Understanding Ratios, Fractions, and Proportions

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. For example, the ratio of 2 to 3 can be written as 2:3.

Front

What is a Fraction?

Back

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, 1/2 means one part out of two equal parts.

Front

What is a Proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, to simplify 8:12, divide both by 4 to get 2:3.

Front

What is the difference between a ratio and a fraction?

Back

A ratio compares two quantities, while a fraction represents a part of a whole. For example, in a ratio of 3:4, both numbers are compared, whereas in 1/4, it indicates one part of four equal parts.

Front

Example of a Ratio: 5 boys to 10 girls. What is the simplified ratio?

Back

The simplified ratio is 1:2.

Front

What does it mean if two ratios are in proportion?

Back

It means that the cross products of the ratios are equal. For example, if a/b = c/d, then a*d = b*c.

Front

If 3 out of 12 students prefer soccer, what is the fraction of students who prefer soccer?

Back

The fraction is 3/12, which simplifies to 1/4.

Front

What is the ratio of 15 apples to 5 oranges?

Back

The ratio is 15:5, which simplifies to 3:1.

Front

If a recipe calls for 2 cups of flour for every 3 cups of sugar, what is the ratio of flour to sugar?

Back

The ratio of flour to sugar is 2:3.