The lesson
This lesson teaches Writing Algebraic Expressions. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
From words to symbols
A variable is a letter that stands for an unknown number. "Five more than a number" becomes n + 5. "Three times a number, minus 7" becomes 3n − 7.
When you study from words to symbols, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Evaluating an expression
To evaluate, substitute the given value for the variable and simplify using the order of operations.
A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.
Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.
Evaluate 2x + 5 when x = 4.
- 1Substitute: 2(4) + 5.
- 2Multiply first: 8 + 5.
- 3Add: 13.
Why this matters
Writing Algebraic Expressions shows up constantly in turn word phrases into math, then plug in numbers to evaluate. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- From words to symbols
- Evaluating an expression
Video walkthrough
Writing Expressions with Variables
Turn word phrases like "five more than x" into algebra.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfWrite an expression for "a number plus 11."
Step-by-step solution
- 1Use a variable for the number, such as n.
- 2Plus 11 gives n + 11.
Exercise 2
Try it yourselfWrite an expression for "7 less than a number."
Step-by-step solution
- 1Let the number be x.
- 2"7 less than" means x − 7, not 7 − x.
Exercise 3
Try it yourselfEvaluate 4a − 6 when a = 5.
Step-by-step solution
- 1Substitute: 4(5) − 6.
- 2Multiply: 20 − 6 = 14.
Exercise 4
Try it yourselfWrite an expression for "twice a number, decreased by 3."
Step-by-step solution
- 1Twice a number is 2n.
- 2Decreased by 3 means subtract 3: 2n − 3.
Exercise 5
Try it yourselfEvaluate 3(x + 2) − x when x = 4.
Step-by-step solution
- 1Substitute: 3(4 + 2) − 4 = 3(6) − 4.
- 2Multiply: 18 − 4 = 14.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Writing Algebraic Expressions
Question 1 of 5
Write an expression for "twice a number plus 9."