In this section of Class 7 Mathematics, we learn about simple arithmetic expressions, their values and how to compare two or more expressions. We also learn how mathematical expressions can represent everyday situations such as spending money, buying things and counting objects.
Class 7 Maths Chapter 2.1 Simple Expressions – Introduction
Understanding simple expressions is important because these concepts form the foundation for learning more complex arithmetic expressions in the next sections.
1. What Are Arithmetic Expressions?
A mathematical phrase formed using numbers and arithmetic operations is called an arithmetic expression.
The four basic arithmetic operations are:
- Addition (+)
- Subtraction (−)
- Multiplication (×)
- Division (÷)
Examples of arithmetic expressions:
- 13 + 2
- 20 − 4
- 12 × 5
- 18 ÷ 3
Every arithmetic expression has a value. The value is the number obtained after performing the required operation.
Example 1: Find the value of 13 + 2.
Solution:
13 + 2 = 15
Therefore, the value of the expression is 15.
2. Writing Expressions for Everyday Situations
We can use arithmetic expressions to represent real-life situations. Let us understand this with an example.
Example: Mallika’s Lunch Expenses
Mallika spends ₹25 every day on lunch at school. Write an expression for the total amount she spends on lunch from Monday to Friday.
Solution:
Mallika spends ₹25 each day.
Number of school days = 5
Daily expense = ₹25
Total expense = Number of days × Daily expense
= 5 × 25
Answer: 5 × 25
The expression 5 × 25 represents five times ₹25.
Different Expressions Can Have the Same Value
We can represent the same number using different arithmetic expressions.
For example, the number 12 can be represented in the following ways:
- 10 + 2 = 12
- 15 − 3 = 12
- 3 × 4 = 12
- 24 ÷ 2 = 12
Although the expressions are different, their values are equal.
3. Comparing Arithmetic Expressions
We can compare arithmetic expressions using three mathematical symbols:
- = means equal to.
- > means greater than.
- < means less than.
To compare two expressions, we compare their values.
Example 1: Compare 10 + 2 and 7 + 1.
Solution:
First expression:
10 + 2 = 12
Second expression:
7 + 1 = 8
Since 12 is greater than 8:
10 + 2 > 7 + 1
Example 2: Compare 13 − 2 and 4 × 3.
Solution:
13 − 2 = 11
4 × 3 = 12
Since 11 is less than 12:
13 − 2 < 4 × 3
4. Comparing Expressions Without Complicated Calculations
Sometimes, we do not need to calculate the complete value of both expressions. We can compare them by observing the numbers and understanding how they change.
Example: Compare 1023 + 125 and 1022 + 128.
Solution:
Initially, Raja has 1023 marbles and Joy has 1022 marbles.
Therefore, Raja has 1 more marble than Joy.
Now, Raja receives 125 more marbles, while Joy receives 128 more marbles.
Joy receives 3 more marbles than Raja.
Since Joy started with 1 fewer marble but received 3 more marbles, Joy has 2 more marbles in total.
Therefore:
1023 + 125 < 1022 + 128
Example: Compare 113 − 25 and 112 − 24.
Solution:
Raja initially has 113 marbles, while Joy has 112 marbles.
Raja has 1 more marble than Joy.
However, Raja loses 25 marbles and Joy loses 24 marbles.
Raja also loses 1 more marble than Joy.
Thus, both have the same number of marbles remaining.
113 − 25 = 112 − 24
Class 7 Maths Chapter 2.1 – Figure It Out Solutions
Here are the step-by-step solutions to the Figure It Out questions from the Simple Expressions section.
Question 1. Fill in the blanks to make the expressions equal on both sides of the equals sign.
(a) 13 + 4 = ____ + 6
Solution:
First, calculate the left-hand side:
13 + 4 = 17
Now, the missing number plus 6 must equal 17.
Missing number = 17 − 6 = 11
Answer: 11
(b) 22 + ____ = 6 × 5
Solution:
Calculate the right-hand side:
6 × 5 = 30
Now:
22 + Missing number = 30
Missing number = 30 − 22 = 8
Answer: 8
(c) 8 × ____ = 64 ÷ 2
Solution:
Calculate the right-hand side:
64 ÷ 2 = 32
Therefore:
8 × Missing number = 32
Missing number = 32 ÷ 8 = 4
Answer: 4
(d) 34 − ____ = 25
Solution:
34 − Missing number = 25
Missing number = 34 − 25
= 9
Answer: 9
Final Answers – Question 1
| Part | Correct Answer |
|---|---|
| (a) | 11 |
| (b) | 8 |
| (c) | 4 |
| (d) | 9 |
Question 2. Arrange the following expressions in ascending order of their values.
The given expressions are:
- (a) 67 − 19
- (b) 67 − 20
- (c) 35 + 25
- (d) 5 × 11
- (e) 120 ÷ 3
Solution:
First, find the value of each expression.
(a) 67 − 19 = 48
(b) 67 − 20 = 47
(c) 35 + 25 = 60
(d) 5 × 11 = 55
(e) 120 ÷ 3 = 40
Now arrange the values from smallest to largest:
40, 47, 48, 55, 60
Therefore, the ascending order is:
120 ÷ 3 < 67 − 20 < 67 − 19 < 5 × 11 < 35 + 25
Final Answer – Question 2
120 ÷ 3, 67 − 20, 67 − 19, 5 × 11, 35 + 25
Question 3. Use >, < or = to compare the following expressions. Can you do it without complicated calculations?
(a) 245 + 289 ____ 246 + 285
Solution:
Compare the numbers:
In the second expression, the first number increases by 1, but the second number decreases by 4.
The total therefore decreases by 3.
So, the first expression is greater.
245 + 289 > 246 + 285
(b) 273 − 145 ____ 272 − 144
Solution:
The first expression starts with a number that is 1 greater, but it also subtracts a number that is 1 greater.
Both changes cancel each other.
273 − 145 = 272 − 144
(c) 364 + 587 ____ 363 + 589
Solution:
In the first expression, the first number is 1 greater, but the second number is 2 smaller.
The total becomes 1 smaller.
Therefore:
364 + 587 < 363 + 589
(d) 124 + 245 ____ 129 + 245
Solution:
Both expressions have 245 as the second number.
Compare the first numbers:
124 is smaller than 129.
Therefore:
124 + 245 < 129 + 245
(e) 213 − 77 ____ 214 − 76
Solution:
The second expression starts with a number that is 1 greater and subtracts a number that is 1 smaller.
Both changes make the second expression 2 greater than the first expression.
Therefore:
213 − 77 < 214 − 76
Final Answers – Question 3
| Part | Correct Symbol |
|---|---|
| (a) | > |
| (b) | = |
| (c) | < |
| (d) | < |
| (e) | < |
Important Points to Remember
- An arithmetic expression is a mathematical phrase formed using numbers and arithmetic operations.
- Every arithmetic expression has a value.
- Different expressions can have the same value.
- The symbol = means equal to.
- The symbol > means greater than.
- The symbol < means less than.
- Ascending order means arranging values from smallest to largest.
- We can sometimes compare expressions by observing how their numbers change, without calculating every value.
Common Mistakes to Avoid
- Confusing ascending and descending order: Ascending order means smallest to largest.
- Using the wrong comparison sign: Remember that the open side of the sign faces the greater value.
- Ignoring the operation: Addition, subtraction, multiplication and division produce different values.
- Comparing only the first numbers: Always consider the complete expressions before deciding which is greater.
- Making calculation errors: Recheck multiplication and division before comparing expressions.
Practice Questions – Simple Expressions
Try these additional questions to check your understanding of simple arithmetic expressions.
Question 1. Fill in the blanks.
- 15 + 5 = ____ + 8
- 30 + ____ = 8 × 5
- 9 × ____ = 81 ÷ 3
- 50 − ____ = 32
Question 2. Arrange in ascending order.
45 + 15, 80 ÷ 2, 9 × 6, 72 − 20, 100 ÷ 4
Question 3. Insert >, < or =.
- 125 + 75 ____ 130 + 70
- 90 − 25 ____ 89 − 24
- 12 × 5 ____ 70 − 10
- 144 ÷ 4 ____ 9 × 4
Practice Questions – Answers
Question 1:
- 12
- 10
- 3
- 18
Question 2:
100 ÷ 4 < 80 ÷ 2 < 45 + 15 < 9 × 6 < 72 − 20
Question 3:
- =
- =
- =
- =
Frequently Asked Questions
1. What is an arithmetic expression in Class 7 Maths?
An arithmetic expression is a mathematical phrase made using numbers and arithmetic operations such as addition, subtraction, multiplication and division.
2. What is the value of an expression?
The value of an expression is the result obtained after performing the required arithmetic operations.
3. Can two different arithmetic expressions have the same value?
Yes. For example, 10 + 2, 15 − 3, 3 × 4 and 24 ÷ 2 all have the same value, which is 12.
4. What is ascending order?
Ascending order means arranging numbers or expression values from the smallest to the largest.
5. Which symbols are used to compare arithmetic expressions?
The three comparison symbols are = (equal to), > (greater than) and < (less than).
Chapter 2.1 Simple Expressions – Quick Revision
In this section, we learned how to form arithmetic expressions, calculate their values, compare expressions and arrange expressions in ascending order. Practising these questions will help students understand the foundation of arithmetic expressions before moving to more complex expressions.