Unit Rates and Proportional Relationships

Mrs. Lopez introduces lesson 12, focusing on ratios and proportions for seventh graders. The lesson includes exercises on calculating unit rates to compare car travel distances, determining proportional relationships in paint mixing, and analyzing candy costs to find the better buy. The video emphasizes converting between fractions and decimals and understanding the constant of proportionality.

What is the constant of proportionality also known as?

• Dependent variable

• Conversion factor

• Independent variable

• Unit rate

How do you find the unit rate for a car's travel in miles per gallon?

• Multiply miles by gallons

• Subtract gallons from miles

• Divide miles by gallons

• Add miles and gallons

How do you convert a mixed number into an improper fraction?

• Add the whole number to the fraction

• Divide the whole number by the fraction

• Multiply the whole number by the denominator and add the numerator

• Subtract the numerator from the whole number

Why is it recommended to convert decimals to fractions in these exercises?

• Fractions are easier to add

• Decimals are harder to multiply

• Fractions can be simplified more easily

• Decimals are less accurate

Which car travels farther based on the unit rate calculation?

• Both travel the same distance

• Cannot be determined

• Red car

• Blue car

What is the first step in simplifying a complex fraction?

• Add the fractions

• Multiply by the reciprocal

• Divide by the numerator

• Subtract the fractions

In the paint mixing exercise, what does the unit rate of 5/3 represent?

• 5 units of red paint to 1 unit of blue paint

• 5 units of red paint to 3 units of blue paint

• 5 units of blue paint to 1 unit of red paint

• 5 units of blue paint to 3 units of red paint

Is the amount of blue paint proportional to the amount of red paint?

• Yes, because the amounts are equal

• No, because the unit rate varies

• No, because the amounts are different

• Yes, because the unit rate is consistent

What is the better buy: 4 pounds of candy for $7.25 or 3 pounds for $5.40?

• Depends on the type of candy

• 3 pounds for $5.40

• 4 pounds for $7.25

• Both are the same

What does the unit rate tell us in the context of the candy exercise?

• The total cost of all candy

• The type of candy

• The cost per pound of candy

• The weight of the candy