Podcast
Questions and Answers
What is the simplest form of the ratio 24 messages to 10 messages?
What is the simplest form of the ratio 24 messages to 10 messages?
- 12/5 (correct)
- 4/3
- 6/5
- 24/10
What is the unit rate of 3 gallons for $10.80?
What is the unit rate of 3 gallons for $10.80?
- $4.00 per gallon
- $3.00 per gallon
- $3.60 per gallon (correct)
- $12.00 per gallon
Do the ratios 4:24 and 11:33 form a proportion?
Do the ratios 4:24 and 11:33 form a proportion?
- Yes, because they are both whole numbers.
- No, because they contain different units.
- Yes, because they can be simplified to the same ratio. (correct)
- No, because their simplified forms are different.
Which statement accurately describes the two rates: 25 cars in 5 days and 60 cars in 12 days?
Which statement accurately describes the two rates: 25 cars in 5 days and 60 cars in 12 days?
What should you use to write a proportion from the data provided?
What should you use to write a proportion from the data provided?
What is the missing value 'x' in the proportion x/4 = 8/10?
What is the missing value 'x' in the proportion x/4 = 8/10?
What is the cost per box if 3 boxes cost $10.80?
What is the cost per box if 3 boxes cost $10.80?
What is the ratio of cashews to peanuts if the numbers are 12 and 16 respectively?
What is the ratio of cashews to peanuts if the numbers are 12 and 16 respectively?
Flashcards
Ratio
Ratio
A comparison of two quantities using division. Can be written as a fraction, with a colon, or with the word 'to'.
Unit Rate
Unit Rate
A ratio that represents the amount of a quantity per one unit of another quantity. Example: 3 miles per gallon.
Proportion
Proportion
Two ratios that are equal. Can be verified using cross-multiplication.
Cross-multiplication
Cross-multiplication
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Solving Proportions
Solving Proportions
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Constant Rate of Change
Constant Rate of Change
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Rate
Rate
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Ratio Table
Ratio Table
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Study Notes
Ratio and Proportion
- A ratio compares two quantities. Express it as a fraction in simplest form. For example, 24 messages to 10 messages is 24/10 which simplifies to 12/5.
- A rate is a ratio that compares two quantities with different units.
- A unit rate compares a quantity to one unit of another quantity.
- A proportion is an equation stating that two ratios are equal. For example, 4/7 = 24/35.
Determining if Ratios Form a Proportion
- To determine if ratios are proportional, check if cross products are equal.
- For example, if 4/7 = 24/35, then 4 * 35 = 140 and 7 * 24 = 168, so they are not proportional.
Determining if Rates Form a Proportion
- To determine if rates are proportional, calculate the unit rate for each and compare.
- For example, 25 cars in 5 days has a unit rate of 5 cars per day. 60 cars in 12 days has a unit rate of 5 cars per day. Therefore, these rates are proportional.
Unit Rates
- Use ratio tables and proportions to find unit rates. For example, using a table that shows 0 gallons, 0 miles; 2 gallons, 3 miles; 4 gallons, 6 miles; 6 gallons, 9 miles; you can calculate miles per gallon.
Solving Proportions
- Cross multiply to solve proportions. For example, if x/10 = 4/5, then 5x = 40, so x = 8.
- Set up and solve a proportion to find unknown values given certain rates.
Ratio Tables
- Ratio tables relate two quantities in a proportion.
- They can be helpful for finding unit rates and determining whether quantities are proportional or not.
Word Problems involving Ratios, Rates, and Proportions
- Read the problem carefully, identify the quantities and their relationship using a ratio or rate.
- Translate it into a proportion.
- Solve it using the appropriate method (cross-multiplication or other relevant strategies).
- Round the answer appropriately, if necessary.
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