Rational Numbers Test

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Rational Numbers Test - 15

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Weekly Quiz Competition

Question 1
1 / -0

In the standard form of a rational numbers, the denominator is always a

A
$$0$$

B
negative integer

C
positive integer

D
$$1$$

Solution

In the standard form of a rational number, the denominator is always a positive integer.
Question 2
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The reciprocal of $$\dfrac{-3}{8} \times \left(\dfrac{-7}{13}\right)$$ is

A
$$\dfrac{104}{21}$$

B
$$\dfrac{-104}{21}$$

C
$$\dfrac{21}{104}$$

D
$$\dfrac{-21}{104}$$

Solution

We have $$\dfrac{-3}{8} \times \left(\dfrac{-7}{13}\right)=\dfrac{3\times 7}{8\times 13}=\dfrac {21}{104}$$

Let $$x$$ be its reciprocal.
Then $$x\times\dfrac{21}{104}=1$$
$$ \Rightarrow x=\dfrac {104}{21}$$

Hence, option A is the correct answer.
Question 3
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$$\dfrac{x + y}{2}$$ is a rational number

A
Between x and y

B
Less than x and y both.

C
Greater than x and y both.

D
Less than x but greater than y.

Solution

$$\dfrac{x+ y}{2}$$ lies in between x and y.

Hence, option A is the correct answer.
Question 4
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Find the rational number in lowest form of the following
$$\dfrac{-3}{7}$$

A
$$-\dfrac{3}{7}$$

B
$$-\dfrac{9}{15}$$

C
$$\dfrac{24}{20}$$

D
$$\dfrac{35}{25}$$

Solution

$$-\dfrac{3}{7}$$ is in the lowest form, while other three were have common factor in their numerator and denominator.
Question 5
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Find the positive rational number out of the following.

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

B
$$\dfrac{-16}{36}$$

C
$$\dfrac{-20}{-45}$$

D
$$\dfrac{28}{-63}$$

Solution

$$\dfrac{-20}{-45}=\dfrac{20}{45}$$ is the only positive rational number among all in the above-given questions . Therefore, the option (c) is the odd one.
Question 6
1 / -0

The reciprocal of the rational number - $$2 \dfrac{3}{7}$$ is

A
$$\dfrac{-17}{7}$$

B
$$\dfrac{7}{17}$$

C
$$\dfrac{-7}{17}$$

D
none of these

Solution
Question 7
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__________ are rational numbers between between 5 and -2.

A
$$\displaystyle 5, \frac{33}{4},\ \frac{3}{2}, -\frac{1}{4}, -2$$

B
$$\displaystyle \frac{13}{4},\ \frac{3}{2}, -\frac{1}{4} $$

C
$$\displaystyle 5, \frac{13}{4},\ \frac{13}{2}, -\frac{1}{4}, -2$$

D
none of the above

Solution

A rational number between two numbers $$ a $$ and $$ b = \dfrac {(a + b)}{2} $$

So, a rational number between $$ 5 $$ and $$ - 2 = \dfrac

{( 5 - 2 )}{2} = \dfrac {3}{2} $$

Now, another rational number between $$ 5 $$ and $$ \dfrac {3}{2} =

\dfrac {( 5 + \dfrac {3}{2})}{2} = \dfrac {13}{4} $$

Another rational number between $$ \dfrac {3}{2} $$ and $$ -2 =

\dfrac {( \dfrac {3}{2}) - 2}{2} = -\dfrac {1}{4} $$

$$ \therefore \dfrac {13}{4}, \dfrac {3}{2}, - \dfrac {1}{4} $$ are the rational numbers between $$ 5 $$ and $$ -2 $$
Question 8
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Choose the rational number, which does not lie, between the rational numbers, $$-\dfrac{2}{3}$$ and $$-\dfrac{1}{5}$$

A
$$-\dfrac{3}{10}$$

B
$$\dfrac{3}{10}$$

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

D
$$-\dfrac{7}{20}$$

Solution

The given rational numbers $$-\dfrac { 2 }{ 3 }$$ and $$-\dfrac { 1 }{ 5 }$$ are negative rational numbers because the numerator and denominator of both the rational numbers are of opposite signs that is the numerator of both the integers is negative while the denominators are positive.

Therefore, none of the positive rational number can lie between the given negative rational numbers $$-\dfrac { 2 }{ 3 }$$ and $$-\dfrac { 1 }{ 5 }$$.

Hence, $$\dfrac { 3 }{ 10 }$$ does not lie between the rational numbers $$-\dfrac { 2 }{ 3 }$$ and $$-\dfrac { 1 }{ 5 }$$.
Question 9
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Rational numbers between $$\displaystyle \frac{3}{8}$$ and $$\displaystyle \frac{7}{12}$$ are

A
$$\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{48}, \frac{7}{12}$$

B
$$\displaystyle \frac{3}{8}, \frac{41}{196}, \frac{23}{48}, \frac{7}{12}$$

C
$$\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{148}, \frac{7}{12}$$

D
none of the above

Solution

A rational number between two numbers $$ a $$ and $$ b = \dfrac {(a +

b)}{2} $$
So, a rational number between $$\dfrac {3}{8} $$ and $$ \dfrac {7}{12}$$
$$ = \dfrac {\dfrac {3}{8} + \dfrac {7}{12}}{2} = \dfrac {23}{48} $$

Now, another rational number between $$ \dfrac {3}{8} $$ and $$ \dfrac {23}{48} $$
$$= \dfrac {\dfrac {3}{8} + \dfrac {23}{48}}{2} = \dfrac {41}{96} $$

Hence, required two rational numbers between $$\dfrac {3}{8} $$ and $$ \dfrac {7}{12} $$ are $$\dfrac {3}{8} ,\dfrac {41}{96}, \dfrac {23}{48}, \dfrac {7}{12}$$
Question 10
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________ are rational numbers between $$\displaystyle -\dfrac{3}{4}$$ and $$\displaystyle \dfrac{1}{2}.$$

A
$$\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{9}{16}$$

B
$$\dfrac{-15}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$$

C
$$\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$$

D
none of the above

Solution

A rational number between two numbers $$ a $$ and $$ b = \dfrac {(a + b)}{2} $$

So,
a rational number between $$ - \dfrac {3}{4} $$ and $$ \dfrac {1}{2} $$
$$= \dfrac {-\dfrac {3}{4} + \dfrac {1}{2}}{2} = - \dfrac {1}{8} $$

Now,
another rational number between $$ - \dfrac {3}{4} $$ and $$ - \dfrac {1}{8} $$
$$=\dfrac {- \dfrac {3}{4} - \dfrac {1}{8}}{2} = - \dfrac {7}{16} $$

Another rational number between $$ - \dfrac {1}{8} $$ and $$ \dfrac {1}{2} =$$

$$\dfrac { - \dfrac {1}{8} + \dfrac {1}{2}} {2} = \dfrac {3}{16} $$

Hence, required three rational numbers between $$ - \dfrac {3}{4} $$ and $$ \dfrac {1}{2} $$ are $$ - \dfrac {3}{4}, - \dfrac {7}{16}, - \dfrac {1}{8}, \dfrac {3}{16}, \dfrac {1}{2} $$

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Rational Numbers Test - 15

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Rational Numbers Test - 15

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Question 1

$$0$$

negative integer

positive integer

$$1$$

Solution

Question 2

$$\dfrac{104}{21}$$

$$\dfrac{-104}{21}$$

$$\dfrac{21}{104}$$

$$\dfrac{-21}{104}$$

Solution

Question 3

Between x and y

Less than x and y both.

Greater than x and y both.

Less than x but greater than y.

Solution

Question 4

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

$$-\dfrac{9}{15}$$

$$\dfrac{24}{20}$$

$$\dfrac{35}{25}$$

Solution

Question 5

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

$$\dfrac{-16}{36}$$

$$\dfrac{-20}{-45}$$

$$\dfrac{28}{-63}$$

Solution

Question 6

$$\dfrac{-17}{7}$$

$$\dfrac{7}{17}$$

$$\dfrac{-7}{17}$$

none of these

Solution

Question 7

$$\displaystyle 5, \frac{33}{4},\ \frac{3}{2}, -\frac{1}{4}, -2$$

$$\displaystyle \frac{13}{4},\ \frac{3}{2}, -\frac{1}{4} $$

$$\displaystyle 5, \frac{13}{4},\ \frac{13}{2}, -\frac{1}{4}, -2$$

none of the above

Solution

Question 8

$$-\dfrac{3}{10}$$

$$\dfrac{3}{10}$$

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

$$-\dfrac{7}{20}$$

Solution

Question 9

$$\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{48}, \frac{7}{12}$$

$$\displaystyle \frac{3}{8}, \frac{41}{196}, \frac{23}{48}, \frac{7}{12}$$

$$\displaystyle \frac{3}{8}, \frac{41}{96}, \frac{23}{148}, \frac{7}{12}$$

none of the above

Solution

Question 10

$$\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{9}{16}$$

$$\dfrac{-15}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$$

$$\dfrac{-7}{16}, \dfrac{-1}{8}, \dfrac{3}{16}$$

none of the above

Solution

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