Translating Words to Algebra

Translation is a word-by-word conversion. A handful of keywords map to operations: "is" means equals, "of" (with a fraction or percent) means multiply, "sum"/"more than"/"increased by" mean add, "difference"/"less than"/"fewer than" mean subtract, and "per"/"for each" signal division or a rate. The one phrase that trips everyone is "less than": "5 less than x" is x − 5, not 5 − x — the order flips. Start by writing "let x = …" for the unknown you want, express every other quantity in terms of it, then turn the sentence's main "is/equals" into an equals sign. Read the final question again before answering: a problem may make you solve for x but ask for 2x + 1. On the GRE, when the numbers are answer choices, it is often faster to plug a choice back into the words and check than to solve the equation forward — the choices are a resource, not just an endpoint.

✅ Solved examples

✏️ Practice — try these, take hints as needed

📝 Topic test — 8 questions

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