NCERT Solutions for Class 7 Maths Chapter 2: Fractions and Decimals - Exercise 2.7

Exercise: 2.7

1. Find

(i) \[0.4\div 2\]

Ans: \[0.4\div 2=\frac{4}{10}\times \frac{1}{2}=\frac{2}{10}=0.2\]

(ii) \[0.35\div 5\]

Ans: \[0.35\div 5=\frac{35}{100}\times \frac{1}{5}=\frac{7}{100}=0.07\]

(iii) \[2.48\div 4\]

Ans: \[2.48\div 4=\frac{248}{100}\times \frac{1}{4}=\frac{62}{100}=0.62\]

(iv) \[65.4\div 6\]

Ans: \[65.4\div 6=\frac{65.4}{10}\times \frac{1}{6}=\frac{109}{10}=10.9\]

(v) \[651.2\div 4\]

Ans: \[651.2\div 4=\frac{6512}{10}\times \frac{1}{4}=\frac{1628}{10}=162.8\]

(vi) \[14.49\div 7\]

Ans: \[14.49\div 7=\frac{14.49}{100}\times 7=\frac{207}{100}=2.07\]

(vii) \[3.96\div 4\]

Ans: \[3.96\div 4=\frac{3.96}{100}\times \frac{1}{4}=\frac{99}{100}=0.99\]

(viii) \[0.80\div 5\]

Ans: \[0.80\div 5=\frac{80}{100}\times \frac{1}{5}=\frac{16}{100}=0.16\]

2. Find

(i) \[4.8\div 10\]

Ans: \[4.8\div 10=\frac{48}{10}\times \frac{1}{10}=\frac{48}{100}=0.48\]

(ii) \[52.5\div 10\]

Ans: \[52.5\div 10=\frac{525}{10}\times \frac{1}{10}=\frac{525}{100}=5.25\]

(iii) \[0.7\div 10\]

Ans: \[0.7\div 10=\frac{7}{10}\times \frac{1}{10}=\frac{7}{100}=0.07\]

(iv) \[33.1\div 10\]

Ans: \[33.1\div 10=\frac{331}{10}\times \frac{1}{10}=\frac{331}{100}=3.31\]

(v) \[272.23\div 10\]

Ans: \[272.23\div 10=\frac{27223}{100}\times \frac{1}{10}=\frac{27223}{1000}=27.223\]

(vi) \[0.56\div 10\]

Ans: \[0.56\div 10=\frac{56}{100}\times \frac{1}{10}=\frac{56}{1000}=0.056\]

(vii) \[3.97\div 10\]

Ans: \[3.97\div 10=\frac{3.97}{100}\times \frac{1}{10}=\frac{397}{1000}=0.397\]

3. Find

(i) \[2.7\div 100\]

Ans: \[2.7\div 100=\frac{27}{10}\times \frac{1}{100}=\frac{27}{1000}=0.027\]

(ii) \[0.3\div 100\]

Ans: \[0.3\div 100=\frac{3}{10}\times \frac{1}{100}=\frac{3}{1000}=0.003\]

(iii) \[0.78\div 100\]

Ans: \[0.78\div 100=\frac{78}{100}\times \frac{1}{100}=\frac{78}{10000}=0.0078\]

(iv) \[432.6\div 100\]

Ans: \[432.6\div 100=\frac{4326}{10}\times \frac{1}{100}=\frac{4326}{1000}=4.326\]

(v) \[23.6\div 100\]

Ans: \[23.6\div 100=\frac{236}{10}\times \frac{1}{100}=\frac{236}{1000}=0.236\]

(vi) \[98.53\div 100\]

Ans: \[98.53\div 100=\frac{9853}{100}\times \frac{1}{100}=\frac{9853}{10000}=0.9853\]

4. Find

(i) \[7.9\div 1000\]

Ans: \[7.9\div 1000=\frac{79}{10}\times \frac{1}{1000}=\frac{79}{10000}=0.0079\]

(ii) \[26.3\div 1000\]

Ans: \[26.3\div 1000=\frac{263}{10}\times \frac{1}{1000}=\frac{263}{10000}=0.0263\]

(iii) \[38.53\div 1000\]

Ans: \[38.53\div 1000=\frac{3853}{100}\times \frac{1}{1000}=\frac{3853}{100000}=0.03853\]

(iv) \[128.9\div 1000\]

Ans: \[128.9\div 1000=\frac{1289}{10}\times \frac{1}{1000}=\frac{1289}{10000}=0.1289\]

(v) \[0.5\div 1000\]

Ans: \[0.5\div 1000=\frac{5}{10}\times \frac{1}{1000}=\frac{5}{10000}=0.0005\]

5. Find

(i) \[7\div 3.5\]

Ans: \[7\div 3.5=7\div \frac{35}{10}=7\times \frac{10}{35}=\frac{10}{5}=2\]

(ii) \[36\div 0.2\]

Ans: \[36\div 0.2=36\div \frac{2}{10}=36\times \frac{10}{2}=18\times 10=180\]

(iii) \[3.25\div 0.5\]

Ans: \[3.25\div 0.5=\frac{325}{100}\div \frac{5}{10}=\frac{325}{100}\times \frac{10}{5}=\frac{65}{10}=6.5\]

(iv) \[30.94\div 0.7\]

Ans: \[30.94\div 0.7=\frac{3094}{100}\div \frac{7}{10}=\frac{3094}{100}\times \frac{10}{7}=\frac{442}{10}=44.2\]

(v) \[0.5\div 0.25\]

Ans: \[0.5\div 0.25=\frac{5}{10}\div \frac{25}{100}=\frac{5}{10}\times \frac{100}{25}=\frac{10}{5}=2\]

(vi) \[7.75\div 0.25\]

Ans: \[7.75\div 0.25=\frac{775}{100}\div \frac{25}{100}=\frac{775}{100}\times \frac{100}{25}=31\]

(vii) \[76.5\div 0.15\]

Ans: \[76.5\div 0.15=\frac{765}{10}\div \frac{15}{100}=\frac{765}{10}\times \frac{100}{15}=51\times 10=510\] 

(viii) \[37.8\div 1.4\]

Ans: \[37.8\div 1.4=\frac{378}{10}\div \frac{14}{10}=\frac{378}{10}\times \frac{10}{14}=27\]

(ix) \[2.73\div 1.3\]

Ans: \[2.73\div 1.3=\frac{273}{100}\div \frac{13}{100}=\frac{273}{100}\times \frac{10}{13}=\frac{21}{10}=2.1\]

6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre petrol?

Ans: In 2.4 litres of petrol, distance covered by the vehicle \[=43.2km\]

Therefore, in 1 litre of petrol, distance covered by the vehicle  \[=43.2\div 2.4\]

\[=\frac{432}{10}\div \frac{24}{10}=\frac{432}{10}\times \frac{10}{24}\]

\[=18Km\]

Thus, it covered 18 km distance in one litre of petrol.

NCERT Maths Solution Class 7 Chapter 2 Exercise 2.7 – A Closer Look.

Decimals and fractions form the basis for understanding concepts of representing some Mathematical information with the highest possible precision. Simply put, a fraction represents a part of something whole, while a decimal represents the smallest portion of something mostly uncountable.

Although these representations often find a place in our day to day life activities, we tend to overlook them. Data like money, amount of fluid, weight, etc. can be represented using fractions and decimals when they are not whole. You can develop a stronghold on this chapter by studying from our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7.

The key takeaways that students can learn from this chapter are:

• They are interchangeable.

• Use a division operator for converting a decimal into fraction.

• Use multiplication to convert fraction into decimal.

On further exploration, you will know certain other essential aspects of using decimals and fractions. They are listed as follows:

• Writing various types of fractions – proper, improper and mixed.

• Reading decimal numbers (after the decimal).

• Reciprocal of a fraction.

• Mathematical operations using fractions and decimals – addition, multiplication, subtraction and division.

• Operations using reciprocal of fractions.

Hence, to gain clarity on such concepts, make sure you go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7. We have implanted every topic most straightforwardly so that students do not miss out on any topic.

Also, we have maintained the use of simple language throughout our explanations to Class 7 Maths NCERT Solutions Chapter 2 Exercise 2.7 to aid students with a simple understanding. Consequently, you can also develop a stronghold on the topic and ace even the twisted questions in exam. 

Students can also keep these study materials downloaded in their devices for future reference. It will help them in the following ways:

• They can regularly revise the formulas and shortcut tricks.

• They can cross-check the answers from our solutions.

• They can also learn an alternative, probably more straightforward process for solving a particular numerical.

Here is a Brief Overview of All These Questions Covered in This Chapter.

Class 7 Maths Chapter 2 Exercise 2.7 – Question 1

In the first question, you are provided with eight short questions, where you have to use the division operator to calculate the numerical. Here you will see that the first term is a decimal and a second term is a whole number.

Students have to learn how to use the division operator. We have provided step by step solutions for the same in our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 to help them develop a clear understanding of the topic right from the grassroots.

You need to be careful when dealing with a decimal number, which can be any of the following types:

• Having no whole number part and only the decimal part.

• Having only one digit after the decimal.

• Having two digits or more after the decimal.

The key to understanding the Mathematical operations using decimals is to know how to read them and also merely them to perform the operations.

You can opt for either of the following two steps before using operators:

• Convert the decimal into a fraction.

• Add a zero before decimal or after the single-digit placed after the decimal, if there is no digit present.

To have a closer look at these concepts, you can refer to our NCERT Solutions Class 7 Maths Chapter 2 Exercise 2.7 and boost your exam preparation. 

NCERT Maths Class 7 Chapter 2 Exercise 2.7 – Question 2

The second question is quite similar to the previous one. You are given seven short numerical where you have to use the division operator. The only difference between the previous and this question is that the whole number here is 10.

Students can solve this question with a short trick, which is presented in our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7. The method is to shift the decimal place when you divide a number with decimal with multiple of 10. Based on the number of zeroes present in the divisor, you have to shift that many places to the left of the number containing a decimal.

As already mentioned, here you will find a decimal number in various forms- single or double digits before/ after the decimal. Students need to be highly careful when dividing, as a slight shift in decimal will lead to a wrong answer, and hence negative marking in exam.

Therefore, make sure you are thorough with the dividing process of every kind possible. Students often get confused while placing the decimal point in a number, so, we have brought to you a step by step guide in simplifying the process.

Our solutions are:

• Standard quality.

• Based on the latest syllabus.

• Compiled by subject experts.

• Written in a simple language.

• Represented in tabular form for more natural extraction of information.

• Helpful for quick revision.

• Help you fetch higher grades in the exam.

We recommend you keep our NCERT Solution of Class 7 Maths Chapter 2 Exercise 2.7 downloaded in your devices as they are readily available on the internet for free. 

Class 7 Maths Chapter 2 Exercise 2.7 – Question 3

Question 3 asks you to use the division operator and here the divisor is 100. Quite similar to the previous question, the only difference is that you have to divide the given decimal numbers by 100. You are given six short numerical in all, and each of the numbers present has either one or two digits after or before the decimal.

While dealing with decimal numbers, the most important thing to look for is the position of the decimal. Once you have appropriately identified the same, it will be easier for you to approach a question and proceed further. Go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7, as it will guide you in the right direction about handling these tricky questions. 

As mentioned in the previous question, you are required to shift the decimal-based on the number of zeroes present. Here, because of 100, you have to shift the decimal two places to your left. However, there is an important trick you need to consider here, which is:

In case there is only one digit before the decimal, and you have to shift the decimal two places to the left, then you have to add a ‘0’ (zero) before placing the decimal.

For instance, 2.36 is to be divided by 100. Here the answer is 0.0236.

Also, note that the following points:

• The zero written before a decimal has absolutely no value.

• It is written only for the sake of convention.

• It does not affect any part of the calculation or the solution. 

Refer to our online solutions of NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 for a more fundamental understanding of the same.

NCERT Maths Solution Class 7 Chapter 2 Exercise 2.7 – Question 4

In Question 4, you have to use the same method of shifting the decimal similar to the previous two questions, only that the divisor in this question is 1000. That implies you have to shift the decimal to three places to the left of the present position. 

For a deeper understanding and gaining clarity on these topics, you can take a look at our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7. These are standard solutions and prepared by professionals who have been teaching students for over many years.

They are well aware of the grey area where students generally make mistakes; hence, they have mentioned those portions exclusively. With this, students will be mindful of the same beforehand and thus can avoid committing the same error in their actual exam. 

Students should also be careful about the usage of zero in decimals. 

• Placing a zero right before/after the decimal does not make any difference. 

• Placing one or more zeroes after the digits already present after the decimal also does not change the meaning.

• Placing zero other than these would change the number.

Therefore, go through our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 for a comprehensive explanation of the same. 

Class 7 Maths Chapter 2 Exercise 2.7 – Question 5

This is the most important question out of all questions present in this exercise as it deals with purely decimal numbers. Here, both the dividend as well as the divisor is in decimal. Only a proper understanding of the topic will help you in building a firm grip on it. 

The numbers have one or two digits both before and after the decimal. Students often find it challenging to deal with numbers when they are in decimal form during exams. Hence, we recommend you to convert these into fractions, whenever possible to simplify the calculation. 

Also, it is mentioned in our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 solutions, that you can covert the division operator into multiplication too for easing the calculations. To know this trick, make sure you go through our study materials before the exam.

NCERT Maths Class 7 Chapter 2 Exercise 2.7 – Question 6

It is the last question in this exercise, and it is a word problem. You have to determine the type of mathematical operation required here. Also, you have to understand – which is to be divided by whom. 

For more in-depth insights into word problems, take a look at our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7. You need to understand the essential requirement of using the division operation. A car covering 43.2 km with 2.4 litres of petrol is going to cover less distance with less amount of petrol. 

You can solve this using the unitary method, where you are required to calculate the distance for 1 litre of petrol first and then move to find higher amounts. 

Class 7 Maths NCERT Solutions Chapter 2 Exercise 2.7 – Other Exercises

Here is a brief overview of all the other exercises present in this chapter.

Exercise 2.1:

There are eight questions, both numerical and word problems in this first exercise which is based on fractions. You are required to:

• Add a fraction to a whole number.

• Arrange several fractions in ascending order.

• Analyse the properties of a magic square and prove it.

• Few word problems using the unitary method based on fractions.

Make sure you are well-versed with the unitary method to be able to solve the questions. Follow our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 for a full description.

Exercise 2.2:

This exercise further deals with fractions in detail, and here you are provided with eight questions. You have to find:

• The shaded region infraction.

• Shade the region has given infraction.

• Match the fraction with the shaded figures given alongside.

• Multiply the fractions and reduce them into their lowest forms.

• Converting mixed fractions into improper fractions.

Make sure you follow our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 for an elaborate explanation of the concept. It will help you to solve faster in exams without silly errors.

Exercise 2.3:

The third exercise also deals with fractions, and there are eight questions which are specifically based on multiplication. In the first four questions, you have to:

• Convert mixed fraction into an improper fraction.

• Multiply the fractions.

• Reduce them into their lowest terms.

• Find which a greater fraction between two is.

• Operator ‘of’ is multiplication. 

• Solving three-word problems. 

• Finding the missing fraction.

In our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7, you will get these explanations most easily. It will boost your exam preparation and help you in finding solutions faster in your actual exam.

Exercise 2.4:

There are four questions in this exercise, and you are likely to learn about:

• Finding the reciprocal of a fraction.

• Classifying fractions into – improper, mixed and proper.

• Division of fractions by a whole number and another fraction. 

You should know that division can be transformed into multiplication for more straightforward calculation. Learn this technique from our study materials of NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7. 

Exercise 2.5:

In this exercise, you will find questions based on decimals and their conversion into single units. Also, there are a few word problems to help you develop a clear understanding of the same. There are nine questions where you will solve:

• Find the greater decimal.

• Convert:  a. Paisa into Rupees b. Gram into Kilogram c. Centimetre in metre and kilometre.

• Expanding a decimal

• Finding the place value of a digit.

Refer to our NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 and gain a more in-depth insight into decimals. We have introduced the concept in a natural way so that you do not miss out on any relevant matter.

Exercise 2.6:

Here are five questions in this exercise based on the multiplication of decimals. Here you will learn about the multiplication of:

• A decimal with a multiple of 10 (10, 100 and 1000)

• A decimal with another decimal.

• Finding the area of a triangle whose sides are given in decimals.

• Finding the distance, a two-wheeler will cover with 10 litres of petrol if it covers 55.3 km in 1 litre of petrol.

Thus, you will know another side of the unitary method being used here. The process is the same; however, you need to multiply here to find a large amount, unlike in division, where you had to find a smaller amount.

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They have penned down these NCERT Solutions for Class 7 Maths Chapter 2 Exercise 2.7 after learning from every bit of their teaching experience to over 40, 000 students.  The use of shortcut techniques and smart tricks in the solutions has helped students break every shackle that may arise while answering questions to decimals and fractions in the exam.

Also, our solutions are not just limited to Class 7 Maths, but we also provide solutions to other subjects and other classes as well to simplify the learning process for students. It is due to our widespread presence in over 1000 cities that students have been able to benefit from our study materials. Moreover, our solutions are available online for easy downloads, which further adds to our accessibility. 

So, are you looking for ways to improve your exam scores? Avail our study notes now and make the most of it!