Problem
Use a ratio to split a percent between items
A bar graph labels three of its five sections. The other two are in a given ratio, and we need each one's percent.
Ratios
Your answer
How to solve
Strategy Analyze the Units — The bar tells us how much is left for the two unlabelled sections; the ratio tells us how to cut that leftover in two. Neither fact alone is enough -- together they are.
1STEP 1
Find how much is left over
Take the three labelled sections off the whole bar.
100 - 42 - 13 - 5 = 40
The two clinics share 40% between them.
6.SP.B.4Identify Subproblems2STEP 2
Split the leftover in the given ratio
A ratio of 5 : 3 means cutting the 40% into 8 equal pieces and giving 5 to one and 3 to the other.
5 + 3 = 8, 40 ÷ 8 = 5
Each piece is 5% of the total.
6.RP.A.3Analyze The UnitsThe leftover splits into eight equal pieces.
Why?
A ratio of says the two amounts are made of the same size piece, five of them and three of them.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Those eight pieces together are exactly the leftover, with nothing beside them, so each is an eighth of it.
🧱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
Count the pieces for each
Family clinics take five of those pieces and oriental clinics take three.
5 × 5 = 25, 5 × 3 = 15
Family clinics are 25% and oriental clinics 15%.
6.RP.A.3Work BackwardsAnswer
Family clinics 25%, oriental clinics 15%
Add all five back: 42 + 25 + 15 + 13 + 5 = 100, and 25 : 15 reduces to 5 : 3, so both conditions hold.
Takeaway
A ratio says how to cut something up, but not how big it is -- you need both.
- Find how much is left over
- Split the leftover in the given ratio
- Count the pieces for each