Let’s find percentages in general.
Is each statement true or false? Be prepared to explain your reasoning.
A school held a jump-roping contest. Diego jumped rope for 20 minutes.
Jada jumped rope for 15 minutes. What percentage of Diego’s time is that?
Lin jumped rope for 24 minutes. What percentage of Diego’s time is that?
Noah jumped rope for 9 minutes. What percentage of Diego’s time is that?
| time (minutes) | percentage | $\text{time} \div 20$ | ||
|---|---|---|---|---|
| row 1 | Diego | 20 | 100 | $\frac{20}{20} = 1\text{ }$ |
| row 2 | Jada | 15 | $\frac{15}{20} = \text{ }$ | |
| row 3 | Lin | 24 | $\frac{24}{20} = \text{ }$ | |
| row 4 | Noah | 9 | $\frac{9}{20} = \text{ }$ |
A restaurant has a sign by the front door that says, “Maximum occupancy: 75 people.” Answer each question and explain or show your reasoning.
Water makes up about 71% of the Earth’s surface, while the other 29% consists of continents and islands. 96% of all the Earth’s water is contained within the oceans as salt water, while the remaining 4% is fresh water located in lakes, rivers, glaciers, and the polar ice caps.
What percentage of 90 kg is 36 kg? One way to solve this problem is to first find what percentage 1 kg is of 90, and then multiply by 36.
From the table we can see that 1 kg is $\left(\frac{1}{90}\boldcdot 100\right) \%$, so 36 kg is $\left(\frac{36}{90}\boldcdot 100\right) \%$ or 40% of 90. We can confirm this on a double number line:
In general, to find what percentage a number $C$ is of another number $B$ is to calculate $\frac{C}{B}$ of 100%. We can find do that by multiplying: $$\frac{C}{B}\boldcdot 100 $$
Suppose a school club has raised \$88 for a project but needs a total of \$160. What percentage of its goal has the club raised?
To find what percentage \$88 is of \$160, we find $\frac {88}{160}$ of 100% or $\frac {88}{160} \boldcdot 100$, which equals $ \frac {11}{20} \boldcdot 100$ or 55. The club has raised 55% of its goal.
