Ratios

A ratio is a comparison of two quantities. It is often written as a fraction or using the colon symbol (:). For example, the ratio of boys to girls in a class of 20 students can be written as 5:3 or 5/3. Ratios are used to compare the sizes of two or more quantities.

Terms related to ratios:

1. Antecedent: The first term in a ratio is called the antecedent. In the ratio a:b, 'a' is the antecedent.
2. Consequent: The second term in a ratio is called the consequent. In the ratio a:b, 'b' is the consequent.

Ways to express ratios:

Ratios can be expressed in the following ways:

• As a fraction: For example, the ratio 3:5 can be expressed as 3/5.
• Using the colon symbol: For example, the ratio of 2:7.
• As a verbal statement: For example, "The ratio of boys to girls is 2 to 3."

Understanding equivalent ratios:

Equivalent ratios are ratios that express the same comparison. For example, the ratios 2:3 and 4:6 are equivalent because they both compare the same relationship, which is 2 to 3.

Solving problems using ratios:

Ratios can be used to solve various types of problems, such as mixing different quantities of ingredients to create a recipe, determining the proportion of different colors used in a painting, or sharing a sum of money in a specific ratio among a group of people.

Practice Problems:

1. Express the ratio 6:9 as a fraction in simplest form.
2. Determine if the ratios 4:6 and 6:9 are equivalent.
3. If a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, how much sugar would you need if you used 4 cups of flour?