Fractions Test

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Fractions Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

The lowest form of $$\displaystyle \frac{20}{50}$$ is ____

A
$$\displaystyle \frac{1}{5}$$

B
$$\displaystyle \frac{1}{2}$$

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

D
$$\displaystyle \frac{10}{25}$$

Solution

For getting the lowest form of the fraction firstly divide the fraction by the same number to the numerator and denominator.
So after dividing both numerator and denominator of $$\dfrac{20}{50}$$ by $$10$$ we get
$$\dfrac{2}{5}$$ as the lowest form
Question 2
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Simplifying the fraction $$\displaystyle \frac{6}{5}\times 4\frac{1}{2}$$ gives

A
$$\displaystyle \frac{27}{5}$$

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

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

D
None of the above

Solution

$$\displaystyle \frac{6}{5} \times 4\frac{1}{2}$$

$$=\displaystyle \frac{6}{5}\times \frac{9}{2}$$

$$= \displaystyle \frac{27}{5}$$

So, option $$A$$ is correct.
Question 3
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$$7\dfrac {1}{2} + 8\dfrac {1}{2} = ?$$

A
$$16$$

B
$$15\dfrac {1}{2}$$

C
$$5\dfrac {1}{2}$$

D
$$15$$
Question 4
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Can we say that following figures represent equal fractions?

A
Yes, 1st and 2nd figure show equal parts.

B
Yes, all the figures show equal parts.

C
Yes, 2nd and 3rd figure show equal parts.

D
No

Solution

In the given first object, there are a total of $$4$$ triangles and $$1$$ triangle is shaded amongst them. Therefore, the ratio of the shaded triangle to the total number of triangles is:

$$\dfrac {Shaded}{Total}=\dfrac { 1 }{ 4 }$$

Now, consider the second circular object, there are a total of $$4$$ parts and $$1$$ part is shaded amongst them. Therefore, the ratio of shaded part to the total number of parts is:

$$\dfrac {Shaded}{Total}=\dfrac {1 }{ 4 }$$

Now, in the third object, there are a total of $$4$$ rectangles and $$1$$ rectangle is shaded amongst them. Therefore, the ratio of the shaded rectangle to the total number of rectangles is:

$$\dfrac {Shaded}{Total}=\dfrac { 1 }{ 4 }$$

Since the fraction of all of the objects is the same that is $$\dfrac {1}{4}$$.

Hence, all the given figures show equal parts.
Question 5
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Subtract the fractions:

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

B
$$\dfrac{2}{4}$$

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

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

Solution

Three out of four sectors of the circles are dark the fraction of darken sectors =$$\dfrac{3}{4}$$
Two out of four sectors of the circles are dark the fraction of darken sectors =$$\dfrac{2}{4}$$
Subtracting them , we get $$\dfrac{3}{4}-\dfrac{2}{4}=\dfrac{1}{4}$$
Question 6
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If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is?

A
Always greater than the original fraction

B
Always less than the original fraction

C
Always equal to the original fraction

D
None of the above

Solution

If the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Let us understand and verify it with the help of couple of examples:

$$(i)$$ Let $$\dfrac{1}{2}$$ be an original fraction.
$$\dfrac{1}{2}=0.5$$
If the numerator and denominator are increased by $$5$$, the fraction becomes:
$$\dfrac{1+5}{2+5}=\dfrac{5}{7}=0.71$$

$$\therefore$$ $$\dfrac{1}{2}<\dfrac{5}{7}$$

$$(ii)$$ Let $$\dfrac{7}{9}$$ be an original fraction.
$$\dfrac{7}{9}\approx 0.78$$
If the numerator and denominator are increased by $$1$$, the fraction becomes:
$$\dfrac{7+1}{9+1}=\dfrac{8}{10}=0.8$$

$$\therefore$$ $$\dfrac{7}{9}<\dfrac{8}{10}$$

Hence, if the numerator and denominator of a proper fraction are increased by the same quantity, then the resulting fraction is always greater than the original fraction.

Therefore, option A is correct.
Question 7
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Ritu painted $$\dfrac{2}{5}$$ of the wall space in her room. Her sister Rashmi helped and painted $$\dfrac{3}{5}$$ of the wall space. How much did they paint together?

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

B
$$\dfrac{6}{25}$$

C
$$\dfrac{1}{5}$$

D
$$1$$

Solution

Total fraction of wall painted by Ritu and Rashmi = $$\dfrac{2}{5} + \dfrac{3}{5}$$ = $$\dfrac{5}{5}$$ = 1
Question 8
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$$2+\cfrac { 1 }{ 100 } +\cfrac { 3 }{ 1000 } =\_ \_ \_ \_ \_ \_ $$

A
$$0.213$$

B
$$2.13$$

C
$$2.013$$

D
$$2.130$$

Solution
Question 9
1 / -0

Reduce the following fractions to their lowest forms.
a. $$\dfrac{36}{144}$$

b. $$\dfrac{65}{117}$$

c. $$\dfrac{180}{120}$$

A
$$a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$$

B
$$a=\dfrac{1}{4}, b=\dfrac{5}{9}, c=\dfrac{3}{2}$$

C
$$a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{3}{2}$$

D
$$a=\dfrac{3}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$$

Solution

$$\\(a.)(\frac{36}{144})=(\frac{3}{12})=(\frac{1}{4})\\(b.)(\frac{65}{117})=(\frac{13\cdot 5}{13\cdot 9})=(\frac{5}{9})\\(c.)(\frac{180}{120})=(\frac{60\cdot 3}{60\cdot 2})=(\frac{3}{2})$$
Question 10
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Compare the following
$$\dfrac{1}{8},\ \dfrac{1}{4}$$.

A
$$\dfrac {1}{4}>\dfrac {1}{8}$$

B
$$\dfrac {1}{4}<\dfrac {1}{8}$$

C
$$\dfrac {1}{4}=\dfrac {1}{8}$$

D
none of these

Solution

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Re-Attempt Weekly Quiz Competition

Fractions Test - 24

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Fractions Test - 24

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Question 1

$$\displaystyle \frac{1}{5}$$

$$\displaystyle \frac{1}{2}$$

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

$$\displaystyle \frac{10}{25}$$

Solution

Question 2

$$\displaystyle \frac{27}{5}$$

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

$$\displaystyle \frac{11}{5}$$

None of the above

Solution

Question 3

$$16$$

$$15\dfrac {1}{2}$$

$$5\dfrac {1}{2}$$

$$15$$

Question 4

Yes, 1st and 2nd figure show equal parts.

Yes, all the figures show equal parts.

Yes, 2nd and 3rd figure show equal parts.

No

Solution

Question 5

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

$$\dfrac{2}{4}$$

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

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

Solution

Question 6

Always greater than the original fraction

Always less than the original fraction

Always equal to the original fraction

None of the above

Solution

Question 7

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

$$\dfrac{6}{25}$$

$$\dfrac{1}{5}$$

$$1$$

Solution

Question 8

$$0.213$$

$$2.13$$

$$2.013$$

$$2.130$$

Solution

Question 9

$$a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$$

$$a=\dfrac{1}{4}, b=\dfrac{5}{9}, c=\dfrac{3}{2}$$

$$a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{3}{2}$$

$$a=\dfrac{3}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$$

Solution

Question 10

$$\dfrac {1}{4}>\dfrac {1}{8}$$

$$\dfrac {1}{4}<\dfrac {1}{8}$$

$$\dfrac {1}{4}=\dfrac {1}{8}$$

none of these

Solution

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