Where this sits. This is one of the five number families — the arithmetic that a little under half the test is made of, and that every algebra family is built out of. Every family page on this site has the same eight parts, in the same order, so once you know the shape of one you know the shape of all of them. Where a part is empty, it says so.
Start hereRatio, Proportion, and PercentIf ratios, proportions or percents are new, begin with this page. It introduces all three from the beginning, one step at a time, with practice in every part. The six quizzes and the practice sheet below go further.Open Ratio, Proportion, and Percent → DrillsTwenty-one drills for this family, one skill each, ten problems at a timeGo to the drills ↓“Per hundred,” and the art of scaling: discounts, tax, tips, interest, unit prices, a recipe doubled, “3 out of every 5,” a map scale.
This family is the test’s workhorse — more everyday questions live here than anywhere outside algebra — and proportion is also the tool that solves similar triangles later, in geometry. Six quizzes cover it, in two legs.
What the test asks in this family
- What percent meansRatio, Proportion, and Percent · Quiz 17 · Percents and Proportion Practice
- Percent, decimal, and fraction as the same numberRatio, Proportion, and Percent · Quiz 17 · Percents and Proportion Practice
- The three percent questionsRatio, Proportion, and Percent · Quiz 18 · Percents and Proportion Practice
- Percent increase and decreaseRatio, Proportion, and Percent · Quiz 19 · Percents and Proportion Practice
- Percent changeRatio, Proportion, and Percent · Quiz 19 · Percents and Proportion Practice
- Tax, tip, and discountRatio, Proportion, and Percent · Quiz 19 · Percents and Proportion Practice
- Simple interestQuiz 19 · Percents and Proportion Practice
- Ratios, and what they compareRatio, Proportion, and Percent · Quiz 23 · Percents and Proportion Practice
- Rates and unit ratesRatio, Proportion, and Percent · Quiz 23 · Percents and Proportion Practice
- Setting up a proportionRatio, Proportion, and Percent · Quiz 24 · Percents and Proportion Practice
- Cross-multiplying, and why it worksRatio, Proportion, and Percent · Quiz 24 · Percents and Proportion Practice
- Scale drawings and mapsRatio, Proportion, and Percent · Quiz 25 · Percents and Proportion Practice
- MixturesQuiz 25
- Telling when a situation is not proportional at allRatio, Proportion, and Percent · Quiz 25 · Percents and Proportion Practice
All 14 have something on this site.
Seven questions across this family — the one the test uses most. Type an answer and press Check. You get the reasoning for every one, right or wrong.
- What is 15% of 80? 12. Percent means per hundred, so 15% is 15⁄100, or 0.15. “Of” means multiply: 0.15 × 80 = 12. Every percent question turns into ordinary multiplication once you have written the percent as a decimal.
- 12 is what percent of 48? 25%. Here you are given the part and the whole and asked for the percent, which is the second of the three percent questions. Divide the part by the whole: 12 ÷ 48 = 0.25, and 0.25 is 25 per hundred. The hard part is never the arithmetic; it is spotting which number is the whole.
- A $60 coat is 25% off. What do you pay? $45. Two steps, and the second is where people stop too early. The discount is 25% of 60 = $15. But the question asks what you pay, not what you save, so subtract: 60 − 15 = 45. The shortcut skips the second step: if 25% comes off, you pay 75%, and 0.75 × 60 = 45.
- A price rises from $40 to $46. What is the percent increase? 15%. Percent change is always measured against what it started at. The change is $6, and 6 ÷ 40 = 0.15, so 15%. Dividing by 46 instead is the usual error — it answers a different question, about what fraction of the new price the rise was.
- Which is the better buy: 12 ounces for $3.60, or 20 ounces for $5.40? The 20-ounce. You cannot compare them until they are the same size, so find the price of one ounce each. 3.60 ÷ 12 = $0.30 an ounce; 5.40 ÷ 20 = $0.27 an ounce. That is what a unit rate is for — it puts two unlike things on the same footing.
- 3 pounds of coffee cost $7.50. What do 5 pounds cost? $12.50. Set up a proportion with the same kinds of thing in the same places: 7.50⁄3 = x⁄5. Cross-multiply and 3x = 37.50, so x = 12.50. Or find one pound first — $2.50 — and take five of them. Both are the same move.
- $400 is put in at 5% simple interest. How much interest after 3 years? $60. The formula is on the sheet they give you: I = Prt, where P is the principal, r the rate as a decimal, and t the time. So 400 × 0.05 × 3 = 60. Simple interest is charged on the original amount every year, which is what keeps it simple.
Missed one? Ratio, Proportion, and Percent under Work it by hand starts from the beginning. Six quizzes cover this family — three on percent and three on ratio and proportion — and they are all in Learn it just below. Percents and Proportion Practice under On paper has 162 problems, tax and discounts included.
Want more than these seven questions? Flyover I asks about all fourteen families in one sitting and ends in a grid that says where to start; Flyover II asks them again later, with different questions, so you can see what has moved.
- Quiz 17What Percent MeansPer hundred, and nothing more mysterious than that.
- Quiz 18The Three Percent QuestionsOnly three kinds get asked. Here they are.
- Quiz 19Percent in the WorldTax, tip, discount, interest, and increase.
- Quiz 23Ratios and Unit RatesComparing two amounts, and price per one.
- Quiz 24Setting Up and Solving ProportionsWriting the two fractions the right way round.
- Quiz 25Proportional Reasoning in the WorldRecipes, maps, scale drawings, and mixtures.
Quizzes 17 to 19 are the end of the Deep Sea Series; 23 to 25 are the whole of Out of All Proportion. If ratios and percents are new, start with Ratio, Proportion, and Percent, in the Start here box at the top of this page, which introduces all three from the beginning.
Twenty-one short drills, one skill each, in order. Each starts with two worked examples, then gives you ten problems (or five) and the reasoning for every answer. Each one prints, with the answer key on the last page. When you get all ten right, or all five right twice in a row, the drill gets a check mark on the Drills page.
- 5.01Write a ratio three ways, in the right order
- 5.02Simplify a ratio
- 5.03From a ratio to a fraction of the whole
- 5.04Equivalent ratios: fill in a ratio table
- 5.05Find a unit rate · calculator allowed
- 5.06Which is the better buy? · calculator allowed
- 5.07Are two ratios equal?
- 5.08Solve a proportion · calculator allowed
- 5.09Proportion word problems: recipes, maps, scale · calculator allowed
- 5.10Proportional or not?
- 5.11Percent to decimal, and back
- 5.12Percent to fraction, and back
- 5.13Find a percent of a number · calculator allowed
- 5.14What percent is one number of another? · calculator allowed
- 5.15Find the whole from a part and a percent · calculator allowed
- 5.16Percents in your head: 10%, 1%, 5%, 15%, 20%
- 5.17Sales tax and the total · calculator allowed
- 5.18Tips · calculator allowed
- 5.19Discounts and the sale price · calculator allowed
- 5.20Percent increase and decrease · calculator allowed
- 5.21Simple interest · calculator allowed
- Ratio, Proportion, and Percent · start here if ratios and percents are new: two ways to compare amounts, ratios and equivalent ratios, rates and unit prices, proportions and three ways to solve them, what percent means, the three percent questions, and percent change. Worked examples, places to practice, and fourteen questions at the end.
- Percents and Proportion Practice · 162 problems: percents, decimals and fractions; the three percent questions; percent change; tax, tips, discounts and simple interest; ratios, unit rates, the better buy, proportions, scale, and telling whether a table is proportional. Answer key at the end. Made to print.
- Khan Academy, math · free videos and practice. Search it for percent word problems, ratios and rates, proportions. These are the clips we start from in class.
- Math Antics · short, plain videos on the basics.
- Light & Salt Learning · free GED classes online, with playlists by topic.
- Get Sum Math · GED math on video, one topic at a time.
- Kaplan GED Test Prep and the McGraw-Hill Mathematical Reasoning Workbook · look up percents, ratios, and proportion in the contents of either.
On to measurement and units, where proportion does the work of every conversion: inches to feet is a proportion, and so is quarts to cups.