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Fractions Worksheet

Fractions Worksheet

Objective Type Questions

Fill in the appropriate sign (+ or –)
Fill in the blank boxes by proper fractions and also represent the final answer in the form of diagram.

Multiple Choice Questions
The fraction representing the number of starts inside the circle is

(a) $begin mathsize 10px style 1 over 6 end style$
(b)   $begin mathsize 10px style 6 over 17 end style$
(c)   $begin mathsize 10px style 1 over 17 end style$
(d)   $begin mathsize 10px style 5 over 6 end style$
20 ml is ___________ of a litre.
(a) $begin mathsize 10px style 1 over 50 end style$
(b) $begin mathsize 10px style 1 over 1000 end style$
(c) $begin mathsize 10px style 1 fifth end style$
(d) $begin mathsize 10px style 1 over 100 end style$
Which of the following fraction is greater than $begin mathsize 10px style 4 over 9 end style$ ?
(a) $begin mathsize 10px style 1 half end style$
(b) $begin mathsize 10px style 2 over 3 end style$
(c) $begin mathsize 10px style 1 over 6 end style$
(d) $begin mathsize 10px style 5 over 18 end style$
The below diagram can be represend as

(a) $begin mathsize 10px style 1 half end style$
(b) $begin mathsize 10px style 3 1 third end style$
(c) $begin mathsize 10px style 3 over 4 end style$
(d) $begin mathsize 10px style 3 1 half end style$
Which of the following number lie between 2 and 3 on the number line?
(a) $begin mathsize 10px style 3 over 5 end style$
(b) $begin mathsize 10px style 7 over 3 end style$
(c) $begin mathsize 10px style 5 over 4 end style$
(d) $begin mathsize 10px style 2 over 2 end style$
Which of the following improper fraction represents the below figure?

(a) $begin mathsize 10px style 16 over 6 end style$

(b) $begin mathsize 10px style 16 over 18 end style$

(c) $begin mathsize 10px style 4 over 6 end style$

(d) $begin mathsize 10px style 2 over 6 end style$
Which of the following is equivalent fraction for $begin mathsize 10px style 5 over 5 end style$ ?
(a) $begin mathsize 10px style 1 fifth end style$
(b) $begin mathsize 10px style 3 over 5 end style$
(c) $begin mathsize 10px style 3 over 3 end style$
(d) $begin mathsize 10px style 5 over 1 end style$

Subjective Questions
word FRACTION, find the fraction of letters, which are vowels.
From natural numbers 7 to 21, what fraction of numbers are prime numbers? Write your answer in the simplest form.
Which is greater among the following?
Swaroop completed reading 40 pages of a novel out of 200 pages. Pratyush completed $begin mathsize 10px style 3 over 5 end style$ of the same novel. Who read more pages?
Anil did cycling for seven-sixth of an hour on Sunday and two-sixth of an hour on Monday. How much more time did Anil cycled on Sunday than on Monday?
Manu emptied $begin mathsize 10px style 5 over 6 end style$ of a can containing soil in a garden and his brother emptied $begin mathsize 10px style 11 over 4 end style$ of a can. How much amount of soil is emptied altogether?
Ritu is standing near a building. Find the distance she need to cover to reach her school via market.
Pinky drank $begin mathsize 10px style 2 over 9 end style$ ml of lemon juice and Bunty drank $begin mathsize 10px style 4 over 9 end style$ ml of it. How much juice will be left in the jar?
A Mathematics exam was conducted of 100 marks in which passing marks were 35. Nandini scored $begin mathsize 10px style 3 over 10 end style$ of marks in an exam. How many more marks are needed by Nandini to pass the exam?
A sparrow drank $begin mathsize 10px style 1 over 7 end style$ of a water kept for birds. How much water is left in the plate?

Objective Type Questions

Fill in the appropriate sign (+ or –)

Solution:
Fill in the blank boxes by proper fractions and also represent the final answer in the form of diagram.

Solution:

Multiple Choice Questions
The fraction representing the number of starts inside the circle is

(a) $begin mathsize 10px style 1 over 6 end style$
(b)   $begin mathsize 10px style 6 over 17 end style$
(c)   $begin mathsize 10px style 1 over 17 end style$
(d)   $begin mathsize 10px style 5 over 6 end style$
Correct option: (b) $begin mathsize 10px style 6 over 17 end style$
Solution:
Total stars = 17

Number of stars inside the circle = 6

Hence, required fraction = $begin mathsize 10px style 6 over 17 end style$
Correct option: (b)

Solution:
20 ml is ___________ of a litre.
(a) $begin mathsize 10px style 1 over 50 end style$
(b) $begin mathsize 10px style 1 over 1000 end style$
(c) $begin mathsize 10px style 1 fifth end style$
(d) $begin mathsize 10px style 1 over 100 end style$
Correct option: (a) $begin mathsize 10px style 1 over 50 end style$
Solution:

1 litre = 1000 ml

⇒ 20 ml = $begin mathsize 10px style 20 over 1000 end style$ $begin mathsize 10px style 1 over 50 end style$
Which of the following fraction is greater than $begin mathsize 10px style 4 over 9 end style$ ?
(a) $begin mathsize 10px style 1 half end style$
(b) $begin mathsize 10px style 2 over 3 end style$
(c) $begin mathsize 10px style 1 over 6 end style$
(d) $begin mathsize 10px style 5 over 18 end style$
Correct option: (b) $begin mathsize 10px style 2 over 3 end style$
Solution:

Equivalent fractions of $begin mathsize 10px style 4 over 9 end style$ are $begin mathsize 10px style 8 over 18 end style$ , $begin mathsize 10px style 12 over 27 end style$ , $begin mathsize 10px style 16 over 36 end style$ ....
Equivalent fractions of $begin mathsize 10px style 1 half end style$ are $begin mathsize 10px style 2 over 6 end style$ , $begin mathsize 10px style 3 over 9 end style$ , $begin mathsize 10px style 4 over 12 end style$ , $begin mathsize 10px style 5 over 15 end style$ , $begin mathsize 10px style 6 over 18 end style$ , ....
Equivalent fractions of $begin mathsize 10px style 2 over 3 end style$ are $begin mathsize 10px style 4 over 6 end style$ , $begin mathsize 10px style 6 over 9 end style$ , $begin mathsize 10px style 8 over 12 end style$ , $begin mathsize 10px style 10 over 15 end style$ , $begin mathsize 10px style 12 over 18 end style$ , ....

So, we have
$begin mathsize 10px style 5 over 18 less than 6 over 18 less than 8 over 18 less than 12 over 18 therefore 2 over 3 greater than 4 over 9 end style$
The below diagram can be represend as

(a) $begin mathsize 10px style 1 half end style$

(b) $begin mathsize 10px style 3 1 third end style$

(c) $begin mathsize 10px style 3 over 4 end style$

(d) $begin mathsize 10px style 3 1 half end style$

Correct Option: (d) $begin mathsize 10px style 3 1 half end style$
Solution:

3 rectangles are completely shaded and $begin mathsize 10px style 1 half end style$ of another rectangle is shaded.
That is, totally $begin mathsize 10px style 3 1 half end style$ rectangles shaded.
Which of the following number lie between 2 and 3 on the number line?
(a) $begin mathsize 10px style 3 over 5 end style$

(b) $begin mathsize 10px style 7 over 3 end style$

(c) $begin mathsize 10px style 5 over 4 end style$

(d) $begin mathsize 10px style 2 over 2 end style$

Correct option: (b) $begin mathsize 10px style 7 over 3 end style$

Solution:
$begin mathsize 10px style 7 over 3 equals 2 1 third end style$

⇒ $begin mathsize 10px style 7 over 3 end style$ lies between 2 and 3.
Which of the following improper fraction represents the below figure?

(a) $begin mathsize 10px style 16 over 6 end style$

(b) $begin mathsize 10px style 16 over 18 end style$

(c) $begin mathsize 10px style 4 over 6 end style$

(d) $begin mathsize 10px style 2 over 6 end style$

Correct option: (a) $begin mathsize 10px style 16 over 6 end style$

Solution:

A hexagon is divided into 6 equal parts.

There are 3 hexagons and total 16 parts are shaded.

So, given diagram is represented by improper fraction $begin mathsize 10px style 16 over 6 end style$ .
Which of the following is equivalent fraction for $begin mathsize 10px style 5 over 5 end style$ ?
(a) $begin mathsize 10px style 1 fifth end style$

(b) $begin mathsize 10px style 3 over 5 end style$

(c) $begin mathsize 10px style 3 over 3 end style$

(d) $begin mathsize 10px style 5 over 1 end style$

Correct option: (c) $begin mathsize 10px style 3 over 3 end style$

Solution:

$begin mathsize 10px style 5 over 5 equals 1 equals 3 over 3 end style$

Subjective Questions
word FRACTION, find the fraction of letters, which are vowels.

Solution:
Total number of letters in a word FRACTION = 8

Number of vowels in a word FRACTION = 3

Required fraction = $begin mathsize 10px style 3 over 8 end style$
From natural numbers 7 to 21, what fraction of numbers are prime numbers? Write your answer in the simplest form.
Solution:
Total natural numbers from 7 to 21 = 15
Prime numbers from 7 to 21 are 7, 11, 13, 17, 19.
⇒ Required fraction = $begin mathsize 10px style 5 over 15 equals 1 third end style$
Which is greater among the following?

Solution:
$begin mathsize 10px style 3 1 third plus 2 1 half equals 10 over 3 plus 5 over 2 equals fraction numerator 20 plus 15 over denominator 6 end fraction equals 35 over 6 5 1 half minus 2 1 fourth equals 11 over 2 minus 9 over 4 equals fraction numerator 22 minus 9 over denominator 4 end fraction equals 13 over 4 LCM space of space 4 space and space 6 space is space 12. space Then comma 35 over 6 equals fraction numerator 35 cross times 2 over denominator 6 cross times 2 end fraction equals 70 over 12 13 over 4 equals fraction numerator 13 cross times 3 over denominator 4 cross times 3 end fraction equals 39 over 12 Here comma space 70 over 12 greater than 39 over 12 rightwards double arrow Sum space of space 3 1 third space and space 2 1 half greater than Difference space of space 5 1 half space and space 2 1 fourth. end style$
Swaroop completed reading 40 pages of a novel out of 200 pages. Pratyush completed $begin mathsize 10px style 3 over 5 end style$ of the same novel. Who read more pages?
Solution:
In fraction form,
number of pages read by Swaroop = $begin mathsize 10px style 40 over 200 equals 1 fifth end style$
number of pages read by Pratyush = $begin mathsize 10px style 3 over 5 end style$
Here, $begin mathsize 10px style 3 over 5 greater than 1 fifth end style$ .
Hence, Pratyush read more pages than Swaroop.
Anil did cycling for seven-sixth of an hour on Sunday and two-sixth of an hour on Monday. How much more time did Anil cycled on Sunday than on Monday?
Solution:
Duration of cycling on Sunday = $begin mathsize 10px style 7 over 6 end style$ of an hour
Duration of cycling on Monday = $begin mathsize 10px style 2 over 6 end style$ of an hour
Difference $begin mathsize 10px style 7 over 6 minus 2 over 6 equals fraction numerator 7 minus 2 over denominator 6 end fraction equals 5 over 6 end style$
Therefore, Anil cycled for $begin mathsize 10px style 5 over 6 end style$ of an hour more on Sunday than on Monday.
Manu emptied $begin mathsize 10px style 5 over 6 end style$ of a can containing soil in a garden and his brother emptied $begin mathsize 10px style 11 over 4 end style$ of a can. How much amount of soil is emptied altogether?
Solution:
Amount watered by Shweta = $begin mathsize 10px style 5 over 6 end style$
Amount watered by her brother = $begin mathsize 10px style 11 over 4 end style$
Total amount of water = $begin mathsize 10px style 5 over 6 plus 11 over 4 equals fraction numerator 10 plus 22 over denominator 12 end fraction equals 43 over 12 equals 3 7 over 12 end style$ can of water.
Ritu is standing near a building. Find the distance she need to cover to reach her school via market.

Solution:
Distance from building to market = $begin mathsize 10px style 8 3 over 8 km end style$
Distance from market to school = $begin mathsize 10px style 41 over 6 km end style$
Therefore, distance covered by Ritu from building to school via market
$begin mathsize 10px style equals space 8 3 over 8 plus 41 over 6 equals space 67 over 8 plus 41 over 6 equals space fraction numerator 201 plus 164 over denominator 24 end fraction equals space 15 5 over 24 end style$
Pinky drank $begin mathsize 10px style 2 over 9 end style$ ml of lemon juice and Bunty drank $begin mathsize 10px style 4 over 9 end style$ ml of it. How much juice will be left in the jar?

Solution:
Juice drank by Pinky and Bunty = $begin mathsize 10px style 2 over 9 equals plus 4 over 9 equals 6 over 9 equals 2 over 3 end style$
Quantity of juice left in the jar = $begin mathsize 10px style 1 minus 2 over 3 equals fraction numerator 3 minus 2 over denominator 3 end fraction equals 1 third end style$
A Mathematics exam was conducted of 100 marks in which passing marks were 35. Nandini scored $begin mathsize 10px style 3 over 10 end style$ of marks in an exam. How many more marks are needed by Nandini to pass the exam?
Solution:
Passing marks = $begin mathsize 10px style 25 over 100 equals 7 over 20 end style$
Marks scored by Nandini = $begin mathsize 10px style 3 over 10 end style$
Therefore, marks needed by Nandini to pass the exam
$begin mathsize 10px style equals space 7 over 20 minus 3 over 10 equals space fraction numerator 7 minus 6 over denominator 20 end fraction equals space 1 over 20 end style$
A sparrow drank $begin mathsize 10px style 1 over 7 end style$ of a water kept for birds. How much water is left in the plate?

Solution:
Water drank by sparrow = $begin mathsize 10px style 1 over 7 end style$
Water left in the plate = $begin mathsize 10px style 1 minus 1 over 7 equals fraction numerator 7 minus 1 over denominator 7 end fraction equals 6 over 7 end style$

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