Constants of Proportionality and Ratios

The video tutorial covers the concept of proportions using real-life examples like marathons and maps. It explains how to calculate distances and times using proportions, and delves into the constant of proportionality. The tutorial also covers fractions, division, and scale calculations, providing a comprehensive understanding of these mathematical concepts.

If Noah runs at a constant speed of 6 miles per hour, how far will he run in 2 hours?

• 24 miles

• 18 miles

• 12 miles

• 6 miles

What is the constant of proportionality when converting 1 kilometer to meters?

• 1/1000

• 1000

• 1/100

• 100

How many meters are there in 0.3 kilometers?

• 3000 meters

• 3 meters

• 300 meters

• 30 meters

What is the relationship between the constants of proportionality 1:1000 and 1000:1?

• They are reciprocals

• They are both less than 1

• They are equal

• They are unrelated

If 1 inch equals 12 feet, what is the reciprocal constant of proportionality?

• 10

• 1/12

• 12

• 1/10

If a map scale is 1:50, what does this mean in terms of inches to miles?

• 1 inch equals 500 miles

• 1 inch equals 0.5 miles

• 1 inch equals 5 miles

• 1 inch equals 50 miles

What is the scale of a map if the Mojave Desert's area is represented as 1:50?

• 1 inch equals 25 miles

• 1 inch equals 50 miles

• 1 inch equals 10 miles

• 1 inch equals 100 miles

Which of the following scales is equivalent to 1 cm to 5 km?

• 3 cm to 15 km

• 1 mm to 150 km

• 5 cm to 1 km

• 5 mm to 2.5 km

If 5 millimeters equal 0.5 centimeters, how many kilometers does 0.5 centimeters equal?

• 2.5 km

• 5 km

• 0.5 km

• 1 km

Which of these shapes has a different ratio compared to the others?

• Shape A: 4:5

• Shape B: 3:4

• Shape C: 4:5

• Shape D: 3:4