Percents
Your game download bar says 75%. A store sign says 20% off. At checkout, sales tax gets added. Different places, same idea: a percent is a way to say "out of 100."
What a percent is
Some percents show up all the time, so it pays to know them as fractions and decimals.
| Percent | Fraction | Decimal |
|---|---|---|
| 1% | $\frac{1}{100}$ | 0.01 |
| 10% | $\frac{1}{10}$ | 0.1 |
| 25% | $\frac{1}{4}$ | 0.25 |
| 50% | $\frac{1}{2}$ | 0.5 |
| 75% | $\frac{3}{4}$ | 0.75 |
| 100% | $1$ | 1 |
Look at the following grid that represents the plan of a recreation area in a shopping center. Each small square represents $1\%$ of the total. If the area shaded in…
Look at the following grid that represents the plan of a recreation area in a shopping center. Each small square represents $1\%$ of the total. If the area shaded in orange is reserved for arcade games, what percentage of the total does this area occupy? Express the result also as a simplified fraction.
Work out the following percentages mentally using the division strategies learned in class (divide by $2$ for $50\%$, by $4$ for $25\%$, and by $10$ for $10\%$): a)…
Work out the following percentages mentally using the division strategies learned in class (divide by $2$ for $50\%$, by $4$ for $25\%$, and by $10$ for $10\%$):
- a) $50\%$ of $84$ viewers in a live stream.
- b) $25\%$ of a $400$ ounce pizza.
- c) $10\%$ of a transit pass that costs $\$35$.
Finding a percent of a number
In an esports tournament, $20\%$ of the $150$ participants play on a tablet, while the rest do so on a computer. Calculate the exact number of players who use a tablet…
In an esports tournament, $20\%$ of the $150$ participants play on a tablet, while the rest do so on a computer. Calculate the exact number of players who use a tablet to compete.
The progress bar of your favorite video game indicates that $75\%$ of the total download has already been completed. If the complete file takes up a space of $40$ GB,…
The progress bar of your favorite video game indicates that $75\%$ of the total download has already been completed. If the complete file takes up a space of $40$ GB, how many gigabytes have already been downloaded?
A popular streamer has carried out a poll in his chat to decide which game to play today. Out of the $1200$ viewers who voted, $65\%$ chose "Minecraft" and the rest…
A popular streamer has carried out a poll in his chat to decide which game to play today. Out of the $1200$ viewers who voted, $65\%$ chose "Minecraft" and the rest preferred "Among Us". How many people voted for "Among Us"?
Finding what percent one number is of another
Sometimes you know the part and the whole, and you want the percent. Write the part over the whole as a fraction, then rewrite it as "out of 100."
Percents are also a fair way to compare. A $\$6$ discount on a $\$40$ pair of jeans is $\dfrac{6}{40} = \dfrac{15}{100} = 15\%$ off. To compare two discounts, find each one as a percent of its own price.
If you split a whole into parts, the percents of the parts add up to $100\%$. Use that as a quick check.
In a survey carried out in your 6th grade class, $18$ of the $30$ students have confirmed that they prefer horror movies to comedies. Calculate the percentage of…
In a survey carried out in your 6th grade class, $18$ of the $30$ students have confirmed that they prefer horror movies to comedies. Calculate the percentage of students who prefer horror movies.
Hint: You can first write the ratio as a fraction $\frac{18}{30}$ and then find an equivalent fraction with a denominator of $100$.
In a multiple-choice math exam with $40$ questions, a student has answered $28$ questions correctly, missed $8$, and left $4$ blank. Calculate the percentage of correct…
In a multiple-choice math exam with $40$ questions, a student has answered $28$ questions correctly, missed $8$, and left $4$ blank. Calculate the percentage of correct answers, incorrect answers, and unanswered questions out of the total. Check that the sum of the three percentages is $100\%$.
In a sale at a sports store, some sneakers that cost $\$85$ have a $20\%$ discount. On the other hand, a hoodie that cost $\$60$ has a discount of $\$12…
In a sale at a sports store, some sneakers that cost $\$85$ have a $20\%$ discount. On the other hand, a hoodie that cost $\$60$ has a discount of $\$12$. Which of the two items has a greater percentage discount? Justify your answer by calculating the percentage for the hoodie.
Finding the whole from a part
Now the other way around. You know a part and the percent it stands for, and you want the whole. Find the value of a "small piece" first (10%, 25%, or 1%), then build up to 100%.
Emma has uploaded a video to TikTok. In the first two hours, she has gotten $180$ "likes". If she knows that $12\%$ of the people who watch the video give it a "like",…
Emma has uploaded a video to TikTok. In the first two hours, she has gotten $180$ "likes". If she knows that $12\%$ of the people who watch the video give it a "like", how many views has the video had in total during those two hours?
In a survey carried out at your school about the use of social media, $45\%$ of the students prefer Instagram, $35\%$ prefer TikTok, and the remaining 48 students choose…
In a survey carried out at your school about the use of social media, $45\%$ of the students prefer Instagram, $35\%$ prefer TikTok, and the remaining 48 students choose other platforms. How many students are there in total at the school? How many of them prefer Instagram?
In the student council elections, candidate A obtained $30\%$ of the votes, candidate B obtained $25\%$, and candidate C received the rest of the votes. If candidate C…
In the student council elections, candidate A obtained $30\%$ of the votes, candidate B obtained $25\%$, and candidate C received the rest of the votes. If candidate C won with 27 more votes than candidate B, how many students voted in total? How many votes did each candidate receive?
Discounts and sales tax
At a store, a percent is usually applied to a price.
-
A discount is an amount taken off. Sale price $=$ original price $-$ discount.
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Sales tax is an amount added at the register. Total $=$ price $+$ tax.
In both cases the discount or the tax is a percent of the original price, so use "percent of a number."
Some sneakers that cost $\$60$ have a $15\%$ discount today. How many dollars do you save by buying them today? What is the final price you will pay for them?
Some sneakers that cost $\$60$ have a $15\%$ discount today. How many dollars do you save by buying them today? What is the final price you will pay for them?
When buying a new gaming keyboard online, the price shown is $\$40$ without taxes. If at checkout a $21\%…
When buying a new gaming keyboard online, the price shown is $\$40$ without taxes. If at checkout a $21\%$ sales tax is added, by how many dollars will the initial price increase?
The price of a laptop in a shop is $\$450$ excluding taxes. If a $21\%$ sales tax must be applied, what will be the final price we will have to pay for the laptop?
The price of a laptop in a shop is $\$450$ excluding taxes. If a $21\%$ sales tax must be applied, what will be the final price we will have to pay for the laptop?
Two percents in a row
Many problems use a percent twice: an extra discount on a sale price, or a percent of what is left. The rule: each percent is taken of the number you have at that moment.
When money is involved, round to the nearest cent. For example, 15% off a yearly price of $\$119.88$ gives $119.88 \times 0.85 = 101.898 \approx \$101.90$.
In a trendy sneaker store, a model that costs $85 \text{ \$}$ has a $20\%…
In a trendy sneaker store, a model that costs $85 \text{ \$}$ has a $20\%$ discount. However, as it is the last day of the sale, they apply an additional discount of $10\%$ on the already reduced price. What is the final price of the sneakers? Is it the same as applying a single discount of $30\%$? Justify your answer by calculating both cases.
In a theater with a capacity for $850$ people, today $12\%$ of the tickets have remained unsold. Of the tickets sold, $65\%$ were for adults and the rest for children…
In a theater with a capacity for $850$ people, today $12\%$ of the tickets have remained unsold. Of the tickets sold, $65\%$ were for adults and the rest for children under 18. How many children under 18 have attended the theater today?
A movie streaming service costs $9,99 \text{ \$}$ a month. If you decide to pay for the whole year at once, they offer you a $15\%…
A movie streaming service costs $9,99 \text{ \$}$ a month. If you decide to pay for the whole year at once, they offer you a $15\%$ discount. However, this month there is a special promotion and, on top of that already reduced annual price, they deduct a fixed $10 \text{ \$}$. How much will you save in total per year if you take advantage of both offers compared to paying month by month?
Undoing a percent: the price before tax
What if you know the final price with tax and need the price before tax? The tax was figured on the original price, so you cannot just take the tax percent off the total. Instead, notice that the total is $100\% + \text{tax}\%$ of the original, and use the "find the whole" method.
Alex has bought a computer to play his favorite video games. The final price he paid, including $21\%$ sales tax, was $1452 \text{ \$}…
Alex has bought a computer to play his favorite video games. The final price he paid, including $21\%$ sales tax, was $1452 \text{ \$}$. His friend tells him that the computer cost $1200 \text{ \$}$ before taxes. Is his friend right? Carry out the necessary calculations to find the pre-tax price (without sales tax) of the computer.
Back to the start: a 75% bar means $\frac{3}{4}$ of the file is done. A 20% sale means you pay 80% of the price. Sales tax means you pay more than 100%. They are all "out of 100."