Ratios, Proportions, and Word Problems

Front

What is a ratio?

Back

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

Front

How do you solve for x in a ratio problem?

Back

To solve for x in a ratio problem, set up an equation based on the given ratios and use cross-multiplication if necessary.

Front

What is a proportion?

Back

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

Front

How can you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross-products are equal.

Front

What is the cross-multiplication method?

Back

The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio to check for equality.

Front

What does it mean for ratios to be in simplest form?

Back

Ratios are in simplest form when the numbers cannot be reduced any further, meaning they have no common factors other than 1.

Front

How do you convert a ratio to a fraction?

Back

To convert a ratio to a fraction, write the first quantity as the numerator and the second quantity as the denominator.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions, and both represent a comparison of quantities.

Front

What is an example of a word problem involving ratios?

Back

If a recipe requires 2 cups of flour for every 3 cups of sugar, how much flour is needed for 9 cups of sugar?

Front

How do you solve a word problem involving proportions?

Back

Identify the quantities involved, set up a proportion based on the relationships, and solve for the unknown variable.