Proportional Reasoning

Front

What is proportional reasoning?

Back

Proportional reasoning is the ability to compare ratios and understand the relationship between quantities in a proportional context.

Front

How do you calculate the number of correct answers based on a percentage score?

Back

To find the number of correct answers, multiply the total number of questions by the percentage score (as a decimal). For example, for 75% on 60 questions: 60 * 0.75 = 45.

Front

If 2 cm on a map represents 250 kilometers, how do you find the actual distance for a different scale?

Back

Use the ratio: (actual distance) = (scale distance) * (actual distance represented by 2 cm) / 2. For 4.5 cm: (4.5 * 250) / 2 = 562.5 kilometers.

Front

What is the formula to find the cost of multiple items based on a known cost?

Back

Cost of multiple items = (Cost of known items / Number of known items) * Number of desired items.

Front

If 5 entrance tickets cost $56.00, how much does one ticket cost?

Back

Cost per ticket = Total cost / Number of tickets = 56 / 5 = 11.20.

Front

How do you find the total cost for 7 entrance tickets if you know the cost of one?

Back

Total cost for 7 tickets = Cost per ticket * 7. If one ticket costs $11.20, then 7 tickets cost 11.20 * 7 = 78.40.

Front

What is a ratio?

Back

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other.

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio or rate.

Front

How can you express a percentage as a fraction?

Back

To express a percentage as a fraction, divide the percentage by 100 and simplify if possible. For example, 75% = 75/100 = 3/4.

Front

What is the relationship between scale and actual distance on a map?

Back

The scale indicates how much the actual distance is reduced to fit on the map. For example, a scale of 1 cm to 100 km means 1 cm on the map represents 100 km in reality.