Rational Numbers Test

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Rational Numbers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Choose the rational number which does not lie between rational numbers $$\dfrac{3}{5}$$ and $$\dfrac{2}{3}$$.

A
$$\dfrac{46}{75}$$

B
$$\dfrac{47}{75}$$

C
$$\dfrac{49}{75}$$

D
$$\dfrac{50}{75}$$

Solution

All the options have a denominator of $$75$$. Hence, let us convert $$\dfrac35$$ and $$\dfrac23$$ into equivalent fractions having denominator $$75$$.
$$\dfrac{3}{5} $$ $$=\dfrac{3\times 15}{5\times 15} $$ $$=\dfrac{45}{75}$$

$$\dfrac{2}{3}$$ $$=\dfrac{2\times 25}{3\times 25}$$ $$=\dfrac{50}{75}$$

Hence, $$\dfrac{50}{75}$$ does not lie between the given rational numbers.
Question 2
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________ are rational numbers between $$\displaystyle \frac{1}{3}$$ and $$\displaystyle \frac{1}{4}$$

A
$$\displaystyle \frac{1}{3}, \frac{7}{64}, \frac{13}{48}, \frac{1}{4}$$

B
$$\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$$

C
$$\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{68}, \frac{1}{4}$$

D
none of the above

Solution

A

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

b)}{2} $$

So, a

rational number between $$\frac {1}{3} $$ and $$ \frac {1}{4} = \frac {(\frac {1}{3} + \frac {1}{4})}{2} = \frac {7}{24} $$

Now, another rational number between $$ \frac {7}{24} $$ and $$ \frac {1}{4} = \frac {(\frac {7}{24} + \frac {1}{4})}{2} = \frac {13}{48} $$

Hence, required two rational numbers between $$\frac {1}{3} $$ and $$ \frac {1}{4} $$ are $$\frac {1}{3} ,\frac {7}{24}, \frac {13}{48}, \frac {1}{4}$$
Question 3
1 / -0

$$\displaystyle \dfrac{4}{11}$$ subtracted from $$\displaystyle \dfrac{9}{11}$$ is

A
$$\displaystyle \dfrac{5}{22}$$

B
$$\displaystyle \dfrac{5}{0}$$

C
$$\displaystyle \dfrac{5}{11}$$

D
$$\displaystyle \dfrac{13}{11}$$

Solution

$$\displaystyle \dfrac{9}{11} - \dfrac{4}{11} = \dfrac{9 - 4}{11} = \dfrac{5}{11}$$
Question 4
1 / -0

The sum of $$\displaystyle \frac{8}{15}$$ and $$\displaystyle \frac{7}{15}$$ is _______

A
1

B
$$\displaystyle \frac{1}{15}$$

C
$$\displaystyle \frac{1}{30}$$

D
none

Solution

$$\frac{8}{15}+ \frac{7}{15} = \frac{8+7}{15} = \displaystyle 1$$
Question 5
1 / -0

Which of the following is not a rational number?

A
$$\displaystyle \frac{3}{17}$$

B
$$\displaystyle \frac{-4}{19}$$

C
$$\displaystyle \frac{0}{8}$$

D
$$\displaystyle \frac{3}{0}$$

Solution

We know that a number that can be made by dividing two integers. (An integer is a number with no fractional part.)
The word comes from "ratio".
For example:
$$\dfrac {1}{2}$$ is a rational number. ($$1$$ divided by $$2$$, or the ratio of $$1$$ to $$2$$)

But $$\dfrac {1}{0}$$ is not a rational number because the result of this fraction is not defined. Similarly, $$\dfrac {3}{0}$$ is not a rational number.

Hence, $$\dfrac {3}{0}$$ is not a rational number.
Question 6
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If all the rational numbers $$\displaystyle \frac{3}{7}, \frac{1}{14},\frac{4}{7}, \frac{2}{7}, \frac{5}{7}$$ and $$\displaystyle \frac{5}{14}$$ are arranged in ascending order of their values, which one will be the third?

A
$$\displaystyle \frac{1}{14}$$

B
$$\displaystyle \frac{3}{7}$$

C
$$\displaystyle \frac{5}{14}$$

D
$$\displaystyle \frac{8}{14}$$

Solution

The given numbers are $$\displaystyle \frac{3}{7}, \frac{1}{14},\frac{4}{7}, \frac{2}{7}, \frac{5}{7}$$ and $$\displaystyle \frac{5}{14}$$

The LCM of the denominators $$7,14$$ is $$14$$.
Therefore, the numbers with denominator $$7$$ will be:

$$\dfrac{3}{7}=\dfrac { 3\times 2 }{ 7\times 2} =\dfrac { 6 }{ 14 } \\ \dfrac{4}{7}=\dfrac { 4\times 2 }{ 7\times 2 } =\dfrac { 8 }{ 14 } \\\dfrac{2}{7}= \dfrac { 2\times 2 }{ 7\times 2} =\dfrac { 4 }{ 14 } \\\dfrac{5}{7}= \dfrac { 5\times 2 }{ 7\times 2 } =\dfrac { 10 }{ 14 }$$

Thus, the numbers in ascending order are shown below:

$$\dfrac { 1 }{ 14 }$$ ,$$\dfrac { 4 }{ 14 }$$ ,$$\dfrac { 5 }{14 }$$ ,$$\dfrac { 6 }{ 14 }$$, $$\dfrac { 8 }{ 14 }$$,$$\dfrac { 10 }{ 14 }$$
So, in simplified form
$$\dfrac { 1 }{ 14 }$$ ,$$\dfrac { 2 }{ 7 }$$ ,$$\dfrac { 5 }{14 }$$ ,$$\dfrac { 3 }{ 7 }$$, $$\dfrac { 4 }{ 7 }$$,$$\dfrac { 5 }{ 7 }$$

$$\dfrac { 5 }{14 }$$ is in third position.

Hence, $$Op-C$$ is correct.
Question 7
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The rational number $${\cfrac{0}{7}}$$:

A
Has a positive numerator

B
Has a negative numerator

C
Has either a positive numerator or a negative numerator

D
Has neither a positive numerator nor a negative numerator

Solution

In the given question numerator is $$0$$ and $$0$$ is neither positive nor negative. So the correct answer will be option D.
Question 8
1 / -0

$$\displaystyle 4\frac{1}{3}$$ + $$\displaystyle 5\frac{2}{3}$$ = _______

A
$$\displaystyle \frac{13}{3}$$

B
$$30$$

C
$$\displaystyle \frac{14}{3}$$

D
$$10$$

Solution

$$\displaystyle 4 \frac{1}{3} + 5 \frac{2}{3} = \frac{13}{3} + \frac{17}{3}$$
$$\displaystyle = \frac{13 + 17}{3} = \frac{30}{3} = 10$$
Question 9
1 / -0

Which of the following statement is true?

A
$$\displaystyle \frac{3}{- 8}\, >\, \displaystyle \frac{- 12}{32}$$

B
$$\displaystyle \frac{3}{- 8}\, =\, \displaystyle \frac{- 12}{32}$$

C
$$\displaystyle \frac{3}{- 8}\, <\, \displaystyle \frac{-12}{32}$$

D
$$\displaystyle \frac{3}{5}\, >\, \displaystyle \frac{4}{3}$$

Solution

$$\displaystyle \frac{3}{- 8}\, =\, \displaystyle \frac{3}{- 8}\, \times\, \displaystyle \frac{- 4}{- 4}\, =\, \displaystyle \frac{- 12}{32}$$
$$\therefore \cfrac{3}{-8} = \cfrac{-12}{32}$$
Question 10
1 / -0

Which of the following rational numbers is in the standard form?

A
$$\displaystyle \frac{8

}{- 36}$$

B
$$\displaystyle \frac{- 7}{56}$$

C
$$\displaystyle \frac{3}{- 4}$$

D
None

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Rational Numbers Test - 16

Result

Rational Numbers Test - 16

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Question 1

$$\dfrac{46}{75}$$

$$\dfrac{47}{75}$$

$$\dfrac{49}{75}$$

$$\dfrac{50}{75}$$

Solution

Question 2

$$\displaystyle \frac{1}{3}, \frac{7}{64}, \frac{13}{48}, \frac{1}{4}$$

$$\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$$

$$\displaystyle \frac{1}{3}, \frac{7}{24}, \frac{13}{68}, \frac{1}{4}$$

none of the above

Solution

Question 3

$$\displaystyle \dfrac{5}{22}$$

$$\displaystyle \dfrac{5}{0}$$

$$\displaystyle \dfrac{5}{11}$$

$$\displaystyle \dfrac{13}{11}$$

Solution

Question 4

1

$$\displaystyle \frac{1}{15}$$

$$\displaystyle \frac{1}{30}$$

none

Solution

Question 5

$$\displaystyle \frac{3}{17}$$

$$\displaystyle \frac{-4}{19}$$

$$\displaystyle \frac{0}{8}$$

$$\displaystyle \frac{3}{0}$$

Solution

Question 6

$$\displaystyle \frac{1}{14}$$

$$\displaystyle \frac{3}{7}$$

$$\displaystyle \frac{5}{14}$$

$$\displaystyle \frac{8}{14}$$

Solution

Question 7

Has a positive numerator

Has a negative numerator

Has either a positive numerator or a negative numerator

Has neither a positive numerator nor a negative numerator

Solution

Question 8

$$\displaystyle \frac{13}{3}$$

$$30$$

$$\displaystyle \frac{14}{3}$$

$$10$$

Solution

Question 9

$$\displaystyle \frac{3}{- 8}\, >\, \displaystyle \frac{- 12}{32}$$

$$\displaystyle \frac{3}{- 8}\, =\, \displaystyle \frac{- 12}{32}$$

$$\displaystyle \frac{3}{- 8}\, <\, \displaystyle \frac{-12}{32}$$

$$\displaystyle \frac{3}{5}\, >\, \displaystyle \frac{4}{3}$$

Solution

Question 10

$$\displaystyle \frac{8}{- 36}$$

$$\displaystyle \frac{- 7}{56}$$

$$\displaystyle \frac{3}{- 4}$$

None

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$$\displaystyle \frac{8

}{- 36}$$