Understanding Proportional Relationships

This video tutorial reviews key concepts from the seventh-grade mathematics curriculum, focusing on proportional relationships. It covers topics such as equivalent ratios, scale factors, and constants of proportionality using practical examples like trail mix and marathon running. The video also explains how to write equations from proportional relationships, analyze graphs, and calculate costs and lengths. Additionally, it includes exercises on determining proportionality in data tables and comparing water tank filling rates. The tutorial concludes with a practical application using a salad dressing recipe.

In the trail mix example, what is the equivalent ratio of peanuts to raisins in the second version?

• 1:1

• 3:2

• 1.5:1

• 2:1

What is the scale factor between cups of milk and tablespoons of chocolate syrup?

• 2:3

• 3:2

• 1:1

• 1:2

If Noah runs at a constant speed of 6 miles per hour, how far will he run in 1.5 hours?

• 6 miles

• 3 miles

• 9 miles

• 12 miles

What is the constant of proportionality in the equation P = 0.8L for the price of rope?

• 2

• 1.25

• 0.8

• 1.5

How many fluid ounces are in 51 bottles if each bottle holds 17 ounces?

• 34 ounces

• 51 ounces

• 102 ounces

• 867 ounces

Which of the following tables represents a proportional relationship?

• Neither

• Table B

• Both

• Table A

In the equation x = M/4, what is the constant of proportionality?

• 4

• 1/4

• x

• M

Which graph represents a proportional relationship between cost and volume?

• Both

• Graph A

• Graph B

• Neither

In the tank filling example, which tank fills more quickly?

• Tank A

• Both fill at the same rate

• Tank B

• Neither

For the salad dressing recipe, what is the ratio of oil to vinegar?

• 1:1

• 1.5:1

• 2:3

• 3:2