NCERT Solutions for Class 7 Maths Chapter 2: Fractions and Decimals - Exercise 2.4

Exercise - 2.4

1. Find:

(i) $\text{12 }\!\!\div\!\!\text{ }\dfrac{\text{3}}{\text{4}}$ 

Ans: Calculating the value,

$12\div \dfrac{3}{4}=12\times \dfrac{4}{3}=16$

(ii) $\text{14 }\!\!\div\!\!\text{ }\dfrac{\text{5}}{\text{6}}$ 

Ans: Calculating the value,

$14\div \dfrac{5}{6}=14\times \dfrac{6}{5}=\dfrac{84}{5}=16\dfrac{4}{5}$

(iii) $\text{8 }\!\!\div\!\!\text{ }\dfrac{\text{7}}{\text{3}}$ 

Ans: Calculating the value,

$8\div \dfrac{7}{3}=8\times \dfrac{3}{7}=\dfrac{24}{7}=3\dfrac{3}{7}$

(iv) $\text{4 }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$4\div \dfrac{8}{3}=4\times \dfrac{3}{8}=\dfrac{3}{2}=1\dfrac{1}{2}$           

(v) $\text{3 }\!\!\div\!\!\text{ 2}\dfrac{\text{1}}{\text{3}}$ 

Ans: Calculating the value,

$3\div 2\dfrac{1}{3}=3\div \dfrac{7}{3}=3\times \dfrac{3}{7}=\dfrac{9}{7}=1\dfrac{2}{7}$           

(vi) \[\text{5 }\!\!\div\!\!\text{ 3}\dfrac{\text{4}}{\text{7}}\] 

Ans: Calculating the value,

$5\div 3\dfrac{4}{7}=5\div \dfrac{25}{7}=5\times \dfrac{7}{25}=\dfrac{7}{5}=1\dfrac{2}{5}$

2. Find the reciprocal of each of the following fractions. Classify the reciprocals as a proper fraction, improper fractions and whole numbers.

(i) $\dfrac{\text{3}}{\text{7}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{3}}{\text{7}}\text{=}\dfrac{\text{7}}{\text{3}}\to \text{Improper}\,\text{fraction}$  

(ii) $\dfrac{\text{5}}{\text{8}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of$\dfrac{\text{5}}{\text{8}}\text{=}\dfrac{\text{8}}{\text{5}}\to \text{Improper}\,\text{fraction}$

(iii) $\dfrac{\text{9}}{\text{7}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{9}}{\text{7}}\text{=}\dfrac{\text{7}}{\text{9}}\to \text{Proper}\,\text{fraction}$

(iv) $\dfrac{\text{6}}{\text{5}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{6}}{\text{5}}\text{=}\dfrac{\text{5}}{\text{6}}\to \text{Proper}\,\text{fraction}$

(v) $\dfrac{\text{12}}{\text{7}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{12}}{\text{7}}\text{=}\dfrac{\text{7}}{\text{12}}\to \text{Proper}\,\text{fraction}$  

(vi) $\dfrac{\text{1}}{\text{8}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{1}}{\text{8}}\text{=8}\to \text{Whole number}$

(vii) $\dfrac{\text{1}}{\text{11}}$ 

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\dfrac{\text{1}}{\text{11}}\text{=11}\to \text{Whole number}$

3. Find:

(i) $\dfrac{\text{7}}{\text{3}}\text{ }\!\!\div\!\!\text{ 2}$ 

Ans: Calculating the value,

$\dfrac{7}{3}\div 2=\dfrac{7}{3}\times \dfrac{1}{2}=\dfrac{7\times 1}{3\times 2}=\dfrac{7}{6}=1\dfrac{1}{6}$

(ii) $\dfrac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ 5}$

Ans: Calculating the value,

$\dfrac{4}{9}\div 5=\dfrac{4}{9}\times \dfrac{1}{5}=\dfrac{4\times 1}{9\times 5}=\dfrac{4}{45}$ 

(iii) $\dfrac{\text{6}}{\text{13}}\text{ }\!\!\div\!\!\text{ 7}$ 

Ans: Calculating the value,

$\dfrac{6}{13}\div 7=\dfrac{6}{13}\times \dfrac{1}{7}=\dfrac{6\times 1}{13\times 7}=\dfrac{6}{91}$ 

(iv) $\text{4}\dfrac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ 3}$

Ans:  Calculating the value,

$4\dfrac{1}{3}\div 3=\dfrac{13}{3}\div 3=\dfrac{13}{3}\times \dfrac{1}{3}=\dfrac{13}{9}=1\dfrac{4}{9}$

(v) $\text{3}\dfrac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ 4}$ 

Ans: Calculating the value,

$3\dfrac{1}{2}\div 4=\dfrac{7}{2}\div 4=\dfrac{7}{2}\times \dfrac{1}{4}=\dfrac{7}{8}$

(vi) $\text{4}\dfrac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ 7}$ 

Ans: Calculating the value,

$4\dfrac{3}{7}\div 7=\dfrac{31}{7}\div 7=\dfrac{31}{7}\times \dfrac{1}{7}=\dfrac{31}{49}$

4. Find:

(i) $\dfrac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{1}}{\text{2}}$

Ans:  Calculating the value,

$\dfrac{2}{5}\div \dfrac{1}{2}=\dfrac{2}{5}\times \dfrac{2}{1}=\dfrac{2\times 2}{5\times 1}=\dfrac{4}{5}$ 

(ii) $\dfrac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{2}}{\text{3}}$ 

Ans: Calculating the value,

$\dfrac{4}{9}\div \dfrac{2}{3}=\dfrac{4}{9}\times \dfrac{3}{2}=\dfrac{2}{3}$

(iii) $\dfrac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{7}}$

Ans:  Calculating the value,

$\dfrac{3}{7}\div \dfrac{8}{7}=\dfrac{3}{7}\times \dfrac{7}{8}=\dfrac{3}{8}$

(iv) $\text{2}\dfrac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{3}}{\text{5}}$ 

Ans: Calculating the value,

$2\dfrac{1}{3}\div \dfrac{3}{5}=\dfrac{7}{3}\div \dfrac{3}{5}=\dfrac{7}{3}\times \dfrac{5}{3}=\dfrac{35}{9}=3\dfrac{8}{9}$

(v) $\text{3}\dfrac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ }\dfrac{\text{8}}{\text{3}}$ 

Ans: Calculating the value,

$3\dfrac{1}{2}\div \dfrac{8}{3}=\dfrac{7}{2}\div \dfrac{3}{8}=\dfrac{7}{2}\times \dfrac{3}{8}=\dfrac{7\times 3}{2\times 8}=\dfrac{21}{16}=1\dfrac{5}{16}$

(vi) $\dfrac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{1}}{\text{2}}$

Ans:  Calculating the value,

$2\dfrac{1}{3}\div \dfrac{3}{5}=\dfrac{2}{5}\div 1\dfrac{1}{2}=\dfrac{2}{5}\div \dfrac{3}{2}=\dfrac{2}{5}\times \dfrac{2}{3}=\dfrac{2\times 2}{5\times 3}=\dfrac{4}{15}$

(vii) $\text{3}\dfrac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{2}}{\text{3}}$

Ans:  Calculating the value,

$3\dfrac{1}{5}\div 1\dfrac{2}{3}=\dfrac{16}{5}\div \dfrac{5}{3}=\dfrac{16}{5}\times \dfrac{3}{5}=\dfrac{16\times 3}{5\times 5}=\dfrac{48}{25}=1\dfrac{23}{25}$

(viii) $\text{2}\dfrac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\dfrac{\text{1}}{\text{5}}$ 

Ans: Calculating the value,

$2\dfrac{1}{5}\div 1\dfrac{1}{5}=\dfrac{11}{5}\div \dfrac{6}{5}=\dfrac{11}{5}\times \dfrac{5}{6}=\dfrac{11}{6}=1\dfrac{5}{6}$

Fraction and Decimals Class 7 Exercise 2.4 – In a Nutshell

Fractions and decimals are the fundamentals of the number system, and they form a basis for understanding how to represent the portions of anything that are not whole. These are used in our daily life but are often overlooked. We do not realise the times and areas where we use fractions and decimals, starting from money, weight to length and many more. 

Decimals are mainly used to define precision, and fractions are used to represent a part of something. Students should know that both of these are interchangeable. All you have to do is either divide or multiply to get the other one, based on the requirement. 

You can clear such concepts from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 in the most straightforward manner. We have jotted down all the essential pointers that a student should consider before going deeper into this topic. Also, we have provided a tabular representation for the tips and tricks that might be helpful for you to solve these problems.

In this chapter, you are likely to learn about:

• How to write decimals along with whole numbers

• How to write fractions

• Reciprocal of fractions

• Types of fractions – regular, improper, mixed

• Mathematical operations using fractions and decimals

For a comprehensive analysis of all the pointers mentioned above, you can refer to our Maths NCERT Solutions Class 7 Chapter 2 Exercise 2.4; it will help you in understanding the concepts from the grassroots as well as in improvising your learning pattern. Here is a brief description of the questions covered in this exercise.

Exercise 2.4 Class 7th – Question 1

In this first question, you are asked to work on mathematical operators like addition and division on six short questions present under it. The critical part of these questions is that you have to perform the addition or division between a whole number and a fraction.

Take a look at our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 offered by Vedantu, where we have tried to simplify the process for you. Students can take help for the shortcut tips that we have listed based on these types of numerical.

You should have a clear understanding of:

• Converting each term into similar fractions before using an operator between them.

• Basics clarity of proper and improper fractions.

• Addition and multiplication are used during the increment of something.

• Subtraction and division are used for decrement.

Understanding these fundamentals is crucial as it will help you in handling advanced level sums too. Also, you can streamline your studying pattern in the right direction. As a result, you can gain an extra edge in the competition prevalent in exams too.

Ex 2.4 Class 7 Maths – Question 2

In the second question, you are asked to find the reciprocals of each fraction given. Seven fractions are provided, and you have to classify them as well. While you study for fractions from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4, you will be aware that:

• In a fraction, a bar divides two numbers, irrespective of the number of digits in them.

• The number written over the bar is called numerator.

• The denominator is the number written under the bar.

So, when you are asked to find the reciprocal, it is simply interchanging their places, irrespective whether it is a proper fraction or not. Further, students should also be aware of the types of fractions and their properties, such that:

• A proper fraction: Numerator < denominator

• An improper fraction: Numerator > denominator

• Mixed fraction: Whole number and fraction together (fraction can be either proper or improper)

Make sure you revise these pointers carefully presented in our NCERT Solution for Class 7 Maths Chapter 2 Exercise 2.4. It will assist you in developing a firm hold on the fundamentals of fractions and decimals.

Exercise 2.4 Class 7 – Question 3

Question 3 is similar to the first question; the only difference is that here the first term is a fraction and a second term is a whole number. It is unlike the previous question, where the first term was a whole number and the second was a fraction. 

Although the operators remain similar – either addition or division - students often tend to get confused between these. Hence, we recommend you to go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 to gain clarity on such crucial pointers.

The procedure for operating remains the same, as you convert the whole number into a fraction by:

• Either adding a denominator 1 to the whole number.

• Follow the essential addition of a whole number to a fraction.  

You can choose to perform either of the methods mentioned above. However, make sure you do them correctly. Having a sound knowledge of fractions will help you to ace this section easily. Take help from our study materials for CBSE Class 7 Maths Chapter 2 Exercise 2.4 to redirect your learning in the right direction.

Exercise 2.4 Class 7 Maths – Question 4

Contrary to the previous questions, here you are given eight short questions that contain two terms each. Each term is a fraction, and you have to perform either addition or division with those, as per requirement. 

Students should understand that the process of conducting the operation is the same as the previous ones. However, they should be careful when:

• The denominators are different for two terms.

• One of the denominators is not a factor of the other.

• The numbers do not have immediate multiple. 

In such cases, the denominators should be multiplied to each other. Go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 and get to know these short tricks as and when required.

It is essential to know when and how should you approach a particular question. To get thorough with such usage, you need to practise the sums regularly. It will not only create a learning environment for you but also keep you ready to face any twisted question during the actual exam. 

Class 7th Maths Chapter 2 Exercise 2.4 – Other exercises

There are other exercises as well in this chapter, where you are likely to find sums based on other operators like subtraction of both improper and mixed fractions. Also, you will know about the following aspects from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4:

• How to find the largest/smallest fraction among others.

• Arranging them in ascending/descending order.

• Word problems based on fractions.

• Deciphering pictorial representation of fractions.

• Multiplication of fractions.

• Conversion into lowest terms.

• Finding the missing number.

• Conversion of fractions to decimals and vice versa.

• Conversion into a single unit (money, length, quantity)

• Place Value of a digit in a decimal number.

Below here is a brief analysis of the topics covered in the exercises of this chapter other than Maths Class 7 Chapter 2 Exercise 2.4.

Exercise 2.1: 

In the first exercise, you are asked eight questions. The questions are of various types, both numerical and word problems. The questions you are likely to solve are as follows:

1. First question: Asks you to solve seven numerical where you have to add two or more fractions. The fractions are either proper or mixed fractions.

2. Second question: Asks you to arrange the fractions in descending order.

3. Third question: It is about a magic square. There is a square box (3x3) with fractions written in them and you have to prove if that is a magic square.

4. Question 4 to 8: These are word problems where you have to find specific portions which are either left or unused as per the question. 

You can go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 for faster learning of these concepts. Our solutions are tailored in a personalised manner to safeguard the students from committing unnecessary silly mistakes in exams.

Exercise 2.2:

The second exercise has eight questions too, similar to the previous one, however, with slightly more interesting concepts. Students may find these a little complicated in the first go, but with regular practise, one can easily master these concepts.

A brief overview of the questions covered in this exercise is given below.

1. The first two questions – They are of objective type and asks you to choose the right shaded region corresponding to the fraction given.

2. The second question – It asks you to multiply the given fractions and reduce them to their lowest forms. The numbers are either one digit or two digits and do not require extensive use of multiplication tables.

3. The fourth question - It is opposite to the first two questions. Here you have to shade the region mentioned in the form of fractions.

4. Question 6 - Asks you to multiply the fractions and express in mixed fractions.

5. Question 5 & 7 –They require you to multiply the given fractions.

6. The last question – It is a word problem, and you have to find the answers infraction for the quantity asked.

Our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 is likely to help you understand all these topics clearly. As a result, you can ace your exam effortlessly.

Exercise 2.3:

This exercise is comparatively an easy one and students will not be over-burdened while solving it. However, faster solving can often lead to silly errors during exams as well as in practice. Hence, you can cross-check your answers from our solutions to NCERT Class 7 Maths Chapter 2 

Exercise 2.4:

Also, you can find alternative solutions to complicated problems. You can learn those from the detailed explanation given in our study materials, and implement them during the actual exam. Usually, the alternative methods are crisp and help in saving a lot of time that you can use for other questions. 

In this exercise, you are asked to:

1. Multiply the fractions in Questions 1 to 3.

2. Find which fraction is greater in Question 4.

3. Word problems in Questions 5 to 7.

4. Fill the missing fraction in Question 8.

Make sure you have an in-depth knowledge of multiplying fractions before solving this exercise. To gain a strong understanding, you can always revise from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4. Our solutions are available in PDF form so that you can download them too for your reference.

Exercise 2.5:

This exercise deals specifically with decimals. Here you will get nine questions in all of the various kinds. Each of them is equally crucial, and students can not overlook any of them. The questions are briefly discussed hereunder for your convenience:

1. You have to determine the greater of two decimals in Question 1.

2. Every option is written in Paisa or other measurement units of lengths and quantity, and you have to convert them into Rupees/lengths (m/km)/ Kilograms in Question 2, 2 and 4.

3. Question 5 asks you to rewrite the decimals into expanded forms.

4. Question 6 asks for the place value of a specific digit in the numbers provided.

5. The last three questions 7 to 9 are word problems, and you have to solve them as per the instructions provided in them.

There are two terms - place value and the face value of a digit in a number that students often get confused. Also, the conversion is a slightly trickier concept that needs more in-depth understanding. Students can easily get confused with units conversion during exams. 

Therefore, we recommend you to gain clarity on such confusing terms most appropriately and easily from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4. Our solutions are penned by subject experts who have been teaching students for years, and they are aware of the grey areas too.

We have provided not only extra descriptions for such topics but also made sure you remember them for a long time with the shortcut tips mentioned alongside. Consequently, it will help you approach the question in the right path even during your exam, in case it is asked. 

Exercise 2.6:

Here, you will get only five questions based on a calculation using decimals. The critical part of dealing with decimals is multiplying them. Hence, students are advised to be careful while answering questions in the exam. Below here is a brief overview of questions you are asked here, and the vital things you will get in our NCERT Maths Class 7 Chapter 2 Exercise 2.4 concerning this exercise.

1. Question 1 - It requires you to determine the answers to a multiplication of a natural number with a decimal. 

2. Question 2 – It asks you to calculate the area of a rectangle whose length and breadth are given in decimal.

3. Question 3 & 5 – They are similar ask they require you to multiply the numbers with decimals. The best part of these questions is that they can be done with a simple trick.

4. Question 4 – It is a word problem wherein students should have the basic knowledge of approaching a particular question. They should be able to tell which mathematical operation is required to solve the sum.

You can download our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 and get to know the trick required in solving Question 2. Multiplying decimals with numbers that are multiples 10 in the form of 10, 100, 1000, and so on requires you to shift the decimal to the right of the number based on the number of zeroes present.

This trick is highly useful during exams, as it saves a lot of time in multiplying larger numbers which can be solved using this trick. Further, you can use a similar trick while division too. Refer to our solutions for quick tips and their elaborate explanations to help you ace your exam in the most simplified way.

Exercise 2.7:

It is the last exercise in this chapter and has six questions for students to develop an overall concept of decimals and fractions. After learning multiplication, division and subtraction, this exercise deals with the division of decimals in details.

Students should understand that decimals are converted into fractions for simplifying the calculations. However, they should know how to convert a fraction easily - before that, reading out a fraction or decimal is also equally essential. Our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 will help you in reading it correctly, which will further aid in easier understanding of the methods involved in calculations.

The first five questions in this exercise require you to solve short numerical based on:

• Divide decimal by the whole number.

• Divide decimal by decimal.

• Division of decimal by ten and its multiples (10, 100, and 1000)

Question 5 is a word problem where you are asked to calculate for the distance you can cover in 1-litre petrol if you have travelled 43.2 km in 2.4 litres petrol. Students should be aware that when finding a quantity smaller than the provided quantity, they should use the division operator. 

Solving a particular exercise can be interesting and comparatively easier than solving mixed bag questions. Therefore, a prior understanding of all the concepts from their grassroots is extremely exceptionally.

You can develop the knowledge from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.4 as we provide a crisp explanation of all the chapters separately too with our study materials. Revising that before then, the exam will help you in dealing with all the questions altogether.

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The techniques and detailed explanation manifested in our NCERT solutions are one of a kind and have been successful in creating a superior environment for students. Besides, our solutions are available online so that you can download them and save for your future reference too. 

So, what are you waiting for? Avail our study materials now from Vedantu and boost your exam preparation.