Complex Word Problems
Multi-step problems that combine ratio, percent and rate.
Key idea
Multi-step problems that combine ratio, percent and rate.
In depth
Multi-step problems need a plan: define unknowns, translate to equations or diagrams, solve in stages, and check each step against the story. Drawing a bar model or table often reveals the structure.
Worked example
A train goes 60 km/h for 2 h then 80 km/h for 1.5 h: 120 + 120 = 240 km total, average 240/3.5 ≈ 68.6 km/h.
Real-world uses
- Solving multi-step business questions, such as a price rise followed by a discount, in exams and work
Common mistake
Averaging 60 and 80 directly. Average speed is total distance over total time.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Complex Word Problems?
Multi-step problems that combine ratio, percent and rate. It is a topic at the advanced level in Arithmetic & Number Sense.
Where is Complex Word Problems used in real life?
Real-world examples: Solving multi-step business questions, such as a price rise followed by a discount, in exams and work.
What should I learn before Complex Word Problems?
Make sure you are comfortable with Number Sense Puzzles, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Complex Word Problems?
Averaging 60 and 80 directly. Average speed is total distance over total time.
How can I practise Complex Word Problems?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Complex Word Problems?
Move on to Financial Math Basics next.
Related advanced topics in Arithmetic & Number Sense
- Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
- Compound Interest – Interest earned on principal and past interest.
- Inverse Proportion – When one quantity doubles, the other halves.
- Rational Numbers – Numbers expressible as p/q with integers p, q, q≠0.
- Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
- Real Numbers – All rational and irrational numbers; the continuous number line.