How to Solve Ratio Problems When the Whole, a Part, or the Difference Is Given
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The key idea: ratios describe equal-sized partsA ratio such as 3:5 means two quantities are made from 3 equal-sized parts and 5 equal-sized parts. It does not tell you the actual amounts until you know how large one part is.Call the size of one part k. Then a 3:5 ratio represents 3k and 5k. Most ratio problems are solved by working out k from the information given.When the whole is givenIf the ratio is 3:5, the whole contains 3 + 5 = 8 parts.Example: Red and blue counters are in the ratio 3:5. There are 40 counters altogether. How many are red and how many are blue?1. Count the total ratio parts: 3 + 5 = 8.
2. Find the value of one part: 40 ÷ 8 = 5.
3. Multiply: red = 3 × 5 = 15; blue = 5 × 5 = 25.
4. Check: 15 + 25 = 40.Common mistake: Dividing the total by one of the ratio numbers. The total belongs to all the parts, so divide by their sum first.When one part is givenIf you know the amount matching one side of the ratio, you can find k directly.Example: Flour and sugar are mixed in the ratio 4:1. A recipe uses 300 g of flour. How much sugar is needed?The 4 flour parts equal 300 g, so one part is 300 ÷ 4 = 75 g. Sugar is 1 part, so the recipe needs 75 g of sugar.If the question asks for the total mixture, remember to add both amounts: 300 + 75 = 375 g.When the difference is givenThe difference between two quantities is the difference between their ratio numbers—not their sum.Example: Two teams have players in the ratio 7:4. The larger team has 15 more players than the smaller team. How many players are on each team?1. The difference in ratio parts is 7 − 4 = 3.
2. Those 3 parts represent 15 players, so one part is 15 ÷ 3 = 5 players.
3. The teams have 7 × 5 = 35 and 4 × 5 = 20 players.
4. Check: 35 − 20 = 15.Common mistake: Dividing 15 by 7 + 4. That would be right if 15 were the total, but it is the difference, so use 7 − 4.Ratios with three quantitiesThe same method works for more than two terms. If a drink uses juice, water, and syrup in the ratio 2:5:1, there are 8 parts altogether. If you make 640 ml, each part is 640 ÷ 8 = 80 ml. That gives 160 ml juice, 400 ml water, and 80 ml syrup.Always read carefully to see whether the amount given is a total, one quantity, or a difference. Those clues determine which calculation finds one part.A 10-minute practice planAtlas · Scribe AI
Subject deep dives · October 11, 2026
- 2 minutes: Write each ratio using k. For 3:5, write 3k and 5k.
- 5 minutes: Try one question where the total is given, one where a part is given, and one where the difference is given. Label the information before calculating.
- 3 minutes: Check each answer by rebuilding the ratio and confirming the stated total or difference.