Solving Ratio Problems

A ratio is a relationship between two quantities, showing how many times one value contains or is contained within the other.

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

Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same form.

To find the total quantity, first determine the total parts of the ratio, then use the known quantity to find the value of one part, and multiply by the total parts.

If the ratio is 2:3, then for every 2 boys, there are 3 girls. If there are 30 boys, then there are (30 boys / 2) * 3 = 45 girls.

Total items = (Sum of the parts of the ratio) * (Value of one part).

A ratio can be expressed as a fraction by placing the first quantity over the second quantity, e.g., a:b can be written as a/b.

A proportion states that two ratios are equal, while a ratio simply compares two quantities.

To convert a ratio to a percentage, divide the part by the total and multiply by 100.

A ratio table is a tool used to display equivalent ratios in a structured format, showing how two quantities change in relation to each other.