Questions and Answers
What is a ratio?
A comparison of 2 numbers that have the same units.
How many ways are there to write a ratio?
3
Simplify the ratio 5/10 and write in two other ways.
1/2, 1 to 2, 1:2
What is a rate?
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Examples of rates are...
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What is a UNIT rate?
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What is the difference between a rate and a unit rate?
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We calculate the unit rate using which operation?
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Calculate the unit rate for 24 miles/3 gallons.
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Calculate the unit rate for making cookies if it takes 1/3 a cup of sugar to make 1/2 a batch of cookies.
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When finding the unit rate of a graph or table, do you use y/x or x/y?
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Find the rate of the graph.
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Find the unit rate of the table.
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What is a proportion?
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2 ratios are considered proportional if they are...
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How do you check to see if 2 ratios are proportional?
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1/3 = 2/6 is proportional?
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3/12 = 1/4 is proportional?
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3/4 = 8/10 is proportional?
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Solve for a missing number in proportions by...
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3/21 = c/35, what is c?
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9/105 = 15/y, what is y?
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26/p = 13/0.4, what is p?
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To see if a table is proportional, you must...
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Is this table proportional?
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Is this table proportional?
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Is this table proportional?
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What is the constant of proportionality?
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What is the CoP of the graph?
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What is the CoP of the graph?
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How do you know if a graph is proportional?
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Is this graph proportional? Prove in 2 ways.
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Is this graph proportional? Prove in 2 ways.
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You can buy six cans of root beer for $2.50. How many cans of root beer can you buy for $10?
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David paints 3 rooms in 7 hours. At the same pace, how long would it take him to paint 15 rooms?
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LHMS has 750 girls. The ratio of boys to girls is 3:5, how many boys are at LHMS?
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Study Notes
Ratios
- A ratio compares two numbers with the same units.
- Ratios can be expressed in multiple formats: as "a to b" (2:3), decimal (2/3), or word form (2 to 3).
Rates
- A rate compares two numbers with different units, e.g., miles per hour or words per minute.
- A unit rate is a specific type of rate with a denominator of 1.
Unit Rates
- To find the unit rate, divide the numerator by the denominator.
- Example: From 24 miles and 3 gallons, the unit rate is 8 miles per gallon.
Proportions
- A proportion compares two ratios and is evident when two ratios are equal.
- Cross-multiplication can be used to determine if two ratios are proportional.
Checking Proportionality
- Example of proportional ratios: 1/3 = 2/6 (yes), 3/12 = 1/4 (yes).
- Example of non-proportional ratios: 3/4 = 8/10 (no).
Solving Proportions
- When solving for a missing number in proportions, cross-multiply and then divide by the remaining number.
Constant of Proportionality
- This reflects the unit rate in a graph, defined as Y/X.
- Graphs can be considered proportional if they pass through the origin.
Recognizing Proportional Graphs
- A graph is considered proportional if the line passes through (0,0) and two points from it form a proportion.
- Example: If a graph shows a line through the origin and maintains consistent ratios, it is proportional.
Word Problems Involving Ratios and Proportions
- Example: To find how many root beer cans can be bought with $10 when 6 cans cost $2.50, set up the equation $2.50/6 = $10/x and solve to find 24 cans.
- Example: David painting rooms involves setting up their rates; if 3 rooms take 7 hours, then 15 rooms would take 35 hours.
Application of Ratios in Real Contexts
- In the context of a school with 750 girls and a boy-to-girl ratio of 3:5, solve for the number of boys by using the equation (x/750 = 3/5) to find 450 boys.
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Description
This quiz focuses on the fundamental concepts of ratios, rates, unit rates, and proportions. Test your knowledge on how to express, compare, and solve problems involving these mathematical concepts. Dive deep into understanding proportionality and the constant of proportionality.
