Exploring Ratios and Rates with Fractions

This video tutorial covers various mathematical concepts for 7th-grade students. It begins with calculating the speed and time of a cyclist using ratios and rates. Next, it explores a recipe for sparkling grape juice, focusing on maintaining ingredient ratios. The tutorial then shifts to geometry, discussing how to create a scaled copy of a circle and comparing its circumference and area. It also includes a cost analysis of different meats to determine the least and most expensive per pound. Finally, it evaluates different scales for a map of Kansas to fit on a book page.

How fast was the cyclist going in miles per hour?

• 12.5 mph

• 10.5 mph

• 20.5 mph

• 15.5 mph

How long will it take the cyclist to travel 4.5 miles at the same rate?

• 21.6 minutes

• 18.6 minutes

• 24.6 minutes

• 15.6 minutes

How much sparkling water is needed to mix with 9 quarts of grape juice?

• 21 quarts

• 12 quarts

• 15 quarts

• 18 quarts

How much grape juice is needed to mix with 15.4 quarts of sparkling water?

• 4.875 quarts

• 1.875 quarts

• 2.875 quarts

• 3.875 quarts

What is the total amount of sparkling water needed to make 100 quarts of punch?

• 60.6 quarts

• 66.6 quarts

• 50.6 quarts

• 70.6 quarts

If the original circle has a diameter of 1 inch, what is the diameter of the scaled copy with a scale factor of 2?

• 4 inches

• 3 inches

• 2 inches

• 1 inch

How does the circumference of the scaled copy compare to the original circle?

• Same

• Twice

• Three times

• Four times

Which meat is the least expensive per pound?

• Ham

• Turkey

• Chicken

• Roast Beef

Which scale is appropriate for fitting the map of Kansas on a 5x8 inch page?

• 1 cm to 1 km

• 1 inch to 100 miles

• 1 inch to 1 mile

• 1 inch to 10 miles

What is the approximate width of Kansas in kilometers?

• 660 km

• 410 km

• 338 km

• 210 km