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NCERT Solutions Class 7 Maths Chapter 2 Arithmetic Expressions
In Arithmetic Expressions Chapter 2 Mathematics Class 7, students are introduced to the ideas of algebraic expressions with varying combinations of numbers and arithmetic operations of addition, subtraction, multiplication and division.
These NCERT Solutions for Class 7 provide step-by-step explanations for all the exercises, making it easy for students to follow along. With solved examples and simple methods, students can practice each type of problem with confidence. Practicing NCERT Solutions from this chapter will help students improve their logical thinking and get better at solving math problems with accuracy.
1.0NCERT Solutions Class 7 Maths Chapter 2 Arithmetic Expressions – Download PDF
Looking for precise and comprehensive solutions for NCERT Solutions Class 7 Maths Chapter 2? Download free PDF solutions for the chapter Arithmetic Expressions, created to match the updated NCERT textbook.
2.0Key Concepts in Chapter 2: Arithmetic Expressions
Chapter 2 helps students understand how to form, simplify, and evaluate arithmetic expressions. Here's a detailed breakdown of the key concepts covered:
1. Introduction to Arithmetic Expressions
Arithmetic expressions combine numbers and operations like addition, subtraction, multiplication, and division.
These expressions help represent real-life problems mathematically.
2. Forming Expressions
Students learn to translate verbal statements into mathematical expressions.
Terms like “sum of”, “difference between”, and “product of” are introduced to form expressions correctly.
3. Terms, Factors, and Coefficients
Terms are parts of the expression separated by addition/subtraction signs.
Factors are the components that are multiplied in a term.
Coefficient is the numerical factor of a term involving a variable.
4. Types of Expressions
Monomial: One term
Binomial: Two terms
Polynomial: Multiple terms
5. Using Expressions Practically
Expressions can represent problems like total cost, area, perimeter, or age relationships.
6. Evaluating Expressions
Substituting a value for the variable to calculate the final answer.
7. Identities and Simplification
The chapter introduces simple identities and simplification rules.
Using the BODMAS rule to simplify expressions.
Avoiding common mistakes while simplifying.
8. Patterns in Expressions
Recognizing patterns like squares of numbers and applying expressions accordingly.
3.0NCERT Solutions for Class 7 Chapter 2 Arithmetic Expressions : All Exercises
Exercise 2.1
Exercise 2.1 from Chapter 2 introduces students to basic arithmetic expressions andteach how to evaluate them correctly. Students learn to balance expressions, compare values, and arrange expressions in increasing order. The exercise helps the students in building a strong foundation in understanding how different operations affect numerical values.
Key Concepts Covered:
- Understanding arithmetic expressions
- Evaluating expressions using basic operations
- Balancing expressions on both sides of an equation
- Comparing and arranging expressions based on their values
Exercise 2.2
Class 7 Maths NCERT Solutions Chapter 2 – Exercise 2.2 focuses on identifying terms within expressions and evaluating them using the correct order of operations. Students also learn to write mathematical expressions for real-life situations. Some examples including ticket costs, coin distributions, and measurements. This exercise looks to enhance the ability of the student to translate everyday scenarios into mathematical expressions.
Key Concepts Covered:
- Identifying terms in expressions
- Evaluating expressions step by step
- Writing expressions for real-life situations
- Understanding multiplication and division within expressions
Exercise 2.3
Exercise 2.3 introduces students to the role of brackets in expressions and how removing or rearranging brackets changes the value of an expression. Students analyse equivalent expressions and learn how to place brackets correctly to achieve a desired result. This helps strengthen understanding of operation rules in arithmetic expressions.
Key Concepts Covered:
- Role of brackets in arithmetic expressions
- Removing brackets correctly
- Identifying expressions with equal values
- Understanding how operations affect expression results
Exercise 2.4
Chapter 2, exercise 2.4 focuses on exploring the properties of operations. It mainly emphasises on the distributive property of multiplication over the properties of addition and subtraction. In this section, students practise rewriting of expressions and comparing expressions without fully calculating them. The exercise encourages logical reasoning and pattern recognition in arithmetic expressions.
Key Concepts Covered:
- Distributive property of multiplication
- Expanding expressions using brackets
- Comparing expressions using reasoning
- Understanding equivalent expressions
Exercise 2.5
In Exercise 2.5, the focus is on applying arithmetic expressions to practical and real-life problem-solving situations. Here, students create expressions for daily activities such as weekly supply calculations, savings over time, and motion-based scenarios like climbing distances. This exercise strengthens analytical thinking and helps students see how arithmetic expressions are used to represent real-world problems.
Key Concepts Covered:
- Writing expressions from word problems
- Interpreting real-life situations mathematically
- Evaluating expressions step by step
- Using arithmetic expressions to solve practical problems
4.0NCERT Class 7 Maths Chapter 2 Arithmetic Expressions: Detailed Solutions
Figure It Out-2.1
- Fill in the blanks to make the expressions equal on both sides of the sign: (a) (b) (c) (d) Sol. (a) Therefore, (b) Since Therefore, (c) Since Therefore, (d) Since Therefore,
- Arrange the following expressions in ascending (increasing) order of their values. (a) 67-19 (b) 67-20 (c) (d) (e) Sol. (a) (b) (c) (d) (e) Since Therefore, Thus,
Figure It Out-2.2
- Find the values of the following expressions by writing the terms in each case. (a) (b) (c) (d) (e) Sol. (a) Terms: , and 8 (b) Terms: , and 11 (c) Terms: , and 10 (d) Terms: (e) Terms:
- Write a story/situation for each of the following expressions and find their values. (a) (b) (c) Sol. (a) Story/Situation: Rahul had 89 stickers in his collection. His friend gifted him 21 more stickers for his birthday. Later, Rahul gave 10 of his stickers to his younger sister. Value: . (b) Story/Situation: There are 5 boxes, and each box contains 12 pencils. 6 pencils were removed from the boxes to be given to a friend. Value: . (c) Story/Situation: In a garden, there are 4 rows of flowerbeds, and each row has 9 plants. In another part of the garden, there are 2 rows of trees, and each row has 6 trees. Value: .
- For each of the following situations, write the expression describing the situation, identify its terms and find the value of the expression.
(a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa used the coins to start a business and doubled her coins. Princess Anna bought jewellery and has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have.
(b) A metro train ticket between two stations is ₹40 for an adult and ₹20 for a child. What is the total cost of tickets:
(i) for four adults and three children?
(ii) for two groups having three adults each?
(c) Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.
Sol. (a) Number of gold coins Princess Elsa got = 100 Number of gold coins Princess Anna got = 100 Princess Elsa used the coins to start the business and doubled her coins. So, the number of coins Princess Elsa has Princess Anna bought jewelry and has only half of the coins left. So, the number of coins Princess Anna has Therefore, the total number of gold coins Princess Elsa and Princess Anna have together Thus, the expression describing the above situation is Terms: Now, gold coins (b) (i) Metro train ticket for an gold coins adult So, the metro train ticket for four adults Metro train ticket for a child= ₹ 20 So, the metro train ticket for three children Therefore, the expression describing the total cost of tickets for four adults and three children is Terms: Now, = ₹220 (ii) Metro train ticket for an adult So, the metro train ticket for a group of three adults Therefore, the expression describing the total cost of tickets for the two groups having three adults each is . Terms: Now, (c) By observing the given picture, the total height of the window number of gaps number of grills number of borders Terms: Now,
Figure It Out-2.3
- Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal. (a) . (b) ) (c) 6-4 (d) (e) 8 3 (f) ) Sol. (a) (b) (c) (d) (e) (f)
- Remove the brackets and write the expression having the same value. (a) (b) (c) (d) (e) (f) Sol. (a) (b) (c) (d) (e)
- Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal? (a) and (b) and (16-8) - 3 (c) and Sol. (a) and and Clearly, Hence, the expressions in part (a) have the same value. (b) 16 - (8-3) and (16-8) - 3 and Hence, the expressions in part (b) do not have the same value. (c) and and Clearly, Hence, the expressions in part (c) have the same value.
- In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms. (a) , 537-319 (b) , Sol. (a)
Expressions having the same terms have equal values. Therefore, have the same value. (b)
Expressions having the same terms have equal values. Therefore, , have the same value. Also, 87-46+109 and (87-46) + 109 have the same value.
- Add brackets at appropriate places in the expressions such that they lead to the values indicated. (a) (b) (c) Sol. Here, the expressions with correctly placed brackets are (a) (b) (c)
- Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal. (a) (b) Sol. Here are the expressions with the correct values bases on reasoning. (a) (b) By analysing how numbers shift, we maintain balance in the equation without direct calculation.
- Using the numbers 2,3 and 5 , and the operators ' + ' and ' - ', and brackets, as necessary, generate expressions to give as many different values as possible. For example, and . Sol. Here are different expressions using the numbers, 2, 3 and 5 along with the operators ' + ' and ' - ' and brackets (i) (ii) (iii) (iv) (v)
- Whenever Jasoda has to subtract 9 from a number, she subtracts 10 and adds 1 to it. For example, . (a) Do you think she always gets the correct answer? Why? (b) Can you think of other similar strategies? Give some examples. Sol. (a) Yes, Jasoda always gets the correct answer. Her strategy works because subtracting 10 removes one extra than needed, so adding 1 afterward restores the correct value. Mathematically, her method follows [here, a is any number] This method is useful because subtracting 10 is often easier to calculate mentally than subtracting 9. (b) Similar strategies include Subtracting 99 Instead of subtracting 99, subtract 100 and add 1 e.g. We have, = 146 Adding 9 Instead of adding 9, add 10 and subtract 1 . e.g. We have, Multiplying by 5 Instead of multiplying by 5, multiply by 10 and divide by 2 . e.g. We have,
- Consider the two expressions: (a) , (b) . For each of these expressions, identify the expressions from the following collection that are equal to it. (i) (ii) (iii) (iv) Sol. Given expressions: and Now, (i) (ii) (iii) (iv) Hence, expressions (ii) and (iii) are equal to the expression 73-14+1, i.e. (a) and expressions (i) and (iv) are equal to the expression 73-14-1. i.e. (b)
Figure It Out-2.4
- Fill in the blanks with numbers, and boxes by signs, so that the expressions on both sides are equal. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) ) (n) ) (o) - (p) (__ ) Sol. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p)
- In the boxes below, fill '<', '>' or '=' after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out and not by evaluating the expressions. (a) (b) (c) (d) Sol. (a) Because, (b) Because, 18 and So, (c) Because, Clearly, (d)
- Here is one way to make 14 : . Are there other ways of getting 14? Fill them out below: (a) ) = 14 (b) + ) = 14 (c) + ) = 14 (d) + ) = 14 Sol. (a) (b) (c) (d)
- Find out the sum of the numbers given in each picture below in at least two different ways. Describe how you solved it through expressions.
(I)(II) Sol. For I: or For II: or
Figure It Out-2.5
- Read the situations given below. Write appropriate expressions for each of them and find their values. (a) The district market in Begur operates on all seven days of a week. Rahim supplies 9 kg of mangoes each day from his orchard and Shyam supplies 11 kg of mangoes each day from his orchard to this market. Find the amount of mangoes supplied by them in a week to the local district market. (b) Binu earns ₹ 20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses every month. What is the amount Binu will save by the end of a year? (c) During the daytime a snail climbs 3 cm up a post, and during the night while asleep, accidentally slips down by 2 cm . The post is 10 cm high, and a delicious treat is on its top. In how many days will the snail get the treat? Sol. (a) Supplies of mangoes by Rahim in the market each day Supplies of mangoes by Shyam in the market each day Total supplies of mangoes in the market on each day Therefore, total supplies of mangoes in the market in all 7 days (b) Binu's per month earning ₹ 20,000 Binu's total monthly expenditures = ₹ 5,000 on rent + ₹ 5,000 on food + ₹ 2,000 on other expenses Therefore, Binu's monthly savings = ₹ = ₹ 20,000 - ₹ 12,000 = ₹ 8,000 Thus, Binu's total yearly savings Hence, Binu will save ₹ 96000 by the end of the year. (c) Since the snail climbs 3 cm up the post in daytime and slips down by 2 cm at night. So, the distance climbed by the snail of the post in a day. The distance climbed in 7 days The height of the post is 10 cm . The distance climbed on the 8th day before slipping So, the snail will take 8 days to reach the top of the post and get the delicious treat
- Melvin reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the expressions below describes this scenario? (a) (b) (c) (d) (e) (f) (g) (h) Sol. Number of days in a week except Tuesday and Saturday Since Melvin reads a two-page story every day except Tuesday and Saturday. Therefore, number of stories read in a week So, number of stories read in 8 weeks or [Expression (b)] or [Expression (g)] Only expressions (b) and (g) describe this scenario.
- Find different ways of evaluating the following expressions: (a) (b) Sol. (a) OR (b) OR
- Compare the following pairs of expressions using '<', '>' or '=' or by reasoning. (a) (b) (c) (d) (e) (f) (g) (h) Sol. (a) ( All the terms on both sides are the same) (b) (c) (d) and (48-35) (e) (f) (g) (h)
- Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression which is equal to the given expression. (a) 83-37-12 (i) (ii) (iii) (iv) (b) (i) (ii) (iii) (iv) Sol. (a) 83-37-12=83-37-12+(1-1) (option (i)) OR (option (iv)) Hence, (i) and (iv) are equal to the given expression 83-37-12. (b) (iv) Rearrange the terms, and we get , which is equal to the given expression. Hence, (iv) is equal to the given expression .
- Choose a number and create ten different expressions having that value. Sol. Let us choose number 24 and create ten different expressions having that value i. ii. iii. iv. v. vi. vii. viii. ix. x.
5.0Key Features of NCERT Solutions Class 7 Maths Chapter 2 : Arithmetic Expressions
- Step-by-Step Explanation : Our experts explain every concept in a stepwise manner so students can understand the logic behind each answer.
- Visual Clarity : Wherever required, diagrams or structured formatting is provided to make expressions and calculations more understandable.
- Error-Free & Updated : The NCERT Solutions Class 7 Maths follow the latest 2025-26 NCERT syllabus and CBSE guidelines, ensuring full curriculum relevance.
- Covers All Exercises : Solutions for every question in every exercise—including challenging word problems and algebraic puzzles—are provided in a structured manner.
- Real-Life Connections : We help students relate abstract algebraic ideas to practical situations, such as calculating distance, money, age, and more.
- Free PDF Access : Students can easily download NCERT Solutions in PDF format and revise without the need for internet access—ideal for quick revisions..