Fractions Class 6 Extra Questions Maths Chapter 7

Class 6 Maths Chapter 7 Extra Questions Fractions

Class 6 Maths Fractions Extra Questions

NCERT Class 6 Maths Chapter 7 Fractions Extra Questions and Answers

Very Short Answer Type Questions

Question 1.
Write a fraction as indicated
Denominator: 4-(-3);
Numerator : -5+7
Solution :
Fraction =\(\frac{\text { Numerator }}{\text { Denominator }}\) =\(\frac{-5+7}{4-(-3)}\) = \(\frac{2}{4+3}\) = \(\frac{2}{7}\)

Question 2.
Reduce \(\frac{16}{28}\) to simplest form.
Solution :
\(\frac{16 \div 2}{28 \div 2}\) = \(\frac{8 \div 2}{14 \div 2}\) = \(\frac{4}{7}\)

Question 3.
Convert 11 \(\frac{9}{17}\) into improper fraction.
Solution :
\(\frac{(11 \times 17)+9}{17}\)=\(\frac{187+9}{17}\)=\(\frac{196}{17}\)

Question 4.
Add \(\frac{7}{10}\) + \(\frac{2}{10}\)
Solution :
Here, denominators are same, so addition will be done directly by adding numerators.
\(\frac{7}{10}\) + \(\frac{2}{10}\) = \(\frac{7+2}{10}\) = \(\frac{9}{10}\)

Short Answer Type Questions

Question 1.
Find \(\frac{7}{9}\) of 108 days.
Solution :
\(\frac{7}{9}\) × 108 = 84 days

Question 2.
Subtract \(\frac{7}{8}\) from \(\frac{7}{8}\).
Solution :
\(\frac{7}{8}\) – \(\frac{5}{6}\)
LCM of 8 and 6 is 24
\(\frac{21-20}{24}\) = \(\frac{1}{24}\)

Question 3.
Add: 2 \(\frac{5}{6}\) + 3 \(\frac{7}{9}\).
Solution :
2 \(\frac{5}{6}\) +3 \(\frac{7}{9}\) = \(\frac{17}{6}\) + \(\frac{34}{9}\)
LCM of 6 and 9 is 18
\(\frac{51+68}{18}\) = \(\frac{119}{18}\) = 6 \(\frac{11}{18}\)

Long Answer Type Questions

Question 1.
Simplify: 5 \(\frac{1}{6}\) + 2 \(\frac{1}{3}\) – 5 \(\frac{1}{12}\) A]
Solution :
5 \(\frac{1}{6}\) + 2 \(\frac{1}{3}\) – 5 \(\frac{11}{12}\) = \(\frac{31}{6}\) + \(\frac{7}{3}\) – \(\frac{71}{12}\)
LCM of 6, 3, 12 is 12.
= \(\frac{62+28-71}{12}\) = \(\frac{90-71}{12}\)
= \(\frac{19}{12}\) = 1 \(\frac{7}{12}\)

Question 2.
Raj walked \(\frac{8}{17}\) km and Rohan walked \(\frac{10}{13}\) km who walked more and by how much?
Solution :
Raj walked \(\frac{8}{17}\) of a km
Rohan walked \(\frac{10}{15}\) of a km
Comparing \(\frac{8}{17}\), \(\frac{10}{13}\)
LCM of 17 and 13
\(\frac{104<170}{221}\)

Rohan walked more than Raj.
Difference =\(\frac{170-104}{221}\)=\(\frac{66}{221}\)
Rohan walked \(\frac{66}{221}\) km more than Raj.

Passage Based Questions

Passage 1: Four children order their own small pizza of the same size. Ria eats \(\frac{3}{5}\) of pizza, Jia eats \(\frac{9}{20}\) of pizza, Sia eats \(\frac{7}{15}\) of pizza and Pia eats \(\frac{3}{10}\) of pizza.

Fractions Class 6 Extra Questions Maths Chapter 7 1

Question 1.
Who eats the most amount of pizza?
(a) Sia
(b) Pia
(c) Ria
(d) Jia
Answer:
(c) Ria
Explanation: \(\frac{3}{5}\), \(\frac{9}{20}\), \(\frac{7}{15}\), \(\frac{3}{10}\)
LCM of 5,20,15,10 = 60
Fractions are: \(\frac{36}{60}\), \(\frac{27}{60}\), \(\frac{28}{60}\), \(\frac{18}{60}\)
The largest fraction is \(\frac{36}{60}\) equivalent to \(\frac{3}{5}\).
Hence Ria eats the most amount of pizza.

Question 2.
Arrange the names of the children in order from lowest to greatest quantity of pizza eaten.
(a) Ria, Sia, Jia, Pia
(b) Pia, Jia, Sia, Ria
(c) Ria, Jia, Sia, Pia
(d) Jia, Sia, Pia, Ria
Answer:
(b) Pia, Jia, Sia, Ria
Explanation: \(\frac{3}{5}\) , \(\frac{9}{20}\), \(\frac{7}{15}\), \(\frac{3}{10}\)
LCM of 5,20,15,10 is 60.
\(\frac{36}{60}\), \(\frac{27}{60}\), \(\frac{28}{60}\), \(\frac{18}{60}\)
Ascending order \(\frac{18}{60}\), \(\frac{27}{60}\), \(\frac{28}{60}\), \(\frac{36}{60}\)
Arrangement of children is Pia, Jia, Sia, Ria.

Question 3.
Which fraction is not equivalent to \(\frac{9}{20}\) ?
(a) \(\frac{180}{400}\)
(b) \(\frac{270}{600}\)
(c) \(\frac{81}{400}\)
(d) \(\frac{360}{800}\)
Answer:
(c) \(\frac{81}{400}\)
Explanation:
\(\frac{180}{400}\) = \(\frac{180 \div 20}{400 \div 20}\) = \(\frac{9}{20}\)
\(\frac{270}{600}\) = \(\frac{270 \div 30}{600 \div 30}\) = \(\frac{9}{20}\)
\(\frac{81}{400}\) can’t be reduced as 81 and 400 have no common factor.
\(\frac{360}{800}\) = \(\frac{360 \div 40}{800 \div 40}\) = \(\frac{9}{20}\)
All are equivalent except \(\frac{81}{400}\).

Question 4.
Find the total amount of pizza eaten by all four children.
Solution :
\(\frac{3}{5}\) + \(\frac{9}{20}\) + \(\frac{7}{15}\) + \(\frac{3}{10}\)
LCM is 60.
So, \(\frac{36+27+28+18}{60}\) = \(\frac{109}{60}\)

Question 5.
Convert \(\frac{109}{60}\) in mixed fraction.
Solution :
Fractions Class 6 Extra Questions Maths Chapter 7 2

Passage 2: Cross country is a running event in which runners completed a pre-decided distance. It includes different activities in which runners cover different environments. A cross country running event of 11 km is as follows.

Activity Distance (in km)
Running on paved road 3
Running on unpaved road 2
Hill climbing 2
Mud run 1
Running in woods 2
Crossing water bodies 1

Question 1.
What fraction of the total distance is the mud run?
(a) \(\frac{11}{1}\)
(b) \(\frac{1}{10}\)
(c) \(\frac{1}{11}\)
(d) \(\frac{1}{12}\)
Answer:
(c) \(\frac{1}{11}\)
Explanation: \(\frac{1}{11}\) (total distance = 3+2+2+1+2+1 )

Question 2.
What fraction of the total distance is the distance covered on paved and unpaved roads?
(a) \(\frac{3}{2}\)
(b) \(\frac{5}{5}\)
(c) \(\frac{5}{6}\)
(d) \(\frac{5}{11}\)
Answer:
(d) \(\frac{5}{11}\)
Explanation: \(\frac{5}{11}\) (paved and unpaved road = 3 + 2 = 5, total distance = 11)

Question 3.
Payl says, ‘By running through woods and climbing hills, half of the total distance in cross country can be covered.’ Is Paul correct? How did you reach the sonclusion?
Solution :
No, because running on hills and woods covers (2 + 2 = 4) \(\frac{4}{11}\) of the distance which is not equal to half of the total distance. (Half of total distance = \(\frac{11}{2}\))

Passage 3: Parul and two of her friends share pizza equally among themselves.

Fractions Class 6 Extra Questions Maths Chapter 7 3

Question 1.
Parul says, ‘Here are three equal halves of the pizza.’ Is Parnl’s statement correct? Give reasons.
Solution :
No, because the pizza is divided into three equal parts, which is not half of the pizza.

Question 2.
Which fraction represents one part of the whole pizza?
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{2}{3}\)
(d) \(\frac{3}{3}\)
Answer:
(b) \(\frac{1}{3}\)
Explanation:
Fractions Class 6 Extra Questions Maths Chapter 7 4
Later, three more friends join Parul.
Parul divides the pizza again to have 6 parts.

Question 3.
Does everyone get an equal portion? Give reasons.
Solution :
Yes, because the pizza is divided into six equal parts.

Question 4.
Suggest a way to divide the pizza into six equal parts.
Fractions Class 6 Extra Questions Maths Chapter 7 5
Answer:
Fractions Class 6 Extra Questions Maths Chapter 7 6

NCERT Exemplar Questions

Multiple Choice Questions

In the following questions, out of the four options, only one is correct. Write the correct answer.

Question 1.
The fraction which is not equal to \(\frac{4}{5}\) is
(a) \(\frac{40}{50}\)
(b) \(\frac{12}{15}\)
(c) \(\frac{16}{20}\)
(d) \(\frac{9}{15}\)
Answer:
Option (d) is correct.

Question 2.
The two consecutive integers between which the fraction \(\frac{5}{7}\) lies are
(a) 5 and 6
(b) 0 and 1
(c) 5 and 7
(d) 6 and 7
Answer:
Option (b) is correct.

Question 3.
When \(\frac{1}{4}\) is written with denominator as 12 , its numerator is
(a) 3
(b) 8
(c) 24
(d) 12
Answer:
Option (a) is correct.

Question 4.
Which of the following is not in the lowest form ?
(a) \(\frac{7}{5}\)
(b) \(\frac{15}{20}\)
(c) \(\frac{13}{33}\)
(d) \(\frac{27}{28}\)
Answer:
Option (b) is correct.

Question 5.
If \(\frac{5}{8}\) = \(\frac{20}{p}\), then value of p is
(a) 23
(b) 2
(c) 32
(d) 16
Answer:
Option (c) is correct.

Fill in the Blanks

Question 1.
A number representing a part of a _____ is called a fraction.
Answer:
whole

Question 2.
A fraction with denominator greater than the numerator is called a _____ fraction.
Answer:
proper

Question 3.
Fractions with the same denominator are called ______ fractions.
Answer:
like

Question 4.
13 \(\frac{5}{18}\) is a _______ fraction.
Answer:
mixed

Question 5.
\(\frac{18}{5}\) is an _______ fraction.
Answer:
improper

True/False

Question 1.
Fractions with same numerator are called like fractions.
Answer:
True

Question 2.
Fraction \(\frac{18}{39}\) is in its lowest form.
Answer:
False

Question 3.
Fractions \(\frac{15}{39}\) and \(\frac{45}{117}\) are equivalent fractions.
Answer:
True

Question 4.
The fraction represented by the shaded portion in the adjoining figure is \(\frac{3}{8}\).
Fractions Class 6 Extra Questions Maths Chapter 7 7
Answer:
True

Question 5.
The fraction represented by the unshaded portion in the adjoining figure is \(\frac{5}{9}\).
Fractions Class 6 Extra Questions Maths Chapter 7 8
Answer:
False

Very Short Answer Type Questions

In each of the questions, fill in the blanks using ‘>’, ‘>’ or ‘=’ .

Question 1.
\(\frac{11}{16}\) … \(\frac{14}{15}\)
Answer:
<

Question 2.
\(\frac{8}{15}\) … \(\frac{95}{14}\)
Answer:
<

Question 3.
\(\frac{12}{75}\) … \(\frac{32}{200}\)
Answer:
=

Question 4.
Write the fraction represented by the shaded portion of the adjoining figure :

Answer:
\(\frac{7}{8}\)

Question 5.
Write the fraction represented by the unshaded portion of the adjoining figure :
Fractions Class 6 Extra Questions Maths Chapter 7 10
Answer:
\(\frac{4}{15}\)

Question 6.
Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?
Solution :
Given, total no, of fruit cake = 1
Here, Ali divided fruit cake equally among six persons.
∴ The part of cake given to one person = \(\frac{1}{6}\)

Question 7.
Express 6 \(\frac{2}{3}\) as an improper fraction.
Solution :
\(\frac{(6 \times 3)+2}{3}\) = \(\frac{20}{3}\),

Question 8.
Arrange the fractions \(\frac{2}{3}\), \(\frac{2}{3}\), \(\frac{1}{2}\) and \(\frac{5}{6}\) in ascending order.
Solution :
Given fractions are \(\frac{2}{3}\), \(\frac{3}{4}\), \(\frac{1}{2}\) and \(\frac{5}{6}\).
As we have to arrange fractions in ascending order, so, we take LCM of denominator of all fractions.

Fractions Class 6 Extra Questions Maths Chapter 7 11

Question 9.
Arrange the fractions \(\frac{6}{7}\), \(\frac{7}{8}\), \(\frac{4}{5}\) and \(\frac{3}{4}\) in descending order.
Solution :
Given fractions are \(\frac{6}{7}\), \(\frac{7}{8}\), \(\frac{4}{5}\) and \(\frac{3}{4}\)
As, we have to arrange the given fractions in descending order, so we take LCM of denominator of all fractions.

Fractions Class 6 Extra Questions Maths Chapter 7 12

Short Answer Type Questions

Question 1.
Katrina rode her bicycle 6 \(\frac{1}{2}\) km in the morning and 8 \(\frac{3}{4}\) km in the evening. Find the distance travelled by her altogether on that day.
Solution :
Fractions Class 6 Extra Questions Maths Chapter 7 13

Question 2.
A rectangle is divided into certain number of equal parts. If 16 of the parts 50 formed represent the fraction \(\frac{1}{4}\), find the number of parts in which the rectangle has been divided.
Solution :
We know that, a part represents by fractions
∴ Fraction of their part = \(\frac{\text { No. of parts }}{\text { Total no. of parts }}\)
\(\frac{1}{4}\) = \(\frac{16}{\text { Total no. of parts }}\)
Total no. of parts = 4 × 16 = 64
(by cross product)
Hence, the total no. of parts is 64.

Question 3.
On an average \(\frac{1}{10}\) of the food eaten is turned into organism’s own body and is available for the next level of consumer in a food chain. What fraction of the food eaten is not avallable for the next level ?
Solution :
Let the complete eaten food be 1.
Part of eaten food which is available for next level
= \(\frac{1}{10}\)
Fractions Class 6 Extra Questions Maths Chapter 7 15

Question 4.
Mr. Rajan got a job at the age of 24 years and he got retired from the job at the age of 60 years. What fraction of his age till retirement was he in the job ?
Solution :
Given, Rajan age on the joining = 24 years
and retirement age = 60 years
The number of years, he did the job
= Retirement age – Joining age
= 60 – 24 = 36 years
∴ The fraction of his age till retirement, when he was in the job
= \(\frac{\text { Total years he did the job }}{\text { Retirement age }}\) = \(\frac{36}{60}\)
Now, HCF of 36 and 60 = 12
∴ \(\frac{36}{60}\) = \(\frac{36 \div 12}{60 \div 12}\) = \(\frac{3}{5}\)
Hence, the required fraction is \(\frac{3}{5}\).

Question 5.
The food we eat remains in the stomach for a maximum of 4 hours. For what fraction of a day, does it remain there?
Solution :
We know that, 1 day = 24 hours
Given, the food we eat remains in the stomach for a maximum hours = 4
∴ Fraction of a day, does food remain there
= \(\frac{\text { Total no. of hour food remains in the stomach }}{\text { Total no. of hours in } 1 \text { day }}\)
= \(\frac{4}{24}\) = \(\frac{1}{6}\)

Long Answer Type Questions

Question 1.
It was estimated that because of people switching to Metro trains about 33000 tonnes of CNG, 3300 tonnes of the diesel and 21000 tonnes of petrol was saved by the end of year 2007. Find the fraction of ;
(i) the quantity of diesel saved to the quantity of petrol saved.
(ii) the quantity of diesel saved to the quantity of CNG saved.
Solution :
Given, Quantity of CNG saved = 33000 tonnes
Quantity of diesel saved = 3300 tonnes
and Quantity of petrol saved = 21000 tonnes

Fractions Class 6 Extra Questions Maths Chapter 7 16

Question 2.
A cup is \(\frac{1}{3}\) full of milk. What part of the cup is still to be filled by milk to make it full ?
Solution :
Part of the cup is still to be filled by milk to make it full
Fractions Class 6 Extra Questions Maths Chapter 7 17

Question 3.
Sunil purchased 12 \(\frac{1}{2}\) litre of juice on Monday and 14 \(\frac{3}{4}\) litre of juice on Tuesday. How many litre of juice did he purchase together in two days ?
Solution :
Fractions Class 6 Extra Questions Maths Chapter 7 18

Question 4.
Nazima gave 2 \(\frac{3}{4}\) litre out of the 5 \(\frac{1}{2}\) litges of juice she purchased to her friends. How many litre of juice is left with her ?
Solution :
Fractions Class 6 Extra Questions Maths Chapter 7 19

Question 5.
Roma gave a wooden board of length 150 \(\frac{1}{4}\) cm to a carpenter for making a shelf. The carpenter sawed off a piece of 40 \(\frac{1}{5}\) cm from it. What is the length of the remaining piece?
Solution :
Fractions Class 6 Extra Questions Maths Chapter 7 20

Class 6 Maths Extra Questions

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