How can I rewrite a word problem as an expression without solving anything?

First identify the quantity the problem wants you to represent. Give it a letter, and write down what that letter means. Then translate the actions or relationships in the description into operations. OpenStax examples use this general approach: assign a symbol to the unknown and translate the described operations into an expression. [S1]

For example, suppose a fictional craft table charges $4 per blank card, plus a one-time $3 setup fee. Let c mean the number of cards. The cost is 4c + 3: 4c is the per-card charge repeated c times, and + 3 adds the fixed fee. This is an expression, not a solved answer. The scenario and amounts here are invented examples, not real prices.

A useful check is to ask: “Have I represented the requested quantity, or have I gone on to answer something else?” If the prompt asks only for an expression, the job ends with the expression.

Translate the meaning, not just individual keywords. Identify the quantity that is being acted on, then use grouping if several words describe one chunk.

For example, “five less than twice a number” means take twice the number, then subtract five. If n is the number, write 2n - 5. But “twice the difference between a number and five” means form the difference first, then double it: 2(n - 5). The parentheses show that the entire difference is the input to multiplication.

You can read your expression back in ordinary words. 2(n - 5) says “twice the quantity n minus five,” while 2n - 5 says “twice n, then subtract five.” If your expression reads differently from the scenario, revise it before stopping. The examples illustrate translation; they do not supply a value for n.

An expression names or represents a quantity, such as m + 8. An equation says that one quantity equals another, such as m + 8 = 20. The equals sign makes a statement of equality; it is not needed just to write an expression. OpenStax distinguishes translating relationships into equations from the earlier work of identifying variables and representing quantities or relationships. For an expression-only task, use the variable and operations without adding an equality statement. [S2]

Suppose a fictional garden group has b bags of soil, with 6 kilograms in each bag, and uses 2 kilograms. The amount left is 6b - 2. That represents the quantity left for any value of b. Writing 6b - 2 = 16 would add another claim—that the amount left is 16 kilograms—which the description would need to give. Solving would go further still. If the prompt only asks for an expression, stop at 6b - 2.

Use this short template:

1. Target quantity: What quantity am I representing?
2. Variable: Let ___ mean ___ .
3. Known amounts: What fixed numbers or rates are given?
4. Operations: What is being added, subtracted, multiplied, or divided—and what quantity is each operation applied to?
5. Expression: Write the operations, adding parentheses where needed.
6. Stop check: Did I write only the requested expression, without an unsupported equals sign or a numerical answer?

Worked example: “A club packs x notebooks into each of 3 boxes, then adds 4 loose notebooks.” Let x be the number of notebooks in each box. Three boxes contain 3x; adding the loose notebooks gives 3x + 4. Read it back: “three times the notebooks per box, plus four.” That matches the description, so stop there. A variable is a placeholder, not a value to guess. If a problem does not specify enough information to express the requested quantity, note what is missing rather than inventing a number.