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Math Word Problems Practice Quiz with a Step-by-Step Interactive Lesson
Use the quiz at the top of the page to practice math word problems (also called math story problems). This practice includes common real-life problem types: totals and differences, equal groups, rates, fractions, ratios, percents, geometry, and probability. If you want a refresher, click Start lesson to open a step-by-step problem-solving guide.
How this math word problems practice works
- 1. Take the quiz: answer the word problems at the top of the page.
- 2. Open the lesson (optional): learn a clear method to translate words into math and solve step-by-step.
- 3. Retry: return to the quiz and apply the strategy right away.
What you’ll learn in the math word problems lesson
Problem-solving steps & vocabulary
- Identify the unknown and the given information
- Track units (miles, students, dollars, \(\text{cm}^2\))
- Common keywords: total, difference, each, per, of
Translate words into math
- Choose the right operation: \(+\), \(−\), \( \times \), \( \div \)
- Write an equation that matches the story
- Use quick models: tables, bar models, and simple sketches
High-value word problem types
- Multi-step word problems (solve in parts)
- Fraction word problems and ratio & proportion
- Percent word problems and rate problems (speed, unit price, conversions)
Check your answer like a pro
- Estimate to see if the answer is reasonable
- Confirm the answer matches the question (not just a step)
- Verify the units and re-read the last sentence
Back to the quiz
When you’re ready, return to the quiz at the top of the page and keep practicing math word problems.
Problems
Lesson overview
Purpose: Learn a repeatable, step-by-step method for solving math word problems (story problems) with clear reasoning and correct units.
Success criteria
- Identify what the problem is asking (the unknown) and what information is given.
- Translate words into an equation using the correct operation(s): \(+\), \(−\), \( \times \), \( \div \).
- Solve one-step and multi-step word problems involving fractions, ratios, percents, and rates.
- Use geometry facts (area formulas, angle sums) inside word problems.
- Compute simple probabilities as \(\frac{\text{favorable outcomes}}{\text{total outcomes}}\).
- Check answers by estimating, using units, and re-reading the question.
Key vocabulary
- Quantity: a number with a unit (like \(30\) students or \(45\) miles per hour).
- Unit: what the number counts or measures (students, miles, dollars, \(\text{cm}^2\)).
- Rate: a ratio with different units (like miles per hour).
- Equation: a math sentence that models the situation.
Quick pre-check
Read the problem and represent the information
Learning goal: Identify the given information, the unknown, and the units — then represent the situation with a simple model (list, table, bar model, or quick sketch).
Key idea
Most word problems become much easier when you organize the story:
- What do I know? List the numbers with their units.
- What do I need? Write the exact question in your own words.
- How are the quantities related? Total? difference? equal groups? “per” rate?
Worked example
Example: A cyclist travels \(20\) miles in \(1\) hour and then \(30\) miles in the next hour. What is the total distance traveled?
Given: \(20\) miles, then \(30\) miles.
Unknown: total distance.
Because the cyclist traveled both distances, add them:
\(20 + 30 = 50\).
Answer: \(50\) miles.
Try it
Summary
- Write down what you know (numbers + units) and what you need (the unknown).
- Use a simple model (list, table, bar model, sketch) before you compute.
Choose the operation and write an equation
Learning goal: Decide which operation(s) match the story and write an equation that models the situation.
Key idea
Word problems often use “signal words,” but the safest method is to match the relationship:
- Total / in all / altogether → addition
- Difference / how many more / left → subtraction
- Each / per / equal groups → multiplication or division
- Of (like \(25\%\) of \(200\)) → multiplication
- Ratio (\(3:4\)) → scale both parts by the same factor
Worked example (ratio)
Example: In a class, the ratio of boys to girls is \(3:4\). If there are \(30\) boys, how many girls are there?
The ratio \(3:4\) means “for every 3 boys, there are 4 girls.”
If \(3\) parts equals \(30\), then \(1\) part is \(30 \div 3 = 10\).
Girls are \(4\) parts: \(4\times 10 = 40\).
Answer: \(40\) girls.
Try it
Summary
- Choose operations by matching the relationship (total, difference, each/per, of, ratio).
- Write an equation before you compute — it prevents many common mistakes.
Multi-step word problems and rate problems
Learning goal: Break multi-step problems into smaller steps and use rate formulas like \( \text{distance} = \text{rate} \times \text{time} \).
Key idea
- Multi-step: Solve one step at a time, and label each intermediate result.
- Rates: Keep units attached to numbers (miles/hour, dollars/item, etc.).
- For speed problems: \(\text{distance} = \text{rate} \times \text{time}\).
- For average speed: \(\text{average speed} = \frac{\text{total distance}}{\text{total time}}\).
Worked example
Example: A car travels at \(45\) miles per hour for \(3\) hours and then at \(60\) miles per hour for \(2\) hours. How far has the car traveled in total?
First part: \(45\times 3 = 135\) miles.
Second part: \(60\times 2 = 120\) miles.
Total distance: \(135 + 120 = 255\) miles.
Answer: \(255\) miles.
Try it
Worked solution
First leg: \(45\times 3 = 135\) miles.
Second leg: \(60\times 2 = 120\) miles.
Total: \(135+120 = 255\) miles.
Summary
- Multi-step word problems: solve one step at a time and keep track of units.
- Average speed depends on total distance and total time, not on averaging the two speeds.
Fractions, ratios, and proportion word problems
Learning goal: Scale ratios, solve “for every” problems, and compute fractions of a whole in word problem form.
Key idea
- Ratios: Multiply (or divide) both parts by the same number to keep the ratio equivalent.
- For every: signals a ratio relationship (like \(2:3\)).
- Fraction of a set: \(\frac{\text{part}}{\text{whole}}\).
Worked example (proportion)
Example: A recipe requires \(2\) cups of flour for every \(3\) cups of sugar. If you use \(10\) cups of flour, how much sugar should you use?
The flour ratio part is \(2\) and you have \(10\). That is a scale factor of \(10 \div 2 = 5\).
Scale the sugar part by the same factor: \(3\times 5 = 15\).
Answer: \(15\) cups of sugar.
Try it
Summary
- Proportions scale both sides of a ratio by the same factor.
- Fractions in word problems are usually “part over whole.”
Percent word problems
Learning goal: Find a percent of a quantity and find what remains — while keeping the meaning of “percent” clear.
Key idea
Percent means “per hundred.” So \(p\%\) equals \(\frac{p}{100}\). To find \(p\%\) of \(N\), compute: \[ \frac{p}{100}\times N \] Then use subtraction if the question asks for “how many are left” or “how many are present.”
Worked example
Example: A school has \(200\) students. If \(30\%\) of them are absent, how many students are present?
Absent: \(30\% \text{ of } 200 = 0.30\times 200 = 60\).
Present: \(200 - 60 = 140\).
Answer: \(140\) students are present.
Try it
Summary
- \(p\%\) means \(\frac{p}{100}\). Use multiplication to find a percent of a number.
- If the question asks what remains, subtract the part from the total.
Geometry word problems: area and angles
Learning goal: Use geometry formulas (area, angle sums) inside word problems and label units correctly.
Key formulas
- Rectangle area: \(A = \text{length}\times \text{width}\)
- Triangle area: \(A = \frac{1}{2}\times \text{base}\times \text{height}\)
- Triangle angles: \( \text{sum of angles} = 180^\circ \)
Worked example
Example: A rectangular field has a length of \(12\) units and a width of \(9\) units. What is the area of the field?
Use \(A = \ell \times w\):
\(A = 12\times 9 = 108\).
Answer: \(108\text{ square units}\).
Try it
Summary
- Geometry word problems often become “plug into a formula, then compute.”
- Always label squared units for area, and degrees for angles.
Probability word problems and checking your answers
Learning goal: Compute simple probabilities and use “reasonableness checks” to confirm your final answer matches the question.
Key idea (probability)
For equally likely outcomes: \[ P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{number of total outcomes}} \] If the event is “red or blue” (and you can’t pick both at once), add the favorable counts.
Worked example
Example: A box contains \(5\) red balls, \(8\) green balls, and \(12\) blue balls. What is the probability of selecting a red ball?
Total balls: \(5+8+12=25\).
Favorable outcomes (red): \(5\).
Probability: \(\frac{5}{25}=\frac{1}{5}\).
Answer: \(\frac{1}{5}\).
Try it
Final recap (a powerful checklist)
- Read: underline the question and identify the unknown.
- Organize: list the given numbers with units; draw a quick model.
- Plan: choose operations and write an equation.
- Solve: compute step-by-step and label units.
- Check: estimate, confirm units, and re-read the question.
Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill (rates, ratios, percents, geometry, or probability).