The ACT Math section includes various types of questions, and word problems can be particularly challenging. These problems require you to interpret written information and translate it into mathematical equations. To solve them efficiently, you need to understand the problem, apply problem-solving strategies, and manage your time effectively.
This guide outlines key strategies to help you approach word problems with confidence.
1. Read the Problem Carefully
Many mistakes occur because students misread or misinterpret the problem. To avoid this:
- Read the question thoroughly to understand what is being asked.
- Identify important details, such as quantities, relationships, and conditions.
- Watch for keywords that indicate mathematical operations. For example, “sum” suggests addition, “difference” suggests subtraction, “product” indicates multiplication, and “quotient” refers to division.
Example:
A store sells notebooks for 5 dollars each. A customer buys five notebooks and gets a 2-dollar discount. What is the total cost?
- The cost of five notebooks is found by multiplying the price of one notebook by the quantity.
- The discount is subtracted from the total cost.
- The correct answer is 23 dollars.
2. Break Down the Information
Complex word problems become easier when broken into steps:
- Identify known and unknown values.
- Assign variables to unknowns if necessary.
- Convert the information into a simple mathematical equation.
Example:
A train travels at 60 miles per hour for 2 hours, then at 50 miles per hour for 3 hours. What is the total distance traveled?
- Multiply the speed by the time for each part of the journey.
- Add both distances together to get the total.
- The final answer is 270 miles.
3. Convert Words into Equations
Recognizing how words translate into mathematical expressions is essential. Common conversions include:
- “More than” or “increased by” means addition.
- “Less than” or “decreased by” means subtraction.
- “Times” or “twice” suggests multiplication.
- “Divided by” or “per” indicates division.
Example:
A number is three more than twice another number. Their sum is 21. Find both numbers.
- Assign variables to represent the unknown numbers.
- Express the relationships in an equation.
- Solve step by step to find the values.
- The two numbers are 15 and 6.
4. Avoid Common Mistakes
Word problems often include unnecessary details or require unit conversions. To minimize errors:
- Ignore information that is not relevant to solving the problem.
- Ensure that all values are in the same units before performing calculations.
- Check whether your answer is reasonable by estimating.
Example:
A car travels 45 miles in 30 minutes. What is its speed in miles per hour?
- Convert 30 minutes into hours.
- Use the formula for speed by dividing distance by time.
- The correct speed is 90 miles per hour, not 45, which would be incorrect if the time was not converted.
5. Use Substitution and Estimation
If solving algebraically is difficult, try plugging in values or working backward from the answer choices.
Example:
A rectangular field is twice as long as it is wide. If the perimeter is 60 meters, what are its dimensions?
- Use the perimeter formula, which adds up all sides of the rectangle.
- Assign a variable to represent the width, and express the length in terms of that variable.
- Solve the equation step by step to find the width and length.
- The final answer is 10 meters for width and 20 meters for length.
6. Manage Time Effectively
Since the ACT Math section has 60 questions to be answered in 60 minutes, time management is crucial.
- If a problem seems too complex, skip it and return to it later.
- Solve the simpler problems first to secure easy points.
- If necessary, estimate answers instead of performing lengthy calculations.
Conclusion
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