In a recent basketball game against the Dallas Wings, Minnesota Lynx star Napheesa Collier took 16 free throws and made 11 of them. The fraction, or proportion, of free throws she made is
\begin{equation*}
\frac{11}{16} = 11 \div 16 = 0.6875
\end{equation*}
To calculate Collier’s free throw percentage, we need to remember how percents work. Luckily, the word “percent” is very descriptive. The “cent” part means “hundred,” like 100 cents in a dollar or 100 years in a century. And, as usual, “per” means “for each.” Together, percent means “per hundred.” For example, the number 20% means 20 for each hundred. Written as a fraction it is \(\frac{20}{100}\text{.}\) Divide to get the decimal \(20 \div 100 = 0.20.\)
\begin{equation*}
\text{Think money: }20\%\text{ is like }20\text{¢ , and }0.20\text{ is like }\$0.20
\end{equation*}
Bottom line: 20%, \(\frac{20}{100}\text{,}\) and 0.20 mean exactly the same number.
\begin{equation*}
20\% = \frac{20}{100} = 20 \div 100 = 0.20
\end{equation*}
Since we divided by 100 to go from percentage to decimal, we can reverse this process and go from decimal to percentage by multiplying by 100. Check it out:
\begin{equation*}
0.20 \times 100 = 20\%
\end{equation*}
Back to Collier. She made 11 out of 16 free throws, which was \(0.6875\) of her free throws. Now we know
\begin{equation*}
0.6875 \times 100 = 68.75 \approx 68.8\%
\end{equation*}
Her free throw percentage that game was 68.8%. Collier’s free throw percentage for the season is actually much lower, at 48.1%. How many free throws out of 16 would we have expected she would make? We need to figure out what 48.1% of 16 is. First, we convert 48.1 to decimal by dividing by 100:
\begin{equation*}
48.1 \div 100 = 0.481
\end{equation*}
Next, we multiply that proportion by 16:
\begin{equation*}
0.481 \times 16 = 7.696
\end{equation*}
We can even do this calculation in just one step:
\begin{equation*}
48.1 \div 100 \times 16 = 7.696
\end{equation*}
Either way, would have expected Collier to make 7 or 8 of her free throws. So, 11 was a really good night. Turns out she scored 29 points that game with 7 rebounds.
Thang attended that Lynx-Wings game and ordered the hot chicken sandwich with pickles for $14.59. When she tapped her debit card to pay, the machine offered her three choices for tip: 10%, 15% or 20%. As you can check, the machine calculated that 10% tip would add $1.46, the 15% tip would add $2.19, and the 20% tip would add $2.92. Knowing that the concession staff that night was fundraising for a group she supports, Thang selected 20% and her total bill was \(14.59 + 2.92 = \$17.51\text{.}\)
Thang’s ticket was good for 10% off the purchase of Lynx merchandise from their website and there was free shipping, so she decided to buy a jersey normally priced at $99. Since 10% of $99 is
\begin{equation*}
0.10 \times 99 = 9.9
\end{equation*}
she knows that her discount will be $9.90. (I added the extra 0 at the end because $9.9 looked strange.) The net price for the jersey will be
\begin{equation*}
\$99 - \$9.90 = 99 - 9.9 = 89.1 = \$89.10
\end{equation*}
With the discount, Thang can buy the jersey for $89.10.
In general, we can find the result of a percent increase, like Thang’s sandwich plus tip, by calculating the percent and adding it to the original amount. And we can find the result of a percent decrease, like Thang’s on-sale jersey, by calculating the percent and subtracting it from the original amount.
