Problem
Reduce the investment ratio to whole numbers
Two people invest different amounts and split the profit in that ratio. We need one person's share.
Ratios
Your answer
How to solve
Strategy Analyze the Units — Simplify the ratio first and the big numbers stop mattering: the profit is cut into as many equal parts as the two terms add to, and each person takes their own number of parts.
1STEP 1
Simplify the ratio of the investments
Both amounts are multiples of 500,000 won.
1500000 ÷ 500000 = 3, 2000000 ÷ 500000 = 4
The ratio is 3 : 4.
6.RP.A.3Analyze The Units2STEP 2
Count the equal parts
The two terms tell how many parts the profit is cut into altogether.
3 + 4 = 7
Seven parts in all.
6.RP.A.3Identify SubproblemsSharing in the ratio cuts the profit into seven equal parts.
Why?
A ratio of says both shares are built from a piece of the same size, three of them and four of them.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The two shares together are the whole profit and nothing else, so those seven pieces fill it exactly.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Take Eunji's parts
Eunji gets three of the seven parts of the profit.
700000 ÷ 7 = 100000, 100000 × 3 = 300000
Eunji gets 300,000 won.
6.RP.A.3Organize Information In More WaysAnswer
300,000 won
Check the other share: Hyunsu gets 100000 × 4 = 400000 won, and 300000 + 400000 = 700000 won.
Takeaway
Sharing in a ratio means cutting into as many equal parts as the terms add to.
- Simplify the ratio of the investments
- Count the equal parts
- Take Eunji's parts