Unit 7: Ratios, Rates, and Proportions
Comparing two quantities, boiling a rate down to one unit, and the straight line through the origin that a proportional relationship always draws.
5 topics · 19 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Ratio Is
- How it worksHow does a ratio compare two quantities while keeping their relationship the same no matter how much you scale it?
- Worked exampleFind an equivalent ratio to 3 to 4 that uses a total of 28 parts.
- Common mistakeWhy isn't the ratio 3 to 4 the same thing as the fraction 3 fourths of a total?
Your turn1 of 2
Leo's recipe uses a ratio of 4 cups of flour to 4 cups of sugar. If he uses 28 cups of flour, how many cups of sugar keep the same ratio?Unit Rates
- How it worksHow does dividing to get an amount per one turn any rate into a unit rate you can compare?
- Worked exampleFind the unit rate if a car travels 240 miles on 8 gallons of gas.
- Worked exampleFind which is the better deal, 12 dollars for 3 pounds of apples or 18 dollars for 5 pounds.
- Going furtherWhat happens to a unit rate when both quantities in the original rate double?
- Common mistakeWhy doesn't a bigger total price always mean a worse deal?
Your turn1 of 2
Amara's car travels 309 miles on 14 gallons of gas. What is the unit rate in miles per gallon?Proportional Relationships and Their Graphs
- How it worksHow does a proportional relationship's graph turn out to be a straight line that passes through the origin?
- Worked exampleGraph the relationship between hours worked and pay earned at 12 dollars per hour, and check that it passes through the origin.
- Going furtherWhat happens to this graph if there's also a flat 5 dollar fee added no matter how many hours you work?
- Common mistakeWhy isn't every straight-line graph a proportional relationship?
Your turn1 of 2
Tom is paid 23 dollars per hour at his part-time job. What is his pay for working 26 hours?The Constant of Proportionality
- How it worksHow do you find the constant of proportionality from a table, a graph, or an equation?
- Worked exampleFind the constant of proportionality if y equals 30 when x equals 5.
- Common mistakeWhy doesn't the constant of proportionality change depending on which point on the line you pick?
Your turn1 of 2
A recipe's proportional relationship has y equal to 79 cups of water when x equals 9 cups of rice. Find the constant of proportionality, water per cup of rice.Solving Proportions with Cross Multiplication
- How it worksHow does cross multiplying two equal fractions turn a proportion into a simple equation?
- Worked exampleSolve 3 over 4 equals x over 20 for x.
- Worked exampleSolve 9 over x equals 3 over 5 for x.
- Common mistakeWhy doesn't cross multiplication work on an equation that isn't set up as two fractions equal to each other?
Your turn1 of 2
A map shows 7 inches for every 7 miles. Solve 7 over 7 equals x over 37 to find x, the number of inches representing 37 miles.