Learn Class 7 Maths Chapter 2.2 Reading and Evaluating Complex Expressions with easy explanations, solved examples, Figure It Out answers and practice questions.
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.
Sometimes, an arithmetic expression contains more than one operation. For example:
When an expression contains multiple operations, we need to understand the correct way to evaluate it.
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.
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
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.
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.
| 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.
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.
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.
When an expression contains multiplication and division along with addition and subtraction, first evaluate the individual terms and then add them.
Solution:
First, calculate the multiplication:
5 × 4 = 20
Now add 30:
30 + 20 = 50
Answer: 50
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
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.
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
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.
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.
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:
Total = 400 + 20 + 10 + 2 = ₹432
Another representation is:
432 = 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1
Explanation:
Total = ₹432
We can sometimes remove brackets from an expression without changing its value. However, we must pay attention to the sign before the brackets.
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
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.
500 − (250 − 100)
= 500 − 250 + 100
= 250 + 100
= 350
Remember: A minus sign before brackets changes the signs of all terms inside the brackets.
Let us understand how brackets work when an expression contains a positive number and a negative number.
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.
Solution:
When brackets are preceded by a plus sign, the signs inside remain unchanged.
24 + (6 − 4) = 24 + 6 − 4
Answer: Minus (−)
Solution:
The expression inside the brackets must be 9 − 4.
38 + (9 − 4) = 38 + 9 − 4
Answer: 9 and −
Solution:
When brackets are preceded by a minus sign, both signs inside change.
24 − (6 + 4) = 24 − 6 − 4
Answer: Minus (−)
Solution:
The expression remains unchanged.
24 − 6 − 4 = 24 − 6 − 4
Answer: Minus (−)
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 (−)
Solution:
The expression inside the brackets is 8 − 3.
27 − (8 − 3) = 27 − 8 + 3
Answer: 8 and −
Solution:
14 + (12 + 10) = 14 + 12 + 10
= 36
Answer: 14 + 12 + 10
Solution:
14 − (12 + 10) = 14 − 12 − 10
= 2 − 10
= −8
Answer: 14 − 12 − 10
Solution:
14 + (12 − 10) = 14 + 12 − 10
= 26 − 10
= 16
Answer: 14 + 12 − 10
Solution:
14 − (12 − 10) = 14 − 12 + 10
= 2 + 10
= 12
Answer: 14 − 12 + 10
Solution:
−14 + (12 − 10) = −14 + 12 − 10
= −2 − 10
= −12
Answer: −14 + 12 − 10
Solution:
14 − (−12 − 10) = 14 + 12 + 10
= 36
Answer: 14 + 12 + 10
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.
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.
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.
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.
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:
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.
Solution:
Place brackets around 9 + 12.
34 − (9 + 12)
= 34 − 21
= 13
Answer: 34 − (9 + 12) = 13
Solution:
Place brackets around 14 + 8.
56 − (14 + 8)
= 56 − 22
= 34
Answer: 56 − (14 + 8) = 34
Solution:
Place brackets around 12 + 10.
−22 − (12 + 10) + 22
= −22 − 22 + 22
= −22
Answer: −22 − (12 + 10) + 22 = −22
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.
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
Solution:
We can arrange the three numbers in different orders and use addition and subtraction to obtain different values.
The different values obtained are:
−6, −4, 0, 4, 6 and 10
Answer: Six different values.
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.
Solution:
We can use similar strategies to make calculations easier.
Examples:
85 − 19 = 85 − 20 + 1 = 66
145 − 99 = 145 − 100 + 1 = 46
48 + 19 = 48 + 20 − 1 = 67
Given expressions:
(a) 73 − 14 + 1
(b) 73 − 14 − 1
Compare them with the following expressions:
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).
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).
Try these original questions to test your understanding of complex expressions.
Question 1 – Terms:
Question 2 – Removing Brackets:
Question 3 – Values:
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.
The commutative property states that changing the order of numbers being added does not change their sum. For example, 5 + 8 = 8 + 5.
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).
The signs of the terms inside the brackets remain unchanged when the brackets are removed.
The signs of all terms inside the brackets change when the brackets are removed.
Brackets help specify which operations should be performed together and make the meaning of an expression clearer.
Subtraction can be written as addition of the negative number. For example, 15 − 7 = 15 + (−7).
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 studying the next section of Chapter 2 to learn more about arithmetic expressions and their mathematical properties.
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