Chapter 4
Ratios, Percents, and Proportion
A photo enlarged for a poster keeps two units of width for every three of height. A map says one inch stands for five miles. A recipe that feeds four has to feed ten tonight. In each case you know exactly how the quantities compare, yet you still do not know how big any of them is. A ratio fixes the shape of a situation without fixing its size. That sounds like a shortcoming. It is closer to the reverse: a ratio keeps working long after the amounts it came from have changed.
What You'll Explore
5 lessons.
- Ratio Problems
A can of paint mixes blue and yellow three parts to five, and the ratio alone never says how much paint is in the can. What would you have to be told before you could name the two amounts, and how much can a total, a difference, or a second ratio each settle on its own?
- Conversion Factors
Sixty miles an hour and one mile a minute are the same speed, though the two numbers look nothing alike. Changing the units changes what you write down without changing the quantity itself. Here you will look into why a swap like that is allowed, and what shifts when the units are squared or cubed.
- Percent Problems
Prices rise twenty percent in the spring and fall twenty percent in the autumn. Is the tag back where it started? Discounts, tax, interest, and changes stacked one on top of another look like separate problems, and this lesson asks whether they are really one problem in different disguises.
- Direct and Inverse Proportion
Buy twice as many oranges and you pay twice as much. Split one prize among twice as many winners and each share halves. Both pairs are locked together, yet they move in opposite directions. This lesson asks what stays fixed in each case, and what happens once a third quantity joins in.
- Rate and Work Problems
One painter can finish a room in four hours and another needs six. Working side by side, do they finish in five? That guess is worth testing, and testing it leads into how jobs, journeys, and even a drain pulling against a tap behave when more than one thing is happening at once.