Writing Algebraic Expressions
Learn how to translate words and real-world situations into algebraic expressions using variables and operations.
Definition
Key Phrases to Know
| Operation | Key Words | Example Phrase | Expression |
|---|---|---|---|
| Addition () | sum, plus, more than, increased by, total | five more than a number | |
| Subtraction () | difference, minus, less than, decreased by, fewer | a number decreased by 3 | |
| Multiplication () | product, times, of, twice, triple | twice a number | |
| Division () | quotient, divided by, ratio, per | a number divided by 4 |
- "5 more than " means
- "5 less than " means (not )
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Worked Examples
Write an expression for: "The sum of a number and 12"
Identify the operation
"Sum" means addition () → Operation:
Identify the quantities
"A number" (unknown) and 12 → Variable and 12
Choose a variable
Let represent "a number" →
Write the expression
Sum means add: →
Answer:
Common Mistakes
Writing "5 less than " as instead of
Why it's wrong: "Less than" reverses the order! "5 less than " means start with and take away 5.
Correct: "5 less than " = . Think: "I have dollars and spend 5" leaves .
Forgetting to use parentheses when needed
Why it's wrong: "Twice the sum of and 3" needs parentheses to show you add first.
Correct: "Twice the sum of and 3" = , not
Confusing "a number" with a specific number
Why it's wrong: "A number" means an unknown value that should be a variable.
Correct: Always use a variable (, , ) when you see "a number," "some number," or "an unknown."
Interactive Visual
Balance Scale
Solution: x = 4
Interactive Sandbox
Expression Calculator
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Practice Problems
16 problemsWhich expression represents "the sum of a number and 8"?
Why It Matters
- Problem Solving: Real-world problems are written in words. To solve them, you must first translate them into mathematical expressions.
- Communication: Expressions let you describe patterns and relationships concisely. Instead of saying "add 5 to whatever number you have," you write .
- Programming: Every app, game, and website uses expressions. When a game calculates your score as "base points times bonus multiplier," that's !
- Science: Formulas like distance = speed time () are algebraic expressions describing how the world works.
Real World Applications
Shopping and Budgeting
Stores use expressions to calculate totals with discounts, tax, and multiple items.
Example:
If shirts cost 15 dollars each and you have a 10 dollar coupon, the cost for shirts is .
A streaming service charges 8 dollars per month plus a one-time 20 dollar setup fee.
Write an expression for the total cost after months.
Step 1: Write the mathematical expression
Monthly cost times months plus setup fee:
Sports Statistics
Athletes and coaches use expressions to track performance and predict outcomes.
Example:
If a basketball player scores points per game, their total after games is .
A runner improves by 30 seconds each week. Their initial time was 8 minutes (480 seconds).
Write an expression for their time after weeks of training.
Step 1: Write the mathematical expression
Initial time minus improvement per week times weeks:
Cooking and Recipes
Recipes are scaled using expressions when cooking for different numbers of people.
Example:
A recipe uses 2 cups of flour per person. For people, you need cups.
A pizza recipe needs 3 cups of cheese for every 2 pizzas, plus 1 extra cup for the crust.
Write an expression for the cheese needed for pizzas (where is even).
Step 1: Write the mathematical expression
Cheese per 2 pizzas times number of pairs plus extra:
Key Takeaways
- 1Algebraic expressions translate words into math using variables and operations
- 2Key words signal operations: sum (+), difference (-), product (x), quotient (/)
- 3Watch word order carefully: "5 less than " means , not
- 4Use parentheses to group operations: "twice the sum" =
- 5Variables represent unknown or changing quantities in real situations
Frequently Asked Questions
Glossary
- Algebraic expression
- A combination of numbers, variables, and operations (like )
- Variable
- A letter that represents an unknown or changing number (like , , or )
- Coefficient
- The number multiplied by a variable (in , the coefficient is 3)
- Constant
- A number without a variable (in , the constant is 5)
- Term
- A single part of an expression separated by + or - (in , the terms are and )