Fractions Test

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Fractions Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

$$\displaystyle \frac { 1 }{ 3 } +\frac { 1 }{ 2 } -\frac { 5 }{ 6 } +\frac { 1 }{ 5 } +\frac { 1 }{ 4 } -\frac { 9 }{ 20 } =$$

A
0

B
$$\displaystyle \frac { 2 }{ 15 } $$

C
$$\displaystyle \frac { 2 }{ 5 } $$

D
$$\displaystyle \frac { 9 }{ 20 } $$

E
$$\displaystyle \frac { 5 }{ 6 } $$

Solution

$$\displaystyle \frac { 1 }{ 3 } +\frac { 1 }{ 2 } -\frac { 5 }{ 6 } +\frac { 1 }{ 5 } +\frac { 1 }{ 4 } -\frac { 9 }{ 20 } $$

$$=\displaystyle \frac { 2 }{ 6 } +\frac { 3 }{ 6 } -\frac { 5 }{ 6 } +\frac { 4 }{ 20 } +\frac { 5 }{ 20 } -\frac { 9 }{ 20 } $$

$$=\displaystyle \frac { 5 }{ 6 } -\frac { 5 }{ 6 } +\frac { 9 }{ 20 } -\frac { 9 }{ 20 } $$

$$=0$$
Question 2
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Convert $$\dfrac{13}{7}$$ into a mixed fraction.

A
$$\displaystyle 1\frac{6}{7}$$

B
$$\displaystyle 2\frac{3}{7}$$

C
$$\displaystyle 3\frac{0}{7}$$

D
$$\displaystyle 3\frac{5}{7}$$

Solution

Divide $$13$$ by $$7$$. The quotient is $$1$$ and remainder is $$6$$.

$$\therefore \dfrac{13}{7}=1\dfrac{6}{7}$$

So, option A is correct.
Question 3
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Which of the following is/are improper fraction(s)?

A
$$\dfrac{21}{20}$$

B
$$\dfrac{23}{24}$$

C
$$\dfrac{14}{15}$$

D
None of the above

Solution

Here, Numerator $$>$$ denominator only in option $$A.$$
Hence, option $$A$$ is correct.
Question 4
1 / -0

Which of the following is improper fraction?

A
$$\dfrac{1}{3}$$

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

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

D
none of the above

Solution

A fraction in which the numerator is greater than the denominator is called an improper fraction.
$$\therefore \dfrac{4}{3}$$ is correct.
Question 5
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The value of expression $$1 + \left \{\dfrac {1}{2} + \dfrac {1}{3} + \dfrac {1}{6} + \left (\dfrac {3}{4} - \dfrac {1}{3} \right )\right \}$$ is

A
$$\dfrac {29}{12}$$

B
$$1$$

C
$$\dfrac {5}{12}$$

D
$$\dfrac {1}{12}$$

Solution

$$ 1+\left [ \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}+\left ( \dfrac{3}{4}-\dfrac{1}{3} \right ) \right ] = 1+\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{3}{4} = \dfrac{9}{4}+\dfrac{1}{6} = \boxed{\dfrac{29}{12}} $$
Question 6
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Simplify: $$\displaystyle \dfrac{\dfrac{3}{5}+\dfrac{1}{3}}{\dfrac{2}{3}+\dfrac{2}{5}}$$

A
$$\cfrac{3}{4}$$

B
$$\cfrac{4}{5}$$

C
$$\cfrac{6}{7}$$

D
$$\cfrac{7}{8}$$

Solution

First, add the fractions in the numerator and denominator:

$$\displaystyle \dfrac{\dfrac{14}{15}}{\dfrac{16}{15}} = \frac{14}{15}\times \frac{15}{16}=\dfrac{14}{16}=\frac{7}{8}$$

Alternatively, to save time, multiply each of the small fractions by 15,which is

the common denominator of all the fractions in the problem. Because you are

multiplying the numerator and the denominator of the whole complex fraction by 15,you are not changing its value:

$$\displaystyle \frac{9+5}{10+6}=\frac{14}{16}=\frac{7}{8}$$
Question 7
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Reduce fraction to lowest form:
$$\dfrac{100}{200}$$

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

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

C
$$\dfrac{2}{5}$$

D
$$\dfrac{2}{6}$$

Solution

$$\dfrac{100}{200}$$

Dividing numerator and denominator by $$100$$, we get
$$\dfrac{100}{200} = \dfrac{1}{2}$$

This is the lowest form
Question 8
1 / -0

Reduce fraction to lowest form:
$$\dfrac{144}{36}$$

A
$$\dfrac{4}{1}$$

B
$$\dfrac{12}{2}$$

C
$$\dfrac{1}{36}$$

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

Solution

$$\dfrac{144}{36}$$

Dividing numerator and denominator by $$12$$, we get
$$\dfrac{144}{36} = \dfrac{12}{3}$$

Dividing both numerator and denominator again by $$3$$, we get
$$\dfrac{12}{3} = \dfrac{4}{1}$$

This is the lowest form
Question 9
1 / -0

Reduce fraction to lowest form:
$$\dfrac{12}{16}$$

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

B
$$\dfrac{1}{4}$$

C
$$\dfrac{1}{16}$$

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

Solution

$$\dfrac{12}{16}$$

Dividing numerator and denominator by $$4$$, we get
$$\dfrac{12}{16} = \dfrac{3}{4}$$

This is the lowest form
Question 10
1 / -0

Reduce fraction to lowest form:
$$\dfrac{25}{100}$$

A
$$\dfrac{25}{10}$$

B
$$\dfrac{1}{4}$$

C
$$\dfrac{5}{10}$$

D
$$\dfrac{5}{100}$$

Solution

$$\dfrac{25}{100}$$

Dividing numerator and denominator by $$25$$, we get
$$\dfrac{25}{100} = \dfrac{1}{4}$$

This is the lowest form

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Fractions Test - 16

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Fractions Test - 16

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Question 1

0

$$\displaystyle \frac { 2 }{ 15 } $$

$$\displaystyle \frac { 2 }{ 5 } $$

$$\displaystyle \frac { 9 }{ 20 } $$

$$\displaystyle \frac { 5 }{ 6 } $$

Solution

Question 2

$$\displaystyle 1\frac{6}{7}$$

$$\displaystyle 2\frac{3}{7}$$

$$\displaystyle 3\frac{0}{7}$$

$$\displaystyle 3\frac{5}{7}$$

Solution

Question 3

$$\dfrac{21}{20}$$

$$\dfrac{23}{24}$$

$$\dfrac{14}{15}$$

None of the above

Solution

Question 4

$$\dfrac{1}{3}$$

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

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

none of the above

Solution

Question 5

$$\dfrac {29}{12}$$

$$1$$

$$\dfrac {5}{12}$$

$$\dfrac {1}{12}$$

Solution

Question 6

$$\cfrac{3}{4}$$

$$\cfrac{4}{5}$$

$$\cfrac{6}{7}$$

$$\cfrac{7}{8}$$

Solution

Question 7

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

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

$$\dfrac{2}{5}$$

$$\dfrac{2}{6}$$

Solution

Question 8

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

$$\dfrac{12}{2}$$

$$\dfrac{1}{36}$$

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

Solution

Question 9

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

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

$$\dfrac{1}{16}$$

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

Solution

Question 10

$$\dfrac{25}{10}$$

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

$$\dfrac{5}{10}$$

$$\dfrac{5}{100}$$

Solution

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