This video tutorial explores the use of ratios and rates to solve mathematical problems. It begins with an introduction to the concepts of ratios and rates, followed by a detailed examination of how to compare ratios using tables, with examples involving lemonade recipes. The tutorial then addresses real-world problems, demonstrating how to find equivalent ratios. The double number line method is introduced as a tool for visualizing and solving ratio problems. The video concludes with a review of the essential question on comparing ratios and solving problems.

What is the essential question discussed in the introduction of the video?

• How can you use ratios and rates to make comparisons and predictions?

• What are the applications of ratios in geometry?

• What is the difference between ratios and fractions?

• How do you solve equations using ratios?

In Anna's lemonade recipe, what is the ratio of concentrate to water?

• 5 to 3

• 3 to 2

• 2 to 3

• 3 to 5

How do you determine which lemonade recipe is stronger?

• By comparing the amount of water used

• By comparing the amount of concentrate used for the same amount of water

• By comparing the number of ingredients

• By comparing the total volume of lemonade

What is the correct ratio of nuts to fruit in Tanya's fruit and nut bar recipe?

• 5 to 3

• 3 to 5

• 6 to 9

• 4 to 6

How can you verify if two ratios are equivalent?

• By dividing the first term by the second term

• By subtracting the terms of the ratios

• By finding equivalent ratios with the same second term

• By adding the terms of the ratios

In the science club scenario, what is the ratio of sixth graders to seventh graders?

• 2 to 3

• 12 to 7

• 3 to 2

• 7 to 12

How is a double number line used to solve problems?

• By adding numbers along the line

• By multiplying or dividing both terms by the same number

• By subtracting numbers along the line

• By using only whole numbers

What is the result of multiplying 15 by 4 in the double number line example?

• 60

• 45

• 30

• 75

How many math problems can Lena complete in 75 minutes?

• 10

• 15

• 12

• 8

What is the key to comparing two ratios effectively?

• Finding equivalent ratios with the same first term

• Finding equivalent ratios with the same second term

• Ensuring both ratios have the same total

• Using only whole numbers in the ratios