1.3.3 Identifying and Representing Relationships

Compare your answer:

• As the base length increases by 1, the height decreases, but not by a steady amount.
• Multiplying the base length and the height gives 48. The area of each parallelogram is 48 square inches.
• $b·h=48$, or $\frac{48}{b}=h$ (or equivalent).
• The height varies inversely as $b$.

Compare your answer:

• The amount in dollars received by each winner is 300 divided by the number of winners.
• $a=\frac{300}{n}$, or $a·n=300$ (or equivalent), where $a$ is the dollar amount a winner receives and $n$ is the number of winners.
• The amount in dollars, $a$, varies inversely as $n$.

Compare your answer:

If 4 cups contain 32 fluid ounces, then 8 cups must contain 64 fluid ounces. Because there are 16 cups in 1 gallon and 16 is twice as much as 8, there must be 128 fluid ounces in a gallon.

• Multiplying the number of gallons by 128 gives the number of fluid ounces.
• $f=8·8·2·g$, or $f=128g$ (or equivalent), where $f$ is the number of fluid ounces and $g$ is the number of gallons.
• The number of fluid ounces, $f$, varies directly as the number of gallons, $g$.