Six hundred korunas in the ratio 2 : 3 — who gets how much?
Two siblings cleaned the garage. The older one worked two hours, the younger three. The reward of 600 Kč is to be shared fairly — in the ratio 2 : 3. How much for whom?
The method has three steps and is always the same:
Add the parts. The ratio 2 : 3 means 2 + 3 = 5 parts in total.
Find one part. Divide the whole by the number of parts: 600 : 5 = 120 Kč per part.
Give out the parts. The first gets 2 × 120 = 240 Kč, the second 3 × 120 = 360 Kč.
A free check: 240 + 360 = 600. If the sum does not match the whole, there is a mistake somewhere.
This method works on money, sweets, litres of paint and minutes of play. And it works for three or more members of a ratio too — you just add more parts. It is one of the most useful things in all of Year 7: fairness turned into times tables.
Ema and Filip sold lemonade at a fair and earned 450 Kč. Ema baked and prepared more — they agreed on the ratio 5 : 4. Filip suggests: “So I take 4 hundreds and you 5… wait, that is 900.” Ema draws on the box: 5 + 4 = 9 parts. 450 : 9 = 50 Kč per part. “I get 5 × 50 = 250, you 4 × 50 = 200.” Filip checks: 250 + 200 = 450. That checks out. “Actually simple,” he admits. “You just must not mix up a part with a koruna.”
Always finish with a check: the sum of the shared parts = the original whole. It takes five seconds and catches almost every mistake.
Three steps of sharing in a ratio
Step 1: add the parts of the ratio. For a ratio a : b it is a + b. For a three-member a : b : c you add three numbers.
Step 2: calculate the value of one part. Whole : number of parts. This is where people most often go wrong — you divide by the number of parts, not by a number from the ratio.
Step 3: give each their multiple. The first member of the ratio times the value of a part, the second member times the value of a part.
Step 4 (check): add the results. It must come out as the whole.
An example with a three-member ratio: 840 Kč in the ratio 1 : 2 : 4. Parts: 1 + 2 + 4 = 7. One part: 840 : 7 = 120. Sharing: 120, 240 and 480 Kč. Check: 120 + 240 + 480 = 840. That checks out.
The reverse question: you know one part and look for the whole. The younger one got 360 Kč and that was 3 parts of the ratio 2 : 3. One part: 360 : 3 = 120. The whole has 5 parts: 5 × 120 = 600 Kč.
Where you meet sharing in a ratio: rewards by hours worked, diluting paints and mortar, a trip budget, even a map (next lesson). A ratio is everywhere something is shared other than in half.
Share 720 Kč in the ratio 4 : 5
Step 1: parts: 4 + 5 = 9.
Step 2: one part: 720 : 9 = 80 Kč.
Step 3: the first gets 4 × 80 = 320 Kč, the second 5 × 80 = 400 Kč.
Check: 320 + 400 = 720. That checks out.
Result: 320 Kč and 400 Kč. Notice the second got more — in the ratio 4 : 5 they have the bigger number. A quick sense check: the ratio numbers are close, so the amounts should be similar too. They are.
Mixing green: blue and yellow 2 : 3, you need 1.5 litres
Step 1: parts: 2 + 3 = 5.
Step 2: one part: 1.5 : 5 = 0.3 litres.
Step 3: blue 2 × 0.3 = 0.6 litres, yellow 3 × 0.3 = 0.9 litres.
Check: 0.6 + 0.9 = 1.5. That checks out.
Result: 0.6 l of blue and 0.9 l of yellow. Sharing in a ratio handles decimals too — the method does not change. Just write the units, so you know 0.3 is a litre, not a cup.
The reverse question: the bigger part is 280 Kč, ratio 3 : 4. What is the whole?
Step 1: the bigger part matches four parts (the bigger number of the ratio).
Step 2: one part: 280 : 4 = 70 Kč.
Step 3: the whole has 3 + 4 = 7 parts: 7 × 70 = 490 Kč.
Result: the whole is 490 Kč (and the smaller part 3 × 70 = 210 Kč). Check: 210 + 280 = 490. That checks out. In a reverse question you divide the known part by its number of parts — not by the sum of parts. The sum comes at the end.
Do not divide the whole by a number from the ratio. For 600 Kč in the ratio 2 : 3 you do not divide by two or by three, but by five — the sum of the parts. Who divides by three gives out money that does not exist.
Practice: now you do it 🎲
Now try it for real. You will see all the questions at once, like on paper. スタート with ten. When it goes well, add more.
Share amounts in a ratio: add the parts, find one part. Write only the first amount, without Kč.
On paper: fair sharing
Write all three steps and a check by adding. Without a check it is not 完了.
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Share 540 Kč in the ratio 2 : 7. Do not forget the check.
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Share 1 200 g of dough into three loaves in the ratio 1 : 2 : 3.
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Tereza and Jonáš share 350 Kč in the ratio 3 : 2. How much would change if they shared in half? Calculate both cases and compare.
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The smaller part from sharing in the ratio 5 : 6 is 250 Kč. Find the bigger part and the whole.
Now you 💪
- I know three steps: add the parts, find one part, give out the multiples.
- I divide the whole by the sum of the parts, not by a number from the ratio.
- I check the result by adding the parts against the whole.
Done when: All four questions have three steps and a check; the reverse question gave you a bigger part of 300 Kč and a whole of 550 Kč.
What to take from this lesson
- Sharing in a ratio: add the parts → one part → multiples.
- One part = whole : sum of the parts of the ratio.
- It works for two, three or more members of a ratio.
- Reverse question: divide the known part by its number of parts.
- A check by adding is required and free.
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