Ratios and Proportions

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as 'a:b' or 'a/b'.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD).

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, typically written as a/b = c/d.

Front

How can you solve a proportion?

Back

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

Front

What does it mean to cross-multiply?

Back

Cross-multiplying involves multiplying the numerator of one ratio by the denominator of the other ratio.

Front

What is the formula for finding a ratio of wins to losses?

Back

The ratio of wins to losses is calculated by dividing the number of wins by the number of losses.

Front

If a team has 25 wins and 45 losses, what is the ratio of wins to total games played?

Back

The total games played is 25 + 45 = 70, so the ratio of wins to total games is 25:70, which simplifies to 5:14.

Front

What is the relationship between ratios and fractions?

Back

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

Front

How do you convert a ratio to a percentage?

Back

To convert a ratio to a percentage, divide the first term by the sum of both terms and multiply by 100.

Front

What is the significance of equivalent ratios?

Back

Equivalent ratios represent the same relationship between quantities, even if the numbers are different.