Proportional Reasoning

Front

What is proportional reasoning?

Back

Proportional reasoning is the ability to compare ratios and understand the relationship between quantities. It involves recognizing that two ratios are equivalent and can be used to solve problems involving scaling, rates, and percentages.

Front

How do you calculate the total cost including sales tax?

Back

To calculate the total cost including sales tax, multiply the original price by the sales tax rate (as a decimal) and then add that amount to the original price. Formula: Total Cost = Original Price + (Original Price × Sales Tax Rate).

Front

If a bike costs $738 and the sales tax is 5.5%, what is the total cost?

Back

Total Cost = $738 + ($738 × 0.055) = $738 + $40.59 = $778.59.

Front

What is the formula to find the percentage of correct answers on a test?

Back

Percentage of Correct Answers = (Number of Correct Answers / Total Questions) × 100.

Front

If Sam scored 80% on a test with 35 questions, how many did he get correct?

Back

Correct Answers = 80% of 35 = (80/100) × 35 = 28.

Front

What is a scale drawing?

Back

A scale drawing is a representation of an object where the dimensions are proportional to the actual dimensions, allowing for a smaller or larger version of the object to be created.

Front

If the Eiffel Tower is 330 meters tall, and the scale drawing height is 9 1/6 centimeters, what is the scale factor?

Back

Scale Factor = Actual Height / Drawing Height = 330 meters / 9.1667 centimeters = 36.

Front

How do you convert inches on a map to actual miles?

Back

To convert inches on a map to actual miles, use the scale provided. For example, if 2 inches represent 70 miles, then 1 inch represents 35 miles.

Front

If 2 inches on a map represents 70 miles, how many miles does 4.8 inches represent?

Back

Actual Distance = (4.8 inches / 2 inches) × 70 miles = 168 miles.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal. Proportions can be used to solve for unknown values in problems involving ratios.