Simple Expressions (Grade 5)
An expression in mathematics is a phrase made up of numbers, variables, and operation signs. Unlike an equation, an expression does not have an equals sign.
In Class 5, you learn to form simple expressions from word phrases, evaluate expressions by substituting values, and understand the parts of an expression.
Expressions are the building blocks of algebra. Knowing how to read and write them prepares you for solving equations and understanding formulas.
What is Simple Expressions - Class 5 Maths (Patterns and Algebra)?
An algebraic expression is a combination of numbers, variables, and operations (+, −, ×, ÷) written without an equals sign.
Examples of expressions:
- 3x + 5
- 2n − 7
- 4a + 2b
- y ÷ 3
Parts of an expression:
- Terms: The parts separated by + or − signs. In 3x + 5, the terms are 3x and 5.
- Coefficient: The number multiplied with a variable. In 3x, the coefficient is 3.
- Constant: A term without a variable. In 3x + 5, the constant is 5.
- Variable: The letter representing an unknown number.
Types and Properties
Types of Expressions:
- Numerical expression: Contains only numbers and operations. Example: 8 + 3 × 2.
- Algebraic expression: Contains at least one variable. Example: 5x − 3.
- Expression with one variable: Contains one letter. Example: 2n + 7.
- Expression with two variables: Contains two letters. Example: 3a + 2b.
Solved Examples
Example 1: Example 1: Forming an Expression
Problem: Write an expression for "7 more than a number."
Solution:
Let the number = n
"7 more than a number" = n + 7
Answer: n + 7
Example 2: Example 2: Expression for Subtraction
Problem: Write an expression for "a number decreased by 12."
Solution:
Let the number = x
Expression: x − 12
Answer: x − 12
Example 3: Example 3: Expression for Multiplication
Problem: Write an expression for "4 times a number, plus 3."
Solution:
Let the number = y
Expression: 4y + 3
Answer: 4y + 3
Example 4: Example 4: Evaluating an Expression
Problem: If a = 5, find the value of 3a + 8.
Solution:
Step 1: Replace a with 5: 3(5) + 8
Step 2: = 15 + 8 = 23
Answer: 23
Example 5: Example 5: Two-Variable Expression
Problem: If x = 4 and y = 3, find the value of 2x + 5y.
Solution:
Step 1: 2(4) + 5(3)
Step 2: = 8 + 15 = 23
Answer: 23
Example 6: Example 6: Real-Life Expression
Problem: Ria buys 'n' notebooks at ₹30 each and 1 pen for ₹15. Write an expression for the total cost.
Solution:
Cost of notebooks = 30n
Cost of pen = 15
Total = 30n + 15
If n = 4: Total = 30(4) + 15 = 120 + 15 = ₹135
Answer: Expression: 30n + 15
Example 7: Example 7: Identifying Parts
Problem: In the expression 7x − 4, identify the coefficient, variable, and constant.
Solution:
Coefficient: 7 (multiplied with x)
Variable: x
Constant: −4
Terms: 7x and −4
Answer: Coefficient = 7, Variable = x, Constant = −4
Example 8: Example 8: Expression from a Pattern
Problem: The pattern 4, 8, 12, 16, 20 can be written as 4n, where n = 1, 2, 3, ... Find the value when n = 15.
Solution:
Expression: 4n
When n = 15: 4 × 15 = 60
Answer: The 15th term = 60
Example 9: Example 9: Simplifying an Expression
Problem: Simplify: 3x + 2x + 5
Solution:
Step 1: Combine like terms: 3x + 2x = 5x
Step 2: Result: 5x + 5
Answer: 5x + 5
Example 10: Example 10: Perimeter Expression
Problem: A rectangle has length (x + 3) cm and breadth x cm. Write an expression for its perimeter.
Solution:
Perimeter = 2 × (length + breadth)
= 2 × (x + 3 + x) = 2 × (2x + 3) = 4x + 6
If x = 5: Perimeter = 4(5) + 6 = 26 cm
Answer: Perimeter = 4x + 6
Key Points to Remember
- An expression is a mathematical phrase with numbers, variables, and operations — no equals sign.
- Terms are the parts separated by + or − signs.
- The coefficient is the number in front of a variable (3 in 3x).
- A constant is a number without any variable (5 in 2x + 5).
- To evaluate an expression, replace each variable with its given value and calculate.
- Like terms have the same variable: 3x and 2x are like terms; 3x and 2y are not.
- Simplify by combining like terms.
Practice Problems
- Write an expression for "5 less than twice a number."
- If p = 6, find the value of 4p − 10.
- Write an expression for the cost of 'n' mangoes at ₹50 each.
- In the expression 8y + 3, identify the terms, coefficient, and constant.
- Simplify: 6a + 3a − 2.
- If x = 3 and y = 7, find the value of x + 2y.
- Aman buys 'a' apples at ₹15 each and 'b' bananas at ₹5 each. Write the total cost as an expression.
- Write the perimeter of a square with side 's' as an expression, then find it when s = 11 cm.
Frequently Asked Questions
Q1. What is the difference between an expression and an equation?
An expression has no equals sign (like 3x + 5). An equation has an equals sign (like 3x + 5 = 20). You evaluate expressions but solve equations.
Q2. What is a term in an expression?
A term is a part of the expression separated by + or − signs. In 4x + 3y − 7, the three terms are 4x, 3y, and −7.
Q3. What is a coefficient?
A coefficient is the number multiplied with a variable. In 5x, the coefficient is 5. If there is no number shown (like x), the coefficient is 1.
Q4. What does it mean to evaluate an expression?
It means substituting the given value of the variable and calculating the result. For example, if x = 4, then 2x + 3 = 2(4) + 3 = 11.
Q5. What are like terms?
Like terms have the same variable raised to the same power. 3x and 7x are like terms. 3x and 3y are not like terms.
Q6. Can an expression have more than one variable?
Yes. An expression like 2a + 3b has two variables, a and b. To evaluate it, you need values for both variables.
Q7. What is a constant?
A constant is a number without a variable. In the expression 5n + 8, the constant is 8. It does not change regardless of the value of n.
Q8. How do you simplify an expression?
Combine like terms. For example, 4x + 3x + 2 simplifies to 7x + 2. Only terms with the same variable can be combined.
