Mastering Ratios and Rates in Mathematics

In this video, Jeff Jacobson explains the concepts of ratios, rates, and unit rates. He provides a detailed explanation of how to write ratios in different forms and distinguishes between rates and unit rates. The video includes examples such as finding the speed of a subway car using a graph, simplifying ratios, and calculating unit rates. The lesson is designed to build on previous knowledge and offers practice problems for viewers to try on their own.

What is a ratio?

• A comparison of two quantities with the same units

• A comparison of two quantities with different units

• A special kind of rate where the denominator is 1

• A method to calculate speed

How can a ratio of 3 to 4 be written?

• 3/4

• 3 - 4

• 3 to 4

• All of the above

What distinguishes a rate from a ratio?

• Rates compare quantities with the same units

• Rates do not involve units

• Rates are always written as fractions

• Rates compare quantities with different units

What is a unit rate?

• A ratio without units

• A rate with a denominator of 1

• A rate that cannot be simplified

• A rate with a numerator of 1

How do you find speed on a graph showing distance over time?

• By finding the slope of the line

• By counting the grid squares under the line

• By measuring the length of the line

• By the height of the line at the y-axis

How can you simplify the ratio 63 to 28?

• Cannot be simplified

• 63 to 28

• 7 to 4

• 9 to 4

What is a complex fraction?

• A fraction with a denominator of 0

• A fraction within a fraction

• A fraction that cannot be simplified

• A fraction with a numerator and denominator of 1

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

• Subtract the numerator from the whole number

• None of the above

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

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

What is the unit rate if you travel 21 and 3/4 meters in two and a half hours?

• 8.7 meters per hour

• 43.5 meters per hour

• 10.75 meters per hour

• 5.5 meters per hour

How do you find a new rate when given different units?

• By dividing the quantities

• By multiplying the quantities

• By adding the quantities

• By subtracting the quantities