Exploring Proportions and Ratios

In this video, Jeff Jacobson introduces the concept of proportions, explaining that they are equations showing two equivalent ratios. He demonstrates three methods to determine if two ratios form a proportion: simplest form, mental math, and cross products. Through examples, he illustrates how to apply these methods to different scenarios, such as comparing ratios and checking if the number of laps is proportional to time. The video concludes with a call to practice and subscribe.

What is a proportion in mathematical terms?

• A formula for calculating area

• A graph plotting method

• An equation stating two ratios are equivalent

• A type of mathematical operation

Which example illustrates a proportion?

• 1 to 2 as 2 to 3

• 5 to 10 as 10 to 20

• 3 to 4 as 6 to 8

• 2 to 3 as 4 to 6

What is the simplest form comparison method for checking proportions?

• Adding numerators and denominators

• Multiplying cross pairs and comparing

• Subtracting ratios from one another

• Reducing ratios to their simplest forms and comparing

What does the cross product method involve?

• Multiplying cross terms and comparing the results

• Adding the products of cross terms

• Dividing the products of cross terms

• Subtracting the products of cross terms

In the example with x and y, what was the simplified form of the ratio 1/2 to 3?

• 1 to 6

• 1 to 3

• 1 to 9

• 1 to 12

How did the simplest form method confirm proportionality between x and y?

• Both ratios simplified to 1 to 12

• Both ratios simplified to 1 to 3

• Both ratios simplified to 1 to 9

• Both ratios simplified to 1 to 6

In the swimming example, why were the lap times not proportional?

• The swimmer got tired

• The swimmer sped up

• The swimmer used different strokes

• The swimmer took breaks

Which method showed that the swimming laps were not proportional using mental math?

• Adding 4 to the time

• Subtracting 4 from the time

• Dividing the time by 4

• Multiplying the time by 4

What was the unit rate of time per lap in the swimming example?

• 0.75 minutes per lap

• 0.6 minutes per lap

• 1.5 minutes per lap

• 1 minute per lap

Why is it important to practice with different ratios to confirm proportionality?

• To ensure consistency across different scenarios

• To improve calculation speed

• To memorize ratios

• To use up extra time