Learn Class 7 Maths Chapter 2.2 Reading and Evaluating Complex Expressions with easy explanations, solved examples, Figure It Out answers and practice questions.
Class 7 Maths Chapter 2.2 – Reading and Evaluating Complex Expressions
In Class 7 Mathematics Chapter 2.2, we learn how to read, understand and evaluate complex arithmetic expressions. Unlike simple expressions, complex expressions may contain several operations, positive and negative numbers, and brackets.
In this section, students will learn how to identify terms, understand the order of operations, use the commutative and associative properties of addition, and remove brackets without changing the value of an expression.
These concepts are important for developing strong mathematical reasoning and solving more complicated arithmetic problems.
1. Understanding Complex Arithmetic Expressions
Sometimes, an arithmetic expression contains more than one operation. For example:
- 30 + 5 × 4
- 18 + 6 × 3 − 5
- 40 − 12 + 8 × 2
When an expression contains multiple operations, we need to understand the correct way to evaluate it.
Example: Mallesh and Arun’s Marbles
Mallesh brought 30 marbles to a playground. Arun brought 5 bags containing 4 marbles each. How many marbles did they bring altogether?
Solution:
Marbles brought by Mallesh = 30
Number of bags brought by Arun = 5
Marbles in each bag = 4
Marbles brought by Arun:
5 × 4 = 20
Total marbles:
30 + 20 = 50
Expression: 30 + 5 × 4
Answer: 50 marbles
We multiply 5 by 4 first and then add 30.
2. Importance of Brackets in Expressions
Brackets are used to make the order of operations clear. When an expression contains brackets, evaluate the expression inside the brackets first.
For example:
30 + (5 × 4)
First, calculate the multiplication inside the brackets:
5 × 4 = 20
Now add 30:
30 + 20 = 50
Final Answer: 50
Another Example: Finding the Change
Irfan purchases a biscuit packet for ₹15 and a packet of dal for ₹56. He gives the shopkeeper ₹100. Find the change he receives.
Solution:
Cost of biscuits = ₹15
Cost of dal = ₹56
Money given = ₹100
Total shopping cost:
15 + 56 = 71
Change received:
100 − (15 + 56)
= 100 − 71
= ₹29
Answer: ₹29
We use brackets because the total cost of both items must be subtracted from ₹100.
3. What Are Terms in an Arithmetic Expression?
Terms are the parts of an arithmetic expression separated by addition signs (+).
For example:
12 + 7
The two terms are 12 and 7.
Consider another expression:
83 − 14
Subtraction can be written as addition of the negative number:
83 − 14 = 83 + (−14)
Therefore, the terms are 83 and −14.
More Examples of Identifying Terms
| Expression | Expression as a Sum of Terms | Terms |
|---|---|---|
| 13 − 2 + 6 | 13 + (−2) + 6 | 13, −2, 6 |
| 5 + 6 × 3 | 5 + 6 × 3 | 5, 6 × 3 |
| 4 + 15 − 9 | 4 + 15 + (−9) | 4, 15, −9 |
| 23 − 2 × 4 + 16 | 23 + (−2 × 4) + 16 | 23, −2 × 4, 16 |
| 28 + 19 − 8 | 28 + 19 + (−8) | 28, 19, −8 |
Important: A multiplication or division expression can form one complete term when it is not separated by an addition sign.
4. Commutative Property of Addition
The commutative property of addition states that changing the order of numbers being added does not change their sum.
For example:
6 + 4 = 10
4 + 6 = 10
Therefore:
6 + 4 = 4 + 6
This property also works when negative numbers are involved.
For example:
6 + (−4) = 2
(−4) + 6 = 2
Thus, the order of terms can be changed without changing the value of their sum.
5. Associative Property of Addition
The associative property of addition states that changing the grouping of three or more numbers being added does not change their sum.
For example:
(5 + 3) + 2 = 8 + 2 = 10
5 + (3 + 2) = 5 + 5 = 10
Therefore:
(5 + 3) + 2 = 5 + (3 + 2)
This property also works with negative numbers.
For example:
(−7 + 10) + (−11) = 3 − 11 = −8
−7 + (10 − 11) = −7 − 1 = −8
Both expressions have the same value.
6. Evaluating Expressions by Finding Their Terms
When an expression contains multiplication and division along with addition and subtraction, first evaluate the individual terms and then add them.
Example 1: Evaluate 30 + 5 × 4.
Solution:
First, calculate the multiplication:
5 × 4 = 20
Now add 30:
30 + 20 = 50
Answer: 50
Example 2: Evaluate 5 × (3 + 2) + 7 × 8 + 3.
Solution:
First, solve the expression inside the brackets:
3 + 2 = 5
Now calculate the multiplication terms:
5 × 5 = 25
7 × 8 = 56
Add the terms:
25 + 56 + 3 = 84
Answer: 84
7. Solving a Long Addition Without Starting Again
Suppose Manasa adds a long list of numbers and obtains 11,749. Later, she realises that she forgot to include the number 9,055.
Does she need to start the addition again?
Solution:
No. She can simply add the missing number to the previous total.
Previous total = 11,749
Forgotten number = 9,055
New total:
11,749 + 9,055 = 20,804
Answer: 20,804
This is possible because the order of addition does not change the sum.
8. More Expressions and Their Terms
Example: Restaurant Bill
Four friends order four dosas at a restaurant. Each dosa costs ₹23. They also give the waiter a tip of ₹5. Find the total amount.
Solution:
Cost of four dosas = 4 × 23 = ₹92
Tip = ₹5
Total amount = 4 × 23 + 5
= 92 + 5
= ₹97
Terms: 4 × 23 and 5.
Answer: ₹97
Example: Students Playing a Group Game
There are 33 students playing a game. Ruby sits out. The teacher asks the remaining students to form groups of 5.
Number of students playing = 33
Number of complete groups = 6
Students in six groups = 6 × 5 = 30
Students remaining = 33 − 30 = 3
Expression:
6 × 5 + 3
Terms: 6 × 5 and 3.
Example: Writing Expressions for Different Group Sizes
If the teacher calls out 4:
33 = 8 × 4 + 1
There are eight complete groups of four and one student remaining.
If the teacher calls out 7:
33 = 4 × 7 + 5
There are four complete groups of seven and five students remaining.
9. Writing Expressions Using Money
Kannan has to pay ₹432 using notes of ₹100, ₹50, ₹20 and ₹10, and coins of ₹5 and ₹1.
One possible representation is:
432 = 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1
Explanation:
- 4 notes of ₹100 = ₹400
- 1 note of ₹20 = ₹20
- 1 note of ₹10 = ₹10
- 2 coins of ₹1 = ₹2
Total = 400 + 20 + 10 + 2 = ₹432
Another representation is:
432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1
Explanation:
- 8 notes of ₹50 = ₹400
- 1 note of ₹10 = ₹10
- 4 coins of ₹5 = ₹20
- 2 coins of ₹1 = ₹2
Total = ₹432
10. Removing Brackets – Part 1
We can sometimes remove brackets from an expression without changing its value. However, we must pay attention to the sign before the brackets.
Rule 1: Removing Brackets After a Plus Sign
When brackets are preceded by a plus sign, the signs of the terms inside the brackets remain unchanged.
For example:
28 + (35 − 10)
= 28 + 35 − 10
= 63 − 10
= 53
Rule 2: Removing Brackets After a Minus Sign
When brackets are preceded by a minus sign, the signs of the terms inside the brackets change.
For example:
200 − (40 + 3)
= 200 − 40 − 3
= 160 − 3
= 157
Notice that both signs inside the brackets become negative.
Another Example
500 − (250 − 100)
= 500 − 250 + 100
= 250 + 100
= 350
Remember: A minus sign before brackets changes the signs of all terms inside the brackets.
11. Removing Brackets – Part 2
Let us understand how brackets work when an expression contains a positive number and a negative number.
Example: Hira’s Coin Collection
Hira has 28 coins in one bag and 35 coins in another bag. She gives 10 coins from the second bag to her friend. Find the total number of coins remaining.
Solution:
Coins in the first bag = 28
Coins in the second bag = 35
Coins gifted = 10
Expression:
28 + (35 − 10)
Removing brackets:
= 28 + 35 − 10
= 63 − 10
= 53
Answer: 53 coins
When brackets are preceded by a plus sign, the signs of the terms inside them do not change.
Class 7 Maths Chapter 2.2 – Figure It Out Solutions
Question 1. Fill in the blanks with numbers and operation signs so that both sides are equal.
(a) 24 + (6 − 4) = 24 + 6 ____
Solution:
When brackets are preceded by a plus sign, the signs inside remain unchanged.
24 + (6 − 4) = 24 + 6 − 4
Answer: Minus (−)
(b) 38 + (____ ____ ) = 38 + 9 − 4
Solution:
The expression inside the brackets must be 9 − 4.
38 + (9 − 4) = 38 + 9 − 4
Answer: 9 and −
(c) 24 − (6 + 4) = 24 ____ 6 − 4
Solution:
When brackets are preceded by a minus sign, both signs inside change.
24 − (6 + 4) = 24 − 6 − 4
Answer: Minus (−)
(d) 24 − 6 − 4 = 24 − 6 ____ 4
Solution:
The expression remains unchanged.
24 − 6 − 4 = 24 − 6 − 4
Answer: Minus (−)
(e) 27 − (8 + 3) = 27 ____ 8 ____ 3
Solution:
Change both signs inside the brackets because the brackets have a minus sign before them.
27 − (8 + 3) = 27 − 8 − 3
Answer: Minus (−), Minus (−)
(f) 27 − (____ ____) = 27 − 8 + 3
Solution:
The expression inside the brackets is 8 − 3.
27 − (8 − 3) = 27 − 8 + 3
Answer: 8 and −
Question 2. Remove the brackets and write an expression having the same value.
(a) 14 + (12 + 10)
Solution:
14 + (12 + 10) = 14 + 12 + 10
= 36
Answer: 14 + 12 + 10
(b) 14 − (12 + 10)
Solution:
14 − (12 + 10) = 14 − 12 − 10
= 2 − 10
= −8
Answer: 14 − 12 − 10
(c) 14 + (12 − 10)
Solution:
14 + (12 − 10) = 14 + 12 − 10
= 26 − 10
= 16
Answer: 14 + 12 − 10
(d) 14 − (12 − 10)
Solution:
14 − (12 − 10) = 14 − 12 + 10
= 2 + 10
= 12
Answer: 14 − 12 + 10
(e) −14 + (12 − 10)
Solution:
−14 + (12 − 10) = −14 + 12 − 10
= −2 − 10
= −12
Answer: −14 + 12 − 10
(f) 14 − (−12 − 10)
Solution:
14 − (−12 − 10) = 14 + 12 + 10
= 36
Answer: 14 + 12 + 10
Question 3. Find the values of the expressions. Decide whether each pair has the same value.
(a) (6 + 10) − 2 and 6 + (10 − 2)
First expression:
(6 + 10) − 2 = 16 − 2 = 14
Second expression:
6 + (10 − 2) = 6 + 8 = 14
Answer: Both expressions are equal. Their value is 14.
(b) 16 − (8 − 3) and (16 − 8) − 3
First expression:
16 − (8 − 3) = 16 − 5 = 11
Second expression:
(16 − 8) − 3 = 8 − 3 = 5
Answer: The expressions are not equal. Their values are 11 and 5.
(c) 27 − (18 + 4) and 27 + (−18 − 4)
First expression:
27 − (18 + 4) = 27 − 22 = 5
Second expression:
27 + (−18 − 4) = 27 + (−22) = 5
Answer: Both expressions are equal. Their value is 5.
Question 4. Identify expressions having the same value without evaluating all of them.
(a) 319 + 537, 319 − 537, −537 + 319, 537 − 319
Solution:
We know that changing the order of terms in addition does not change the sum.
319 − 537 can be written as:
319 + (−537)
−537 + 319 has the same two terms in a different order.
Therefore:
319 − 537 = −537 + 319
Their common value is −218.
The other expressions are not equal to this pair.
(b) Identify equal expressions from the following collection.
- 87 + 46 − 109
- 87 + (46 − 109)
- 87 − (−46 + 109)
- 87 − 46 + 109
- 87 − (46 + 109)
- (87 − 46) + 109
Solution:
First, consider the original expression:
87 + 46 − 109 = 133 − 109 = 24
Now:
87 + (46 − 109) = 87 − 63 = 24
87 − (−46 + 109) = 87 − 63 = 24
Therefore, these three expressions have the same value:
- 87 + 46 − 109
- 87 + (46 − 109)
- 87 − (−46 + 109)
Also:
87 − 46 + 109 = 41 + 109 = 150
(87 − 46) + 109 = 41 + 109 = 150
These two expressions form another equal pair.
Answer: The first three expressions are equal, and the fourth and sixth expressions are equal.
Question 5. Add brackets at appropriate places so that the expressions have the given values.
(a) 34 − 9 + 12 = 13
Solution:
Place brackets around 9 + 12.
34 − (9 + 12)
= 34 − 21
= 13
Answer: 34 − (9 + 12) = 13
(b) 56 − 14 − 8 = 34
Solution:
Place brackets around 14 + 8.
56 − (14 + 8)
= 56 − 22
= 34
Answer: 56 − (14 + 8) = 34
(c) −22 − 12 + 10 + 22 = −22
Solution:
Place brackets around 12 + 10.
−22 − (12 + 10) + 22
= −22 − 22 + 22
= −22
Answer: −22 − (12 + 10) + 22 = −22
Question 6. Fill in the blanks using reasoning about how terms change.
(a) 423 + ____ = 419 + ____
Solution:
The first number on the left is 4 greater than the first number on the right.
To keep both expressions equal, the second number on the right must be 4 greater than the second number on the left.
One possible answer is:
423 + 4 = 419 + 8
= 427
Answer: 423 + 4 = 419 + 8
There are other correct answers as well.
(b) 207 − 68 = 210 − ____
Solution:
207 is 3 less than 210.
To keep the difference equal, we must also increase the number being subtracted by 3.
68 + 3 = 71
Therefore:
207 − 68 = 210 − 71
= 139
Answer: 71
Question 7. Use the numbers 2, 3 and 5 with addition, subtraction and brackets to generate as many different values as possible.
Solution:
We can arrange the three numbers in different orders and use addition and subtraction to obtain different values.
- 2 + 3 + 5 = 10
- 2 + 3 − 5 = 0
- 2 − 3 + 5 = 4
- 3 + 5 − 2 = 6
- 3 − (5 + 2) = −4
- 2 − (3 + 5) = −6
The different values obtained are:
−6, −4, 0, 4, 6 and 10
Answer: Six different values.
Question 8. Jasoda subtracts 9 by subtracting 10 and adding 1. Is her method always correct?
(a) Explain why her method works.
Solution:
Subtracting 9 is the same as subtracting 10 and then adding 1.
For example:
36 − 9
= 36 − 10 + 1
= 26 + 1
= 27
Answer: Yes, her method is always correct.
This works for any number because subtracting 10 and adding 1 has the same overall effect as subtracting 9.
(b) Give other similar strategies.
Solution:
We can use similar strategies to make calculations easier.
- Subtract 19 by subtracting 20 and adding 1.
- Subtract 29 by subtracting 30 and adding 1.
- Subtract 99 by subtracting 100 and adding 1.
- Add 19 by adding 20 and subtracting 1.
Examples:
85 − 19 = 85 − 20 + 1 = 66
145 − 99 = 145 − 100 + 1 = 46
48 + 19 = 48 + 20 − 1 = 67
Question 9. Identify the expressions having the same value.
Given expressions:
(a) 73 − 14 + 1
(b) 73 − 14 − 1
Compare them with the following expressions:
- (a) 73 − (14 + 1)
- (b) 73 − (14 − 1)
- (c) 73 + (−14 + 1)
- (d) 73 + (−14 − 1)
Solution for Expression 1: 73 − 14 + 1
73 − 14 + 1 = 59 + 1 = 60
Now check the options:
73 − (14 − 1) = 73 − 13 = 60
73 + (−14 + 1) = 73 − 13 = 60
Answer: Options (b) and (c).
Solution for Expression 2: 73 − 14 − 1
73 − 14 − 1 = 59 − 1 = 58
Now check the options:
73 − (14 + 1) = 73 − 15 = 58
73 + (−14 − 1) = 73 − 15 = 58
Answer: Options (a) and (d).
Important Rules to Remember
- Terms are the parts of an expression separated by addition signs.
- Subtraction can be written as addition of a negative number.
- The commutative property allows us to change the order of terms in addition.
- The associative property allows us to change the grouping of terms in addition.
- When brackets are preceded by a plus sign, the signs inside the brackets remain unchanged.
- When brackets are preceded by a minus sign, the signs inside the brackets change.
- Always evaluate the expression inside brackets first.
Common Mistakes Students Should Avoid
- Changing signs incorrectly: A minus sign before brackets changes every sign inside the brackets.
- Confusing terms: Multiplication expressions such as 5 × 4 can be one complete term.
- Ignoring negative numbers: Remember that subtracting a number is equivalent to adding its negative.
- Incorrect grouping: Changing brackets in subtraction can change the value of an expression.
- Rushing calculations: Solve each expression step by step and check the final result.
Additional Practice Questions
Try these original questions to test your understanding of complex expressions.
Question 1. Identify the terms.
- 25 − 8 + 12
- 10 + 4 × 5
- 35 − 6 × 3 + 9
- 50 + 20 ÷ 4 − 7
Question 2. Remove the brackets.
- 25 + (12 − 5)
- 40 − (15 + 8)
- 60 − (25 − 10)
- −12 + (8 − 4)
Question 3. Find the values.
- (12 + 8) − 5
- 25 − (10 − 4)
- 18 + (−7 + 3)
- 50 − (20 + 15)
Answers to Additional Practice Questions
Question 1 – Terms:
- 25, −8, 12
- 10, 4 × 5
- 35, −6 × 3, 9
- 50, 20 ÷ 4, −7
Question 2 – Removing Brackets:
- 25 + 12 − 5
- 40 − 15 − 8
- 60 − 25 + 10
- −12 + 8 − 4
Question 3 – Values:
- 15
- 19
- 14
- 15
Frequently Asked Questions
1. What are terms in arithmetic expressions?
Terms are the parts of an arithmetic expression separated by addition signs. For example, the terms in 12 − 5 + 8 are 12, −5 and 8.
2. What is the commutative property of addition?
The commutative property states that changing the order of numbers being added does not change their sum. For example, 5 + 8 = 8 + 5.
3. What is the associative property of addition?
The associative property states that changing the grouping of numbers being added does not change the sum. For example, (2 + 3) + 4 = 2 + (3 + 4).
4. What happens when brackets are preceded by a plus sign?
The signs of the terms inside the brackets remain unchanged when the brackets are removed.
5. What happens when brackets are preceded by a minus sign?
The signs of all terms inside the brackets change when the brackets are removed.
6. Why are brackets used in arithmetic expressions?
Brackets help specify which operations should be performed together and make the meaning of an expression clearer.
7. How can subtraction be written as addition?
Subtraction can be written as addition of the negative number. For example, 15 − 7 = 15 + (−7).
Chapter 2.2 – Quick Revision
In this section, we learned how to identify terms, evaluate complex expressions, use the commutative and associative properties of addition, and remove brackets correctly.
Practise the solved questions and additional exercises to strengthen your understanding before moving to the next subchapter.
Continue Learning Class 7 Mathematics
Continue studying the next section of Chapter 2 to learn more about arithmetic expressions and their mathematical properties.