Questions and Answers
What is the ratio 16 to 40 written as a fraction in lowest terms?
2/5
What is the ratio 15 : 75 in lowest terms?
1 : 5
What is the ratio 175/250 written in word form and in lowest terms?
7 to 10
What is the ratio of dimes to pennies in a jar that contains 11 pennies and 8 dimes?
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What is the ratio of roses to the total number of flowers in a vase containing 12 tulips and 20 roses?
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Which rate represents Keisha walking 12 miles in 3 hours?
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Which rate represents Daniel reading 3 books in 2.5 weeks?
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What unit rate represents the 48 ounces in 3 bottles?
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What unit rate represents a printer printing 70 pages in 5 minutes?
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What unit rate describes a plane traveling 3300 miles in 6 hours?
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Which ratio is equivalent to 3 : 11?
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Which ratio is equivalent to 10 : 85?
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Which ratio is NOT equivalent to 24/36?
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Which ratio is proportional to 3/5?
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Which pair of ratios is proportional?
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What is the solution to the proportion n/18 = 5/9?
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What is the solution to the proportion 6/15 = x/20?
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What is the solution to the proportion 3/m = 12/15?
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How much does it cost to buy 5 stamps if twenty stamps cost $8.40?
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How many cups of flour are needed to make 6 servings if a recipe calls for 3 cups for 8 servings?
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What is 3/5 written as a decimal?
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What is 0.28 written as a fraction in simplest form?
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What is 5.61 written as a percent?
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What is 82.4% written as a decimal?
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What is 0.32% written as a decimal?
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What is 4/5 written as a percent?
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To the nearest tenth of a percent, what is 3/11 written as a percent?
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What is 3.25% written as a fraction in lowest terms?
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What fraction of people prefer a certain brand of toothpaste if a survey showed 62% prefer it?
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What is 2.3% written as a decimal?
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What is 28% of 75?
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Twenty-two is what percent of 55?
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Forty-five is 30% of what number?
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Which proportion can be used to find the amount of tax Ben will pay if he bought a camera for $90 and the tax rate is 6%?
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What percent of Lee's 40 e-mails were from her friend Cara if 8 were from her?
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What is the percent of increase from 50 to 90?
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What is the percent of decrease from 110 to 77?
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What is the percent of decrease in the number of cars at a dealership that dropped from 64 to 48?
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Study Notes
Ratios
- The ratio of 16 to 40 simplified is 2/5, with a greatest common factor (GCF) of 8.
- The ratio 15:75 reduces to 1:5, using a GCF of 15.
- Written as words, the ratio 175/250 is 7 to 10, with a GCF of 25.
- A jar with 11 pennies and 8 dimes has a ratio of dimes to pennies as 8 to 11.
- In a vase with 12 tulips and 20 roses, the ratio of roses to the total (32 flowers) is 5 to 8.
Unit Rates
- Keisha's walking rate is 12 miles in 3 hours (4 miles/hour).
- Daniel read 3 books in 2.5 weeks, yielding a rate of 3 books/2.5 weeks.
- 48 ounces in 3 bottles results in a unit rate of 16 ounces per bottle.
- A printer’s output of 70 pages in 5 minutes equates to 14 pages per minute.
- A plane's speed is 550 miles per hour after traveling 3300 miles in 6 hours.
Equivalent and Proportional Ratios
- An equivalent ratio to 3:11 is 15:55, with a GCF of 5.
- For 10:85, an equivalent form is 20/170, with a GCF of 2.
- The ratio 24/36 is not equivalent to 3/4.
- The ratio 12/20 is proportional to 3/5, with a GCF of 4.
- Ratios 7/14 and 20/40 are proportional to each other.
Solving Proportions
- For the proportion n/18 = 5/9, the solution is n = 10.
- In the proportion 6/15 = x/20, solving gives x = 8.
- The proportion 3/m = 12/15 leads to m = 3.75.
Percent and Cost Calculations
- The cost for 5 stamps, given that twenty stamps cost $8.40, is $2.10.
- A pastry recipe using 3 cups flour for 8 servings requires 2.25 cups for 6 servings.
Converting between Decimal, Fraction, and Percent
- 3/5 is expressed as the decimal 0.6.
- The decimal 0.28 simplifies to the fraction 7/25.
- Converting 5.61 gives 561% as a percent.
- 82.4% written as a decimal is 0.824.
- 0.32% is 0.0032 when converted to a decimal.
- The fraction 4/5 is represented as 80% when converted.
Percentages from Fractions
- 3/11 translates to approximately 27.3% when expressed as a percent.
- The decimal equivalent of 3.25% in fraction form is 13/400.
- A survey indicates that 62% prefer a specific toothpaste brand, simplifying to 31/50.
- Converting 2.3% results in a decimal of 0.023.
Finding Percentages and Increases/Decreases
- 28% of 75 equals 21.
- Twenty-two is 40% of 55.
- 45 is 30% of 150.
- The proportion x/90 = 6/100 calculates the tax on a $90 camera at a 6% tax rate.
- Out of Lee’s 40 emails, 20% (8 emails) were from Cara.
Percent of Change
- The percent increase from 50 to 90 is 80%.
- The percent decrease from 110 to 77 is 30%.
- A drop in cars from 64 to 48 signifies a percent decrease of 25%.
Studying That Suits You
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Description
Test your understanding of ratios, proportions, and percentages with these flashcards designed for DRHS Algebra. Each card presents a scenario requiring you to simplify ratios or express them in different forms. Perfect for quick review or study sessions!