Ratio to percentage
A ratio of 2 : 7 makes 9 equal parts. Each ingredient is its parts out of all the parts.
How much millet in the kanji?
To make millet kanji (a porridge), millet and water are mixed in the ratio 2 : 7.
What percentage of the mixture is millet?
What this lesson covers
The idea
A ratio of parts is converted to the fraction each part makes of the whole (its ratio term over the sum of the terms) and then to a percentage; the parts' percentages total 100%.
How much millet in the kanji?
To make millet kanji (a porridge), millet and water are mixed in the ratio 2 : 7.
What percentage of the mixture is millet?
- About 29%
- About 22%
- About 78%
Build the mixture from parts
A ratio is a number of equal parts for each ingredient. Change the parts and read the fraction and the percentage of each ingredient.
Parts out of all the parts
A ratio of parts is converted to the fraction each part makes of the whole (its ratio term over the sum of the terms) and then to a percentage; the parts' percentages total 100%.
The ratio 2 : 7 means 2 parts of millet and 7 parts of water, so there are 2 + 7 = 9 parts in all. Millet is 2 of the 9 parts and water is 7 of the 9 parts.
As percentages: Millet: 2/9 × 100 ≈ 22.22% Water: 7/9 × 100 ≈ 77.78% Together: 22.22% + 77.78% = 100%
Estimate first. 20% of 9 is 1.8 and 25% of 9 is 2.25. The 2 lies between them, so millet is between 20% and 25%. For 500 mL of kanji, the millet is about 5 × 22.22 = 111.1 mL.
Notes
A ratio of parts is converted to the fraction each part makes of the whole (its ratio term over the sum of the terms) and then to a percentage; the parts' percentages total 100%.
Check yourself
Juice and water are mixed in the ratio 1 : 4. What percentage of the mixture is juice?
Answer: 20 %
1 + 4 = 5 parts in all. Juice is 1/5 of the mixture, and 1/5 × 100 = 20%.
A garden has red and white flowers in the ratio 3 : 7. What percentage of the flowers are white?
Answer: 70 %
3 + 7 = 10 parts in all. White is 7/10, and 7/10 × 100 = 70%.
Milk and water are mixed in the ratio 3 : 2 to make 500 mL. How many mL of milk are in the mixture?
Answer: 300 mL
3 + 2 = 5 parts. Milk is 3 out of 5 parts, which is 60%. And 60% of 500 mL = 300 mL.
Red and white paint are mixed in the ratio 5 : 3. Which pair of percentages is correct?
- 62.5% red and 37.5% white — correct. Yes! 5 + 3 = 8 parts. 5/8 = 62.5% and 3/8 = 37.5%, and they total 100%.
- 50% red and 30% white. These total only 80%. The parts of the whole must total 100%.
- 60% red and 40% white. These total 100%, but red is 5 out of 8 parts, which is 62.5%, not 60%.
- 5% red and 3% white. These total only 8%. Red is 5 of the 8 parts, and 5/8 is 62.5%.