



What is the ratio of perimeters of similar figures? What is the ratio of areas of similar figures?
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- Explain the relationship between two quantities in a direct proportion. What are inverse proportions?
- How do you calculate the scale factor? Give an example of using a scale factor to enlarge an image.
- Explain the trigonometric ratios (sine, cosine, tangent). How are ratios and proportions used in physics?
- Define variables appropriately.
- How do you simplify a ratio?
- Give examples of using ratios and proportions in business and finance (e.g., profit margins). How are ratios and proportions used in everyday cooking?
- How do you write a ratio?
- What does the graph of an inverse proportion look like? What are the key characteristics of a direct proportional relationship? What are the key characteristics of an inverse proportional relationship? How can you determine from a table of values if two quantities are directly proportional? How can you determine from a table of values if two quantities are inversely proportional? Write an equation that represents a direct proportion between x and y with a constant of proportionality k. Write an equation that represents an inverse proportion between x and y with a constant of proportionality k. If the scale on a blueprint is 1/4 inch = 1 foot, what is the actual length of a wall that measures 3 inches on the blueprint? If a map has a scale of 1 100,000, what actual distance does 1 cm on the map represent? A photograph is enlarged by a scale factor of 2.5. If the original photograph was 4 inches wide, what is the width of the enlarged photograph? A model airplane is built to a scale of 1 72. If the wingspan of the actual airplane is 36 feet, what is the wingspan of the model airplane in inches? What is the simplest form of the ratio 12 18? What is the simplest form of the ratio 25 40? Express the ratio 15 to 9 in simplest form. Express the ratio 32 is to 24 in simplest form. Write three ratios equivalent to 2 5. Write three ratios equivalent to 3 7. Find a ratio equivalent to 4 9 with a first term of 12. Find a ratio equivalent to 5 6 with a second term of 30. Which ratio is greater 3 4 or 5 7? Explain your reasoning. Which ratio is smaller 2 3 or 4 7? Explain your reasoning. Convert the ratio 3 8 to a fraction. Convert the ratio 7 10 to a fraction. Convert the fraction 2/5 to a ratio. Convert the fraction 9/11 to a ratio. Convert the ratio 1 4 to a percentage. Convert the ratio 3 5 to a percentage. Convert the percentage 25% to a ratio in simplest form. Convert the percentage 60% to a ratio in simplest form. Compare the ratios 2 3 and 4 6. Are they equivalent? Compare the ratios 1 2 and 3 5. Are they equivalent? In a recipe, the ratio of flour to sugar to butter is 4 2 1. If you use 2 cups of sugar, how much flour and butter do you need? A school has 400 students, and the ratio of boys to girls is 3 5. How many boys and girls are there? A company's profits increased in the ratio of 5 3. If the original profit was $15,000, what is the new profit? The length and width of a garden are in the ratio 7 4. If the perimeter is 88 meters, find the length and width. The number of red, blue, and green balls in a bag are in the ratio 2 3 5. If there are 30 balls in total, how many are of each color? If a map scale is 1 inch = 25 miles, what is the actual distance between two towns that are 4.5 inches apart on the map? A blueprint has a scale of 1 cm = 2 meters. What is the length of a room that is 6.5 cm long on the blueprint? A model train is built to a scale of 1 87. If the actual train car is 17.4 meters long, how long is the model car in centimeters? If the ratio of apples to oranges in a basket is 5 2, and there are 14 fruits in total, how many apples are there? If the ratio of cats to dogs in a shelter is 3 4, and there are 28 animals in total, how many dogs are there? Explain how ratios can be used to compare quantities with different units. Give an example of using ratios to compare quantities with different units (e.g., speed in miles per hour vs. kilometers per hour). How can unit rates simplify comparisons? Calculate the unit rate for 10 apples costing $4. Calculate the unit rate for 3 hours of work earning $36. Compare the unit rates of two different brands of cereal to determine which is cheaper per ounce. If a store sells a pack of 6 batteries for $4.50 and another pack of 10 batteries for $7.00, which is the better buy? A car travels 300 miles on 15 gallons of gas. What is the car's fuel efficiency in miles per gallon? A person walks 6 kilometers in 1.5 hours. What is their average speed in kilometers per hour? If a factory produces 1200 widgets in 8 hours, what is the production rate in widgets per hour? How can proportions be used to solve problems involving scaling recipes? If a recipe for 4 servings requires 1 cup of flour, how much flour is needed for 10 servings? If a recipe for 6 cookies calls for 1/2 cup of sugar, how much sugar is needed for 15 cookies? How can proportions be used to convert units of measurement? Convert 10 inches to centimeters using the proportion 1 inch / 2.54 cm. Convert 50 kilometers to miles using an appropriate conversion factor and proportion. How can proportions be used to calculate percentages? If 30 out of 50 students passed a test, what percentage passed? Set up a proportion to solve. If 15% of a class of 40 students are absent, how many students are absent? Set up a proportion to solve. How can proportions be used in calculating discounts and sales tax? If an item originally costs $50 and is on sale for 20% off, what is the discount amount? Set up a proportion. If the sales tax rate is 7%, how much tax will you pay on a $30 purchase? Set up a proportion. What is a rate of change? How is it related to ratios? Give an example of a rate of change (e.g., speed, population growth). How can ratios be used to represent probabilities? If a bag contains 3 red balls and 5 blue balls, what is the ratio of red balls to the total number of balls? This ratio represents the probability of picking a red ball. What is the odds of an event occurring? How is it related to ratios? If the probability of winning a game is 1/4, what are the odds of winning? (Ratio of favorable outcomes to unfavorable outcomes). Explain the difference between probability and odds. How can ratios be used in genetics (e.g., Punnett squares)? Explain how Mendelian ratios are derived from genetic crosses. How can ratios be used in photography (e.g., aspect ratio of an image)? What does an aspect ratio of 16 9 mean for a screen or image? How can ratios be used in music (e.g., intervals)? Explain how musical intervals can be expressed as ratios of frequencies. What are some historical applications of ratios and proportions? How were ratios and proportions used in ancient Egypt or Greece? Explain the Golden Ratio. How is it related to proportions? What are some examples of the Golden Ratio in art, architecture, and nature? How are ratios and proportions used in map projections? Explain how different map projections distort scales and ratios. How are ratios and proportions used in fluid dynamics (e.g., flow rates)? Explain how flow rate can be expressed as a ratio of volume to time. How are ratios and proportions used in electrical circuits (e.g., Ohm's Law)? Explain how voltage, current, and resistance are related by ratios (V=IR). What are some common mistakes students make when solving ratio problems? What are some common mistakes students make when solving proportion problems? How can you double-check your answers to ratio and proportion problems? Explain the importance of maintaining consistent units when working with ratios and proportions. When comparing ratios, why is it helpful to have a common denominator or numerator? How can you use a calculator to simplify ratios or solve proportions? Explain how to use the "cross-multiply" function on a calculator for proportions. What are some strategies for tackling complex word problems involving ratios and proportions? Break down the problem into smaller parts.
- Explain how to determine the dimensions of a model based on a scale. What are some common word problems involving ratios?
- What is the ratio of perimeters of similar figures? What is the ratio of areas of similar figures?
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