Exploring Rates and Ratios in Depth

The video tutorial introduces the concepts of rates, ratios, and proportions, providing real-life examples such as rental rates and speed limits. It explains how to simplify ratios and calculate unit rates, using examples like subway speed and paint mixing. The tutorial also covers graphing rates and emphasizes the importance of unit rates for easier comparison. Students are guided through practice exercises and assignments to reinforce their understanding.

What is the essential question for understanding rates?

• What is the unit rate of a given ratio?

• How do you convert fractions to decimals?

• How do rates help you describe real-life problems?

• What is the difference between a rate and a ratio?

Which of the following is an example of a rate?

• 45 males to 60 females

• 3 to 4

• 3/4

• 8.75 dollars per hour

How do you simplify the ratio 45 to 60?

• Subtract 15 from both numbers

• Multiply both numbers by 3

• Divide both numbers by 15

• Divide both numbers by 5

What is the unit rate if a subway car travels 2.5 miles in 5 minutes?

• 1 mile per minute

• 0.5 miles per minute

• 2 miles per minute

• 5 miles per minute

How do you find the speed of a subway car from a graph?

• By measuring the distance between two points

• By adding the coordinates of the points

• By looking at the slope of the line

• By counting the number of points on the graph

What is the speed of a subway car if it travels 14.4 miles in 3 seconds?

• 4.8 miles per second

• 3.5 miles per second

• 5 miles per second

• 4 miles per second

If you mix 1/2 cup of yellow paint for every 3/4 cup of blue paint, how many cups of yellow paint do you need for 15 cups of green paint?

• 7 cups

• 9 cups

• 8 cups

• 6 cups

What fraction of the total paint is yellow if you mix 1/2 cup of yellow paint with 3/4 cup of blue paint?

• 1/4

• 1/2

• 2/5

• 3/5

How do you estimate the unit rate to the nearest whole number for $74.75 for 5 gallons?

• Subtract 5 from 74.75

• Multiply 74.75 by 5

• Round 74.75 to 75 and then divide by 5

• Divide 74.75 by 5

Why are unit rates usually written as per one unit?

• To make rates easier to compare

• To use the same unit of measure

• To provide more information

• To have fewer numbers