Ratio
What is a ratio?
A ratio is a comparison of two quantities by division.
What is a unit rate?
A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity of one.
How can you describe a percent as “per 100”?
A percent is a ratio that compares a number to 100, expressed as "per 100."
How would you use ratio reasoning to compare two quantities?
Use ratio reasoning to compare quantities by finding a common ratio or unit rate.
What is a tape diagram?
A tape diagram is a visual model that represents the parts of a ratio as segments of tape.
Write the ratio of 4 apples to 6 oranges in three different ways.
The ratio of 4 apples to 6 oranges can be written as:
1) 4:6
2) 4664
3) 2:3 (simplified)
If a car travels 150 miles in 3 hours, what is the unit rate in miles per hour?
The unit rate in miles per hour is 50 miles/hour (150 miles ÷ 3 hours).
50/1
Convert 0.75 to a percent.
0.75 as a percent is 75% (0.75 × 100)
If a recipe calls for 2 cups of flour for every 3 cups of sugar, how much sugar is needed for 8 cups of flour?
For 8 cups of flour, you would need 12 cups of sugar .
How can you use a double number line to represent the ratio 3:2?
A double number line for the ratio 3:2 would show two lines, with one line marking 3's multiples and the other marking 2's multiples.
Provide a real-world example of a ratio relationship.
A real-world example of a ratio relationship could be the ratio of boys to girls in a classroom, such as 10 boys to 15 girls (10:15)
Solve: If 5 pencils cost $3, what is the unit rate per pencil?
The unit rate per pencil is $0.60 (divide $3 by 5 pencils)
If a shirt costs $40 and is on sale for 25% off, how much will it cost?
The cost after 25% off a $40 shirt is $30 (25% of $40 = $10, $40 - $10 = $30)
Describe how you would solve a problem involving ratios and rates.
You would first identify the ratio or rate, set up an equation, and then solve for the unknown quantity.
Solve a problem using a tape diagram to show the relationship between 5:10
A tape diagram showing the relationship 5:10 would have one segment twice as long as the other, indicating the ratio
Find an equivalent ratio for 3:5 using multiplication.
An equivalent ratio for 3:5 using multiplication would be 6:10 (multiply both parts by 2)
Explain how you would find the unit rate from a ratio of 8:4.
To find the unit rate from the ratio 8:4, divide both numbers by 4, giving you 2:1.
Explain how to convert the fraction 3/4 to a percent.
To convert 3/4 to a percent, multiply by 100 to get 75%
Give an example of a real-world problem that requires using both ratios and unit rates.
An example could be calculating the cost of buying 3 pounds of apples at a rate of $2 per pound (total cost = $6).
Explain how you would use a double number line to find equivalent ratios.
To find equivalent ratios using a double number line, you would mark equal distances that correspond to the ratios.
Complete the ratio table for the quantities 2, 4, 6 (start 2:3)
Ratio table completion:
2:3, 4:6, 6:9 (all equivalent ratios).
Describe a real-world scenario where you would need to calculate a unit rate.
A real-world scenario could be calculating how much one gallon of paint costs if 5 gallons cost $100 (unit rate = $20 per gallon).
Create a real-world problem where you need to use percentages to find a solution.
A real-world problem could be: If you scored 18 out of 20 on a test, what percentage did you score? (Answer: 90%).
How can you represent your solution to a real-world problem using a table or diagram?
You can use a table to display the quantities and their ratios or a diagram to visualize the relationships.
Create a problem where you need to use both a tape diagram and a double number line for the solution.
You might create a problem where a tape diagram shows the total of two quantities while a double number line illustrates their individual ratios.