Proportional Reasoning

Front

What is proportional reasoning?

Back

Proportional reasoning is the ability to compare ratios and understand the relationship between quantities in terms of their proportions.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and then solve for the unknown variable.

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 if two ratios form a proportion?

Back

It means that the two ratios are equivalent, or that they represent the same relationship between the quantities.

Front

If 3/4 = x/12, what is x?

Back

x = 9 (Cross-multiply to solve: 3 * 12 = 4 * x).

Front

What is the unit rate?

Back

The unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something.

Front

How do you find the unit rate from a ratio?

Back

To find the unit rate, divide the first quantity by the second quantity to express it as a rate per one unit.

Front

If a car travels 150 miles in 3 hours, what is its speed in miles per hour?

Back

Speed = 50 miles per hour (150 miles ÷ 3 hours).

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, where the first quantity is the numerator and the second quantity is the denominator.