NCERT Solutions for Class 6 Maths Chapter 7 (Ex 7.1)
Exercise 7.1
1. Write the fraction representing the shaded portion:
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts are 2. The total number of parts are 4.
Therefore, the fraction representing the shaded portion is $\dfrac{2}{4}$.
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts are 8. The total number of parts are 9.
Therefore, the fraction representing the shaded portion is $\dfrac{8}{9}$.
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 4. The total number of parts is 8.
Therefore, the fraction representing the shaded portion is $\dfrac{4}{8}$.
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 1. The total number of parts are 4.
Therefore, the fraction representing the shaded portion is $\dfrac{1}{4}$.
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 3.
The total number of parts are 7.
Therefore, the fraction representing the shaded portion is $\dfrac{3}{7}$.
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 3. The total number of parts in the given figure are 12.
Therefore, the fraction representing the shaded portion is $\dfrac{3}{{12}}$.
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 10.
The total number of parts in the given figure are 10.
Therefore, the fraction representing the shaded portion is $\dfrac{{10}}{{10}}$.
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 4. The total number of parts is 9.
Therefore, the fraction representing the shaded portion is $\dfrac{4}{9}$.
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 4. The total number of parts are 8.
Therefore, the fraction representing the shaded portion is $\dfrac{4}{8}$.
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
Our quantity in consideration is the number of shaded parts in the given figure.
The number of shaded parts is 1.
The total number of parts are 2.
Therefore, the fraction representing the shaded portion is $\dfrac{1}{2}$.
2. Colour the part according to the given fraction:
$\dfrac{1}{6}$
Ans: A fraction represents the part of a whole entity.All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to shade the parts according to the given fractions. Hence, our quantity in consideration is the number of shaded parts in the given figure.
The numerator of our fraction is 1. Hence, we need to shade 1 part out of all the given parts in the figure.
The denominator of our fraction is 6. Hence, the total number of parts are 6 as shown in the figure.
Therefore, the required shaded portions in the given diagram will be as follows,
$\dfrac{1}{4}$
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to shade the parts according to the given fractions. Hence, our quantity in consideration is the number of shaded parts in the given figure.
The numerator of our fraction is 1. Hence, we need to shade 1 part out of all the given parts in the figure.
The denominator of our fraction is 4. Hence, the total number of parts are 4 as shown in the figure.
Therefore, the required shaded portions in the given diagram will be as follows,
$\dfrac{1}{3}$
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to shade the parts according to the given fractions. Hence, our quantity in consideration is the number of shaded parts in the given figure.
The numerator of our fraction is 1. Hence, we need to shade 1 part out of all the given parts in the figure.
The denominator of our fraction is 3. Hence, the total number of parts are 3 as shown in the figure.
Therefore, the required shaded portions in the given diagram will be as follows,
$\dfrac{3}{4}$
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to shade the parts according to the given fractions. Hence, our quantity in consideration is the number of shaded parts in the given figure.
The numerator of our fraction is 3. Hence, we need to shade 3 parts out of all the given parts in the figure.
The denominator of our fraction is 4. Hence, the total number of parts are 4 as shown in the figure.
Therefore, the required shaded portions in the given diagram will be as follows,
$\dfrac{4}{9}$
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to shade the parts according to the given fractions. Hence, our quantity in consideration is the number of shaded parts in the given figure.
The numerator of our fraction is 4. Hence, we need to shade 4 parts out of all the given parts in the figure.
The denominator of our fraction is 9. Hence, the total number of parts are 9 as shown in the figure.
Therefore, the required shaded portions in the given diagram will be as follows,
3. Identify the error, if any?
This is $\dfrac{1}{2}$ This is $\dfrac{1}{4}$ This is $\dfrac{3}{4}$
Ans:A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
In the first figure, we can see that the triangle is divided into two parts. However, the two parts are not equal. The shaded part of the triangle is clearly bigger than the non-shaded part. Therefore, the shaded portion cannot be represented with the given fraction $\dfrac{1}{2}$ as both the portions are unequal.
Similarly, in the second figure, we can see that the rectangle is divided into four parts. However, the four parts are not equal. The shaded part of the rectangle is clearly bigger than the non-shaded parts. Therefore, the shaded portion cannot be represented with the given fraction $\dfrac{1}{4}$ as all the portions are unequal.
Also, in the third figure, we can see that the circle is divided into four parts. However, the four parts are not equal. The shaded parts of the circleare clearly bigger than the non-shaded part. Therefore, the shaded portion cannot be represented with the given fraction $\dfrac{3}{4}$ as all the portions are unequal.
Thus, the error in all the figures is that they are not divided into equal parts so the given fractions cannot represent the shaded portions.
4. What fraction of a day is 8 hours?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to find what fraction of a day is 8 hours. So, our quantity in consideration is the number of hours.
The numerator of our fraction will be 8 hours since we have to calculate the fraction for 8 hours.
We also know that 1 day has 24 hours. This will be the denominator of our fraction as it is the total number of hours in a day.
So, the required fraction will be given as,
$\dfrac{8}{{24}} = \dfrac{1}{3}$
Therefore, 8 hours is $\dfrac{1}{3}$portion of a day.
5. What fraction of an hour is 40 minutes?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
So, our quantity in consideration is the number of minutes.
The numerator of our fraction will be 40 minutes since we have to calculate the fraction for 40 minutes.
We also know that 1 hour has 60 minutes. This will be the denominator of our fraction as it is the total number of minutes in an hour.
So, the required fraction will be given as,
$\dfrac{{40}}{{60}} = \dfrac{2}{3}$
Therefore, 40 minutes is $\dfrac{2}{3}$portion of an hour.
6. Arya, Abhimanyu and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetables and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
How can Arya divide his sandwiches so that each person has an equal share?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given that Arya has two different types of sandwiches which he is sharing equally with Abhimanyu and Vivek.
We are required to find how Arya can divide his sandwiches equally. So, our quantity in consideration is the sandwiches.
Arya will have to divide each of his sandwiches into three equal parts first. He will then have to give each part to both of his friends. This way Arya will be able to divide the sandwiches equally.
What part of a sandwich will each boy receive?
Ans:A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given that Arya has two different types of sandwiches which he is sharing equally with Abhimanyu and Vivek.
We are required to know what part of a sandwich each boy will get. So, our quantity in consideration is the sandwiches.
Arya will have to divide each of his sandwiches into three equal parts first. He will then have to give each part to both of his friends. This way Arya will be able to divide the sandwiches equally.
The numerator of our fraction will be 1 since each boy will get 1 part from each sandwich.
The total number of parts in which each sandwich is divided is 3.
So, the required fraction will be given as,
$\dfrac{1}{3}$
Therefore, each boy will receive $\dfrac{1}{3}$ part of a sandwich.
7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given that Kanchan has to dye 30 dresses and she has finished 20 dresses.
We are required to find what fraction of dresses Kanchan has finished dyeing. So, our quantity in consideration is the dresses dyed.
The numerator of our fraction will be 20 since Kanchan has finished dyeing 20 dresses.
The total number of dresses that Kanchan has to dye are 30.
So, the required fraction will be given as,
$\dfrac{{20}}{{30}} = \dfrac{2}{3}$
Therefore, Kanchan has finished dyeing $\dfrac{2}{3}$ portion dresses.
8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given natural numbers from 2 to 12. Therefore, the numbers given to us are as follows,
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
We are required to find what fraction of the above given numbers are prime. Hence, the quantity in consideration is the prime numbers.
Prime numbers are those numbers which are only divisible by 1 and the number itself.
The prime numbers between 2 to 12 are as follows,
2, 3, 5, 7, 11
The numerator of our fraction will be 5 since we have 5 prime numbers between 2 to 12.
The total numbers given to us are 11.
So, the required fraction will be given as,
$\dfrac{5}{{11}}$
Therefore, the fraction of prime numbers between 2 to 12 is$\dfrac{5}{{11}}$.
9. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given natural numbers from 102 to 113. Therefore, the numbers given to us are as follows,
102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113
We are required to find what fraction of the above given numbers are prime. Hence, the quantity in consideration is the prime numbers.
Prime numbers are those numbers which are only divisible by 1 and the number itself.
The prime numbers between 102 to 113 are as follows,
103, 107, 109, 113
The numerator of our fraction will be 4 since we have 4 prime numbers between 102 to 113.
The total numbers given to us are 12.
So, the required fraction will be given as,
$\dfrac{4}{{12}} = \dfrac{1}{3}$
Therefore, the fraction of prime numbers between 102 to 113 is $\dfrac{1}{3}$.
10. What fraction of these circles have ‘X’s in them?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are required to write the fractions for the circles which have ‘X’s in them. Hence, our quantity in consideration is the number of circles with X.
The number of circles with the ‘X’s in the given figure are 4. This is the numerator of the fraction.
The total number of circles are 8.
Therefore, the required fraction representing the circles with ‘X’s is $\dfrac{4}{8}$.
11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal.
The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.
We are given that Kristin bought 3 CDs and she received 5 CDs as gifts.
We are required to find what fraction of CDs she bought and what fraction of CDs she received as gifts.
Let us first find out the fraction of the CDs Kristin bought. Here the CDs bought are into our consideration.
The numerator of our fraction will be 3 since Kristin bought 3 CDs.
The total number of CDs that Kristin has will be the sum of CDs she bought and the CDs she received. Hence, the total number of CDs will be,
$3 + 5 = 8$
The denominator of our fraction is 8 since this is the total number of CDs.
So, the required fraction will be given as,
$\dfrac{3}{8}$
Let us now find out the fraction of the CDs received by Kristin as gift. Here the CDs received as gifts are into our consideration.
The numerator of our fraction will be 5 since Kristin received 5 CDs as gifts.
The denominator of our fraction is 8 since this is the total number of CDs.
So, the required fraction will be given as,
$\dfrac{5}{8}$
Therefore, the fraction of CDs that Kristin bought is $\dfrac{3}{8}$ and the fraction of CDs received by Kristin as gifts is $\dfrac{5}{8}$.
NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.1
Opting for the NCERT solutions for Ex 7.1 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 7.1 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 7 Exercise 7.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
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