Important Practice Problems for CBSE Class 7 Maths Chapter 2: Fractions and Decimals FREE PDF
1 Mark Questions:
1. Convert the given fraction into mixed fraction \[\dfrac{{22}}{7}\].
Ans. A fraction can be written in the form of mixed fraction in the following way:
\[Q\dfrac{R}{D}\] , where Q is the quotient, R is the remainder and D is the divisor of the fraction.
So, \[\dfrac{{22}}{7}\] in mixed fraction form will be \[3\dfrac{1}{7}\] .
2. Write an equivalent fraction of \[\dfrac{9}{{15}}\].
Ans. To find an equivalent fraction, we simply multiply the numerator and denominator of the given fraction with the same number.
A fraction equivalent to \[\dfrac{9}{{15}}\] will be \[\dfrac{9}{{15}} \times \dfrac{2}{2} = \dfrac{{18}}{{30}}\] .
3. Find the value of \[3\dfrac{4}{7} \div 7\].
Ans. We solve the expression \[3\dfrac{4}{7} \div 7\] as follows:
\[ \Rightarrow \dfrac{{25}}{7} \div 7\]
\[ \Rightarrow \dfrac{{25}}{7} \times \dfrac{1}{7}\]
\[ \Rightarrow \dfrac{{25}}{{49}}\]
4. Express \[8\] rupee \[5\] paise in decimal.
Ans. \[8\] rupees and \[5\] paise in decimal form can be written as Rs. \[8.05\].
5. Write the place value of \[5\] in \[498.05\].
Ans. The place value of \[5\] in \[498.05\] is hundredths.
Refer to page 2 - 6 for 2 Mark Questions
6. Find the value of \[\dfrac{5}{6}\] of:
(i) \[30\]
Ans. The value of \[\dfrac{5}{6}\] of \[30\] is:
\[\dfrac{5}{6} \times 30 = 25\]
(ii) \[54\]
Ans. The value of \[\dfrac{5}{6}\] of \[54\] is:
\[\dfrac{5}{6} \times 54 = 45\]
7. Multiply and reduce to lowest form:
(i) \[\dfrac{3}{8} \times \dfrac{4}{9}\]
Ans. Multiplying and simplifying \[\dfrac{3}{8} \times \dfrac{4}{9}\] :
\[ \Rightarrow \dfrac{{12}}{{72}}\]
\[ \Rightarrow \dfrac{1}{6}\]
(ii) \[\dfrac{{11}}{{10}} \times \dfrac{2}{5}\]
Ans. Multiplying and simplifying \[\dfrac{{11}}{{10}} \times \dfrac{2}{5}\] :
\[ \Rightarrow \dfrac{{22}}{{50}}\]
\[ \Rightarrow \dfrac{{11}}{{25}}\]
8. Multiply and express as mixed fractions:
(i) \[4 \times 6\dfrac{2}{3}\]
Ans. Solving the expression:
\[4 \times 6\dfrac{2}{3}\]
\[ \Rightarrow 4 \times \dfrac{{20}}{3}\]
\[ \Rightarrow \dfrac{{80}}{3}\]
\[ \Rightarrow 26\dfrac{2}{3}\]
(ii) \[3\dfrac{2}{3} \times 5\]
Ans. Solving the expression:
\[3\dfrac{2}{3} \times 5\]
\[ \Rightarrow \dfrac{{11}}{3} \times 5\]
\[ \Rightarrow \dfrac{{55}}{3}\]
\[ \Rightarrow 18\dfrac{1}{3}\]
9. Shade:
(i) \[\dfrac{1}{3}\] of the ice creams in box:
Ans. There are total \[9\] ice creams in the box. We have to shade \[\dfrac{1}{3}\] , that is, \[\dfrac{1}{3} \times 9 = 3\] ice creams.
(ii) \[\dfrac{3}{4}\] of the apples in box:
Ans. There are a total of \[16\] apples in the box. We have to shade \[\dfrac{3}{4}\] , that is, \[\dfrac{3}{4} \times 16 = 12\] apples.
10. Sarah and Darshan went for a picnic. Their mother gave them a juice bottle of \[3\] litres.
Sarah consumed \[{\dfrac{1}{3}^{rd}}\] of the juice. Darshan consumed the rest.
(a) How much did Sarah drink?
Ans. Total quantity of juice in the bottle is \[3\] litres.
Sarah consumed \[{\dfrac{1}{3}^{rd}}\] of the juice, that is, \[\dfrac{1}{3} \times 3 = 1\] litre.
(b) What fraction of the total quantity did Darshan drink?
Ans. Darshan consumed \[1 - \dfrac{1}{3} = \dfrac{2}{3}\] of the total juice.
11. Find:
(i) \[\dfrac{2}{9} \div 4\]
Ans. Solving:
\[\dfrac{2}{9} \div 4\]
\[ \Rightarrow \dfrac{2}{9} \times \dfrac{1}{4}\]
\[ \Rightarrow \dfrac{2}{{36}}\]
\[ \Rightarrow \dfrac{1}{{18}}\]
(ii) \[\dfrac{{11}}{7} \div 2\]
Ans. Solving:
\[\dfrac{{11}}{7} \div 2\]
\[ \Rightarrow \dfrac{{11}}{7} \times \dfrac{1}{2}\]
\[ \Rightarrow \dfrac{{11}}{{14}}\]
12. Find:
(i) \[\dfrac{{12}}{7} \div \dfrac{3}{{14}}\]
Ans. Solving:
\[\dfrac{{12}}{7} \div \dfrac{3}{{14}}\]
\[ \Rightarrow \dfrac{{12}}{7} \times \dfrac{{14}}{3}\]
\[ \Rightarrow \dfrac{{168}}{{21}}\]
\[ \Rightarrow 8\]
(ii) \[\dfrac{2}{5} \div \dfrac{4}{5}\]
Ans. Solving:
\[\dfrac{2}{5} \div \dfrac{4}{5}\]
\[ \Rightarrow \dfrac{2}{5} \times \dfrac{5}{4}\]
\[ \Rightarrow \dfrac{2}{4}\]
\[ \Rightarrow \dfrac{1}{2}\]
13. Which is greater:
(i) \[{\bf{0}}.{\bf{02}}\] or \[{\bf{0}}.{\bf{2}}\]
Ans. We convert the decimals into equivalent fractions:
\[0.02 = \dfrac{2}{{100}}\] and \[0.2 = \dfrac{{20}}{{100}}\]
On comparing, we conclude that \[\dfrac{{20}}{{100}} > \dfrac{2}{{100}}\] .
Hence, \[0.2\] is greater.
(ii) \[1.98\] or \[1.98\]
Ans. We convert the decimals into equivalent fractions:
\[1.98 = \dfrac{{198}}{{100}}\] and \[1.89 = \dfrac{{189}}{{100}}\]
On comparing, we conclude that \[\dfrac{{198}}{{100}} > \dfrac{{189}}{{100}}\] .
Hence, \[1.98\] is greater.
14. How much \[5.6\] kg is less than \[9.4\] kg?
Ans. Calculating the difference:
\[9.4 - 5.6 = 3.8\] kg
Hence, \[5.6\] kg is \[3.8\] kg less than \[9.4\] kg.
15. Find:
(i) \[1.08 \times 0.3\]
Ans. Converting into fractions and solving:
\[1.08 \times 0.3\]
\[ \Rightarrow \dfrac{{108}}{{100}} \times \dfrac{3}{{10}}\]
\[ \Rightarrow \dfrac{{324}}{{1000}}\]
\[ \Rightarrow 0.324\]
(ii) \[158.3 \times 2.9\]
Ans. Converting into fractions and solving:
\[158.3 \times 2.9\]
\[ \Rightarrow \dfrac{{1583}}{{10}} \times \dfrac{{29}}{{10}}\]
\[ \Rightarrow \dfrac{{45907}}{{100}}\]
\[ \Rightarrow 459.07\]
3 Mark Questions
16. Arrange in ascending order \[\dfrac{3}{5},\dfrac{4}{7},\dfrac{3}{{10}},\dfrac{4}{5}\] .
Ans. To arrange given fractions in ascending order, we first make their denominators equivalent.
L.C.M. of all the denominators \[5,7,10\] is \[70\] .
\[\dfrac{3}{5} \times \dfrac{{14}}{{14}} = \dfrac{{42}}{{70}}\]
\[\dfrac{4}{7} \times \dfrac{{10}}{{10}} = \dfrac{{40}}{{70}}\]
\[\dfrac{3}{{10}} \times \dfrac{7}{7} = \dfrac{{21}}{{70}}\]
\[\dfrac{4}{5} \times \dfrac{{14}}{{14}} = \dfrac{{56}}{{70}}\]
Now, \[\dfrac{{21}}{{70}} < \dfrac{{40}}{{70}} < \dfrac{{42}}{{70}} < \dfrac{{56}}{{70}}\] .
Hence, \[\dfrac{3}{{10}} < \dfrac{4}{7} < \dfrac{3}{5} < \dfrac{4}{5}\] .
17. Find the perimeter of the rectangle whose length is \[7\dfrac{3}{{10}}\] cm and breadth is \[\dfrac{3}{5}\] cm.
Ans. We know that the perimeter of a rectangle is twice the sum of its length and breadth, that is, \[2(l + b)\] .
\[ \Rightarrow 2(7\dfrac{3}{{10}} + \dfrac{3}{5})\]
\[ \Rightarrow 2(\dfrac{{73}}{{10}} + \dfrac{6}{{10}})\]
\[ \Rightarrow 2(\dfrac{{79}}{{10}})\]
\[ \Rightarrow \dfrac{{79}}{5}\]
\[ \Rightarrow 15\dfrac{4}{5}\] cm
18. Find \[\dfrac{3}{7}\] of:
(i) \[3\dfrac{5}{8}\]
Ans. The value of \[\dfrac{3}{7}\] of \[3\dfrac{5}{8}\] is:
\[\dfrac{3}{7} \times 3\dfrac{5}{8} = \dfrac{3}{7} \times \dfrac{{29}}{8}\]
\[ \Rightarrow \dfrac{{87}}{{56}}\]
\[ \Rightarrow 1\dfrac{{31}}{{56}}\]
(ii) \[4\dfrac{3}{9}\]
Ans. The value of \[\dfrac{3}{7}\] of \[4\dfrac{3}{9}\] is:
\[\dfrac{3}{7} \times 4\dfrac{3}{9} = \dfrac{3}{7} \times \dfrac{{39}}{9}\]
\[ \Rightarrow \dfrac{{13}}{7}\]
\[ \Rightarrow 1\dfrac{6}{7}\]
19. Find:
(i) \[3\dfrac{1}{8} \div 2\dfrac{1}{4}\]
Ans. Solving:
\[3\dfrac{1}{8} \div 2\dfrac{1}{4}\]
\[ \Rightarrow \dfrac{{25}}{8} \times \dfrac{4}{9}\]
\[ \Rightarrow \dfrac{{25}}{{18}}\]
\[ \Rightarrow 1\dfrac{7}{{18}}\]
(ii) \[4\dfrac{4}{3} \div 6\dfrac{1}{2}\]
Ans. Solving:
\[4\dfrac{4}{3} \div 6\dfrac{1}{2}\]
\[ \Rightarrow \dfrac{{16}}{3} \times \dfrac{2}{{13}}\]
\[ \Rightarrow \dfrac{{32}}{{39}}\]
20. Write the following decimal number in expanded form:
(i) \[208.183\]
Ans. In expanded form, the given decimal can be written as:
\[(2 \times 100) + (0 \times 10) + (8 \times 1) + (1 \times \dfrac{1}{{10}}) + (8 \times \dfrac{1}{{100}}) + (3 \times \dfrac{1}{{1000}})\]
(ii) \[5.018\]
Ans. In expanded form, the given decimal can be written as:
\[(5 \times 1) + (0 \times \dfrac{1}{{10}}) + (1 \times \dfrac{1}{{100}}) + (8 \times \dfrac{1}{{1000}})\]
(iii) \[360.05\]
Ans. In expanded form, the given decimal can be written as:
\[(6 \times 100) + (3 \times 10) + (0 \times 1) + (0 \times \dfrac{1}{{10}}) + (5 \times \dfrac{1}{{100}})\]
5 Important Formulas of Class 7 Chapter 2 Fractions and Decimals You Shouldn’t Miss!
Understanding the key formulas in fractions and decimals is essential for mastering this chapter in Class 7. Here are five important formulas that will help you solve problems effectively:
1. Addition of Fractions:
When the denominators are the same: $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$
When the denominators are different: $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$
2. Subtraction of Fractions:
When the denominators are the same: $\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$
When the denominators are different: $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$
3. Multiplication of Fractions:
To multiply two fractions:$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
4. Division of Fractions:
To divide one fraction by another: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$
5. Conversion Between Fractions and Decimals:
To convert a fraction to a decimal, divide the numerator by the denominator:$\frac{a}{b} = a \div b$
To convert a decimal to a fraction, write the decimal as a fraction with a power of 10 in the denominator, then simplify. For example, $ \left (0.75 = \frac{75}{100} = \frac{3}{4}\right )$.
Benefits of CBSE Class 7 Maths Chapter 2 Important Questions
There are several benefits of solving CBSE Class 7 Maths Important Questions. They are:
These important questions are made by our experts referring to the CBSE syllabus, therefore, solving the CBSE Class 7 Maths Important Questions will help you to be more clear with the Math topics, formulas, and concepts.
These questions will help you prepare for the examination and you will be able to self-analyse your mistakes and work on them.
Solving these important questions will boost your confidence and you will be able to solve any sum easily.
CBSE Class 7 Maths Important Questions available at Vedantu are solved by our experts with 100% accuracy, therefore, you can completely rely on them for your preparation.
These important questions are available in PDF format which can be downloaded for free and students can access them anytime.
Conclusion
Vedantu's Important Questions for CBSE Class 7 Maths Chapter 2 - Fractions and Decimals are a great help for students who want to understand this important topic better. The carefully selected questions focus on key concepts, helping students develop their critical thinking and problem-solving skills. By exploring fractions and decimals, students gain the confidence to tackle more difficult maths problems. The engaging and interactive materials make learning enjoyable, encouraging students to do well in their studies and build a solid foundation for future maths. Vedantu truly shows its dedication to quality education through this helpful resource.
Important Study Materials for Class 7 Maths Chapter 2
CBSE Class 7 Maths Important Questions for All Chapters
Class 7 Maths Important Questions and Answers cover key topics, aiding in thorough preparation and making revision simpler.
Important Study Materials for Class 7 Maths
FAQs on CBSE Class 7 Maths Important Questions Chapter 2 - Fractions and Decimals
1. Do I need to practise all the questions provided in Chapter 2 of Class 7 Maths?
Practising all the questions provided in NCERT Solutions of Chapter 2 of Class 7 Maths ensures clear concepts and understanding of the applications of the various methods in solving the sums. Fractions and Decimals is a short chapter with a fair weightage in the exam. Hence, it is essential to grasp all the topics covered in this chapter to be well prepared and for better learning, regular practice is extremely important.
2. How many questions are there in NCERT Solutions Chapter 2 of Class 7 Maths?
Chapter 2 of Class 7 Maths has a total of six exercises with 42 questions. These questions are divided unevenly based on different methods for multiplication and division of fractions and decimals. Long questions have multiple steps that the students need to ensure are correct because each step holds some marks in the examinations. It is suggested that you make a habit of rechecking the solution while at the learning stage so you make fewer errors.
3. Where can I find ‘Important Questions’ for Chapter 2 of Class 7 Maths?
Vedantu provides you with important questions PDF free of cost. These questions include all the methods by which you can solve all the problems given in this particular chapter. You can also download the PDF of important questions, notes and other study materials from Vedantu website and mobile app. The important questions are the best way to prepare if you are running short on time since they cover all the fundamental topics and formulas.
4. How are ‘Important Questions’ for Chapter 2 of Class 7 Maths helpful?
Solving the important questions establishes basic clarity on the application for each type of problem in the chapter. It helps you revise better around the exams so you do not miss out on any kind of question that may be vital with respect to the exam. In case you are late in starting your preparation you can easily solve the important question to cover the majority of the course in a short span of time.
5. How should I prepare Chapter-Fractions and Decimals for Class 7 Maths?
Fractions and decimals in Class 7 is a relatively simple chapter. You should focus on learning the methods used in solving the questions. The chapter helps you revise the addition and subtraction of fractions and decimals and further introduces multiplication and division of the same. Practising all problems is the easiest way to prepare the chapter. Right before the exams is a time crunch for the students so, these important questions come in handy at the time.
6. Are solutions provided for these important questions?
Yes, detailed solutions accompany each question to help students understand the methods used to arrive at the answers.
7. What types of questions can I expect in this chapter?
You can expect various types of questions, including operations with fractions and decimals, word problems, and applications in real-life scenarios.
8. How often should I practise these important questions?
Regular practice is recommended, ideally several times a week, to strengthen your understanding and retention of the concepts.
9. Is there a strategy for effectively solving these questions?
Carefully read each question, identify the required operations, break down the problem, and refer to the solutions for guidance when needed.
10. Are these questions sufficient for my exam preparation?
While these questions provide a strong foundation, it’s also important to review the entire chapter and other resources for comprehensive preparation.
11. Will I find word problems among the important questions?
Yes, the set includes word problems that help students apply their knowledge of fractions and decimals to real-world situations.
12. Can I study these questions in a group?
Absolutely! Studying in groups can facilitate discussion, clarification of doubts, and a deeper understanding of the material.
13. How can I track my progress while practising these questions?
Keep a record of the questions you have completed and note any difficulties you encounter, allowing you to focus on those areas during revision.
