Article
Mathematical word problems can be challenging because they present calculations through sentences rather than directly showing an equation. Before solving the problem, you must understand what information is provided and what the question is asking you to find. For students preparing for the HESI A2, developing a consistent approach to word problems can improve accuracy and reduce unnecessary calculations.
1. Identify what the question is asking
Read the final sentence of the problem first. This helps you identify the unknown value. For example: "A student buys four notebooks at the same price. The total cost is $12. How much does each notebook cost?" The unknown is the price of one notebook. Let the price of one notebook be \(x\).
2. Identify the important information
The problem tells you: - Number of notebooks: 4 - Total cost: $12 - Price of each notebook: Unknown Since all four notebooks cost the same amount, multiplication can represent the total.
3. Translate words into mathematical operations
Certain words often suggest particular operations. Words or phrases Possible operation Sum, total, combined Addition Difference, less than, decreased by Subtraction Product, times, twice Multiplication Quotient, divided equally, per Division Is, equals, results in Equals sign These clues are helpful, but always consider the full sentence. For example, "5 less than a number" means \(x-5\), not \(5-x\).
4. Build an equation
Return to the notebook example. Four notebooks cost $12 in total. The equation is: \[ 4x=12 \] Divide both sides by 4: \[ x=\frac{12}{4}=3 \] Each notebook costs $3.
5. Solve problems involving more than one operation
Consider another example: "A number is multiplied by 3, and then 5 is added. The result is 20. Find the original number." Let the unknown number be \(x\). Translate the statement: \[ 3x+5=20 \] Subtract 5 from both sides: \[ 3x=15 \] Divide by 3: \[ x=5 \] The original number is 5.
6. Pay attention to percentages and proportions
Some word problems involve percentages. For example: "A jacket costs $80. It is discounted by 25%. What is the discount amount?" Convert 25% to a decimal: \[ 25\div100=0.25 \] Multiply by the original price: \[ 80\times0.25=20 \] The discount is $20. If the question asks for the final price, subtract the discount from the original amount: \[ 80-20=60 \]
7. Check whether your answer makes sense
After solving a word problem, return to the original statement. Ask yourself: - Did I answer the question that was asked? - Did I use the correct operation? - Did I include the correct units? - Is the answer reasonable? For instance, if four notebooks cost $12, an answer of $48 for one notebook should immediately raise a question.
8. Build confidence through practice
Practice translating short sentences into equations before attempting longer problems. You can begin with simple addition and multiplication problems, then progress to percentages, ratios, and multi-step equations. Do not rush to calculate. Correctly understanding the problem is often the most important step.
Final tip
Underline the quantities, circle the unknown, and write an equation before performing calculations. This simple routine can help you avoid many common word-problem mistakes. Practice question: Three times a number, minus 4, equals 17. What is the number? A. 5 B. 6 C. 7 D. 9 Answer: C. 7.
