Math Word Problems Practice Quiz with a Step-by-Step Interactive Lesson

Read the problem and represent the information

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

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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

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)

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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

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

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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

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)

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Summary

• Proportions scale both sides of a ratio by the same factor.
• Fractions in word problems are usually "part over whole."

Percent word problems

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

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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

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

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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

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 cannot pick both at once), add the favorable counts.

Worked example

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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.