Expressions using Letter-Numbers
What if a number is unknown or can change? This Class 7 Ganita Prakash chapter introduces algebra by letting letters stand for numbers. Students form expressions with these 'letter-numbers', evaluate them for given values, and use them to describe patterns and rules.
Learning objectives
- Use letters to represent numbers.
- Form algebraic expressions from situations.
- Identify terms and coefficients.
- Evaluate expressions for given values.
Key concepts
Letters as numbers
A letter such as x or n can stand for a number that is unknown or that can change — a variable. Writing 'a box of n pencils plus 2 loose pencils' as n + 2 captures the situation for any value of n. The letter behaves exactly like a number in calculations.
Forming expressions
We build algebraic expressions by combining letters and numbers with operations. 'Three times a number' is 3 × x, written 3x; 'five more than a number' is x + 5; 'a number halved' is x/2. The skill is translating words into these compact forms.
Terms and coefficients
An algebraic expression is made of terms separated by + or −. In 3x + 5, the terms are 3x and 5; the number multiplying the letter, here 3, is the coefficient. Knowing terms and coefficients helps in reading and later simplifying expressions.
Evaluating expressions
To evaluate an expression, we replace the letter with a given number and calculate. If x = 4, then 3x + 5 = 3 × 4 + 5 = 17. The same expression gives different values for different values of the letter, which is what makes it powerful.
Important formulas
Multiplication shorthand
3 × x is written 3x
Evaluate
substitute the value of the letter and calculate
Key definitions
- Variable
- A letter that stands for a number that is unknown or can change.
- Algebraic expression
- A combination of letters and numbers joined by operations.
- Coefficient
- The number multiplying a letter in a term, as 3 in 3x.
- Term
- A part of an expression separated by + or −.
Solved examples
Q1. Write 'seven more than a number x' as an expression.
Solution: x + 7.
Q2. Find the value of 2x + 3 when x = 5.
Solution: 2 × 5 + 3 = 13.
Q3. What is the coefficient of x in 4x − 1?
Solution: 4.
Common mistakes to avoid
- Reading 3x as 'three and x' instead of 'three times x'.
- Forgetting the order of operations when evaluating, e.g. 2x + 3.
- Confusing the coefficient with the constant term.
- Thinking a letter can only mean one fixed number.
Expressions using Letter-Numbers — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
A letter that stands for a number is called a:
Practice questions
Short answer
What is a variable?
A letter that stands for a number that is unknown or can change.
Write 'four more than twice a number x'.
2x + 4.
Evaluate 5x when x = 3.
5 × 3 = 15.
Long answer
Explain how letters are used to form expressions, with examples.
In algebra we use a letter, such as x or n, to stand for a number that is unknown or that can vary — this is called a variable. We then combine letters and numbers using the usual operations to form expressions that describe situations. For example, 'three times a number' is written 3x, 'five more than a number' is x + 5, and 'a number halved' is x/2. The letter behaves just like a number, so 3x means 3 multiplied by whatever x stands for. This lets a single short expression describe a rule for many different values.
What does it mean to evaluate an expression? Show with 3x + 5.
To evaluate an algebraic expression means to find its value for a particular value of the letter, by substituting that value and then calculating using the order of operations. For the expression 3x + 5: if x = 4, we replace x by 4 to get 3 × 4 + 5, then multiply first to get 12 + 5 = 17. If instead x = 0, we get 3 × 0 + 5 = 5. The same expression gives different values for different values of x, which is exactly why variables are useful for describing changing quantities.
HOTS (Higher Order Thinking)
A pattern uses 3n + 1 matchsticks for the n-th figure. How many for the 5th figure?
3 × 5 + 1 = 16 matchsticks.
For what value of x does x + x equal 2x? Explain.
For every value of x, because x + x always equals 2x — they are equal expressions.
Quick revision
Revision notes
- A variable is a letter standing for a number.
- 3 × x is written 3x; coefficient of x is 3.
- Terms are separated by + and −.
- Evaluate by substituting the value and using order of operations.
Key takeaways
- Letters let us describe rules for any number.
- Coefficient = number multiplying the letter.
- Evaluate by substitution.
Frequently asked questions
What does 3x mean?
Three times the number x.
What is a coefficient?
The number multiplying a variable, like 3 in 3x.
How do I evaluate an expression?
Replace the letter with its value and calculate.