BeginnerTopic 5 of 104Engineering Mathematics
Ratios, proportions and percentages
Scaling relationships used in mixing, gear ratios, efficiency and error reporting.
In depth
A ratio compares two quantities and a proportion states two ratios are equal. Percentages express a ratio per hundred. Direct proportion means y=kx, inverse proportion means y=k/x. They underlie scaling laws, gear ratios and efficiency.
Key points
- Percent change = (new-old)/old×100
- Efficiency = useful output / input
- Doubling a pipe diameter changes many quantities non-linearly
ExampleA gear pair with 20 and 60 teeth has ratio 3:1, so the output turns three times slower.
What is Ratios, proportions and percentages?
Scaling relationships used in mixing, gear ratios, efficiency and error reporting.
Why is it important to understand ratios, proportions and percentages?
Most engineering design is about scaling, so ratios and percentages let you transfer results from a test or a drawing to a real system.
What is the difference between a percentage change and a percentage point change?
A percentage change is relative to the starting value. A change from 10% to 15% is a 5 percentage point rise but a 50% increase.
How does a gear ratio affect torque?
Torque is multiplied by the ratio and speed is divided by it, ignoring losses. A 4:1 reduction gives roughly four times the torque.
How is Ratios, proportions and percentages used in practice?
Typical applications include choosing a gear ratio to get the speed and torque a motor needs, mixing concrete or fuel in a fixed proportion and stating the efficiency of a pump as a percentage of input power.
What should I learn before Ratios, proportions and percentages?
Study "Scientific notation" first (topic 4 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Ratios, proportions and percentages?
Percent change = (new-old)/old×100. Efficiency = useful output / input. Doubling a pipe diameter changes many quantities non-linearly.
Can you give an example of Ratios, proportions and percentages?
A gear pair with 20 and 60 teeth has ratio 3:1, so the output turns three times slower.
What comes after Ratios, proportions and percentages?
The next topic is "Algebraic manipulation", which builds directly on this one.
How difficult is Ratios, proportions and percentages?
It is classed as Beginner in Engineering Mathematics (topic 5 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.