ACT Math Translating Words Into Algebra: Convert English Into Equations Accurately

"Is" or "equals" becomes =. "More than" or "greater than" becomes >. "Less than" or "fewer than" becomes <. "Times" or "product" becomes ×. "Per" or "for every" becomes division. "Sum" becomes +. "Difference" becomes -. Example: "A number is 5 more than twice another number" becomes x=2y+5. "The cost per item times the number of items equals total cost" becomes (cost/item)×quantity=total. Memorize these key phrases and their algebraic equivalents. They appear in every word problem on the ACT.

Longer example: "The sum of three consecutive integers equals 30." Let x be the first integer. Sum: x+(x+1)+(x+2)=30. This equation captures the entire verbal statement once you translate each phrase.

Mistake 1: Confusing "more than" with "times." "5 more than a number" is x+5, not 5x. Mistake 2: Mixing up the order in subtraction. "5 less than a number" is x-5, not 5-x. Mistake 3: Forgetting to translate comparison inequalities. "At least 10" means ≥10, not =10. "At most 20" means ≤20. The subtle difference between "x more than y" (x+y) and "x times y" (x×y) trips up many students.

During practice, read a word problem and translate each phrase separately before combining them into an equation. This step-by-step approach prevents mixing up operations.

Problem 1: "A number is 7 more than another. Their sum is 23." Translate: x and x+7. Equation: x+(x+7)=23. Solve: 2x+7=23, 2x=16, x=8. Problem 2: "The product of two numbers is 24. One is 3 times the other." Translate: x and 3x. Equation: x×3x=24, 3x^2=24, x^2=8, x=2√2. Problem 3: "John is twice as old as Mary. Together they are 30." Translate: Mary=x, John=2x. Equation: x+2x=30, 3x=30, x=10 (Mary), 2x=20 (John). Problem 4: "A store sells apples for $2 each. If you buy 5, how much?" Translate: cost=2×5. Equation: cost=10. Problem 5: "The sum of consecutive odd numbers 1, 3, 5, 7 is what?" Translate: 1+3+5+7=16. Translate and solve each, showing the equation before solving.

Find 10 word problems from a practice test. For each, translate the verbal statement into an equation before solving. By the tenth problem, translation will feel automatic.

Word translation appears throughout ACT Math. Many students understand the math but set up equations wrong because they misread the verbal setup. Mastering phrase translation picks up 1-2 points because you'll set up equations correctly even if the math is complex.

Commit one week to drilling phrase translation. For every word problem you encounter, translate verbally into an equation before solving. By test day, translation will be automatic and you'll avoid costly setup errors.