q=0$$

$$p\ne 0,q=0$$

$$p=1,q=0$$

Solution

Question 4

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

$$\dfrac {3}{8}$$

$$\dfrac {1}{8}$$

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

Solution

Question 5

No rational number

Only one rational number

Infinite numbers of rational numbers

No irrational number

Solution

Question 6

$$q=0$$

$$q=1$$

$$q\neq 1$$

$$q\neq 0$$

Solution

Question 7

$$1$$

$$0$$

unlimited

$$100$$

Solution

Question 8

2

3

$$\frac{2}{3}$$

$$\frac{3}{2}$$

Solution

Question 9

$$0$$

$$1$$

$$-2$$

$$2$$

Solution

Question 10

$$\dfrac{-1}{2}$$

$$0$$

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

$$-2$$

Solution

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