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I-01: Fractions, percentages and ratios

IntoChemistry | General Chemistry I Math Readiness

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Module I-01 · Recommended before: Before the first chemistry problem

Fractions, percentages and ratios

Ratios describe how two quantities compare. A percent is a ratio with 100 as its denominator. When reading a word problem, distinguish a part from the whole.

Learn the method

percent = (part / whole) × 100

  1. Identify the part and total.
  2. Write part ÷ total.
  3. Multiply by 100 only when the question asks for percent.
  4. Check whether the result should be above or below 100%.

Common mistake: Never divide by the solvent mass when the denominator is total solution mass.

Worked example

Problem: A sample contains 3.0 g of solute in 12.0 g of solution. Find mass percent.

Step-by-step solution: 3.0 ÷ 12.0 × 100 = 25%; the denominator is the total solution, not the solvent.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Proportion by scaling

A recipe uses a 2:3 solute-to-solvent mass ratio. With 8 g solute, solvent mass is 8 × 3/2 = 12 g.

Percent change

A measurement increases from 40 g to 50 g. Change = (50−40)/40×100 = 25% increase.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. What percentage of a mixture is 6 g of solute in 24 g of total mixture?
Hint for question 1

Use the whole mixture as denominator.

Question 2. What percentage of a mixture is 7 g of solute in 28 g of total mixture?
Hint for question 2

Use the whole mixture as denominator.

Question 3. What percentage of a mixture is 8 g of solute in 40 g of total mixture?
Hint for question 3

Use the whole mixture as denominator.

Question 4. What percentage of a mixture is 9 g of solute in 36 g of total mixture?
Hint for question 4

Use the whole mixture as denominator.

Question 5. What percentage of a mixture is 10 g of solute in 50 g of total mixture?
Hint for question 5

Use the whole mixture as denominator.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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