Fractions, Ratios & Proportions in Science
See a fraction as both a part of a whole and a division, then use ratios and proportions to solve dilutions, doses, crosses, and scale problems.
Fractions, ratios, and proportions are the quiet backbone of almost every measurement in biomedical science. A fraction is two ideas at once: a part of a whole (3 of 4 offspring show a trait) and a division (3 divided by 4). A ratio compares two amounts, like the 1 part stock to 100 parts total in a 1:100 dilution, or the 3:1 pattern Gregor Mendel saw in a monohybrid cross. A proportion sets two ratios equal so you can solve for the missing piece by cross-multiplying. Medical laboratory scientists lean on this to mix dilutions that are neither too strong nor too weak. Nurses and pharmacists use proportions to scale a stock concentration to the exact dose a patient needs, where a slip is a real safety risk. Geneticists predict offspring ratios, and anyone reading a microscope or a map scale is really reading a ratio. Being fluent moving between a fraction, a decimal, and a percent means you can check any of these against common sense in seconds.
- Common Core · HSN-Q.A.1Use units and quantities to reason through multi-step problems, choosing and interpreting the numbers (including fractions and rates) that fit the situation.
- Ohio · Ohio HS N.Q.1Reason quantitatively with ratios, rates, and proportional relationships, and use them to solve real measurement problems.
- Common Core · HSS-ID.A.1Represent and interpret data, including parts of a whole expressed as fractions, decimals, and percents, so comparisons are fair.
- NGSS · SEP-5Using Mathematics and Computational Thinking: apply ratios, proportions, and simple calculations when analyzing scientific data.
- AP · AP Bio SP 6 (Quantitative)Perform mathematical routines such as ratios and proportions when analyzing and evaluating biological data, including genetic-cross ratios.
- Read a fraction (part of a whole and a division): Ratios and proportions are built on fractions, so students must see the top as the part and the bottom as the total, and know the bar also means divide.
- Multiply and divide whole numbers and decimals: Simplifying fractions and cross-multiplying both depend on quick, correct multiplication and division.
- Find common factors to simplify: Reducing a fraction like 6/8 to 3/4 requires spotting the largest number that divides both the top and the bottom.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
Learn to write and simplify a ratio, then set two ratios equal as a proportion and cross-multiply to solve for a missing amount. This is how dilutions, doses, and scales are worked out in the lab.
Simplify the fraction 3/12 to lowest terms.
Reviewed- A.1/2
- B.1/3
- C.1/4
- D.3/12 is already lowest
Show the worked solution ▾
Answer: C. 1/4
- Step 1: Find a common factor: Both 3 and 12 divide by 3.
- Step 2: Divide top and bottom: 3 divided by 3 is 1, and 12 divided by 3 is 4, so 3/12 becomes 1/4. No number bigger than 1 divides both 1 and 4, so it is done.
Why it's right: Dividing the top and bottom of 3/12 by 3 gives 1/4, which is in lowest terms.
- A: 1/2 would need 3/6, not 3/12.
- B: 1/3 would need 4/12, not 3/12.
- D: 3 and 12 share the factor 3, so it can still be reduced.
Aligned to Common Core HSN-Q.A.1: simplify a fraction · reading level ~grade 9
A protocol calls for a 1:100 dilution, meaning 1 part sample to 100 parts total. If you start with 2 mL of sample, what should the total volume be?
Reviewed- A.50 mL
- B.100 mL
- C.102 mL
- D.200 mL
Show the worked solution ▾
Answer: D. 200 mL
- Step 1: Set up the proportion: The ratio of sample to total is 1/100. With 2 mL of sample, write 1/100 = 2/x, where x is the total volume.
- Step 2: Cross-multiply and solve: 1 times x equals 100 times 2, so x = 200. The total volume is 200 mL.
Why it's right: Keeping the ratio 1 part to 100 parts, 2 mL of sample needs a total of 2 times 100, which is 200 mL.
- A: 50 mL would divide by 100 instead of scaling up from the sample.
- B: 100 mL ignores that the sample is 2 mL, not 1 mL.
- C: 102 mL adds 2 and 100 instead of scaling the ratio.
Aligned to Ohio HS N.Q.1: apply a ratio (dilution) · reading level ~grade 9
Convert the fraction 3/5 to a percent.
Reviewed- A.3.5%
- B.35%
- C.53%
- D.60%
Show the worked solution ▾
Answer: D. 60%
- Step 1: Divide to get a decimal: 3/5 means 3 divided by 5, which is 0.6.
- Step 2: Multiply by 100: 0.6 times 100 is 60, so 3/5 is 60 percent.
Why it's right: 3 divided by 5 is 0.6, and 0.6 times 100 is 60, so 3/5 equals 60 percent.
- A: 3.5% just reuses the digits 3 and 5 with a decimal.
- B: 35% reverses the digits instead of dividing.
- C: 53% flips the digits of the fraction.
Aligned to Common Core HSS-ID.A.1: convert a fraction to a percent · reading level ~grade 9
- A lab tech mixes a 1:100 dilution and uses a proportion to find the total volume needed for a 2 mL sample.
- A nurse sets 5 mg / 10 mL equal to the ordered dose over an unknown volume and cross-multiplies to find how many mL to draw.
- A student reports 3 of 5 trials as 60 percent so the class results can be compared on the same scale.
Fill these in as you work through the lesson.
- Fraction (part over whole, and top divided by bottom):
- Ratio (a comparison like 1:100 or 3:1):
- Proportion (two equal ratios, solve by cross-multiplying):
- Percent (a fraction out of 100):
To solve a proportion a/b = c/d, multiply a by and b by , set the two products , then divide to find the unknown.
- Explain the two meanings of the fraction 3/4 in one sentence.
- Write a 1:100 dilution as a fraction, a decimal, and a percent.
- In 5/10 = 8/x, show the cross-multiplication step and state what x equals.
Convert 3/5 to a percent. First divide 3 by 5 to get the decimal 0.6, then multiply 0.6 by 100 to get ____ percent.
The vocabulary of this topic, shown in the way you will meet it.