Ratio Word Problems

Ratio word problems: a reliable method

A ratio compares two or more quantities by showing how much of one there is relative to another. In word problems, the key is to identify the parts of the ratio and the total amount you know.

1. Read carefully and label the quantities

Look for phrases like “for every,” “in the ratio,” or “split between.” Write the ratio in order. For example, if the ratio is 3:5, the first quantity has 3 parts and the second has 5 parts.

2. Find the value of one part

If the problem gives a total, add the parts of the ratio. Then divide the total by the number of parts.

• Example idea: ratio 3:5 has 3 + 5 = 8 parts total.
• If the total is known, one part equals total ÷ 8.

3. Multiply to get each quantity

Once one part is known, multiply by each ratio number.

• First quantity = 3 × one part
• Second quantity = 5 × one part

4. Keep answers exact and simplified

If the answer is a fraction, leave it exact unless it can be simplified. If the numbers do not divide evenly, use fractions rather than decimals.

5. Check your result

Add the quantities and make sure they match the total. Also check that the ratio matches the original numbers after simplifying.

A good habit is to write a small table with “ratio parts,” “one part,” and “final amount” before calculating.