A concentration is not a rate
mg/mL describes how much is in each volume. Multiply by mL/min to obtain mg/min. Dividing by flow would give the wrong units.
SKILLS · QUANTITATIVE REASONING
Rates, ratios & units
Write the quantity being requested as a fraction or product. Then let the units and the comparison tell you what belongs in it.
01 · THE IDEA
“Per” names a denominator; “relative to control” asks for a second ratio.
Relative A per B = (Anew / Acontrol) ÷ (Bnew / Bcontrol)
A fold change is a ratio, not a percentage-point difference. Keep units until they cancel, and distinguish the value remaining from the percentage decrease.
Normalize both quantities
If output is 80% of control and input is 40%, output per input is 0.80/0.40 = 2 times control. That does not mean total output increased.
Combine independent factors once
If a stated model says total output = amount × active fraction × rate per active unit, multiply their relative factors. Do not multiply by a factor again if it is already included in a measured total.
CHANGE ONE PART OF THE MODEL
Less total output, more output per input
ATP production stays at 80% of control. Change oxygen consumption and watch the normalized ATP-per-oxygen ratio.
Total ATP80%
Total oxygen40%
ATP per oxygen2× control
(80 / 100) ÷ (40 / 100) = 2
“ATP per oxygen” is a ratio. It is not the same quantity as total ATP production.
02 · WORKED EXAMPLES
Follow the setup, then the numbers
1. The rate falls, but the ratio rises
Control produces 120 units of ATP per minute while consuming 60 units of oxygen per minute. Treatment gives ATP = 90 and oxygen = 30 in the same units.
- Control ATP per oxygen = 120/60 = 2.
- Treatment ATP per oxygen = 90/30 = 3.
- Relative ratio = 3/2 = 1.5, or 150% of control.
- Total ATP output nevertheless fell to 90/120 = 75%.
Carry this forward: A higher ratio can coexist with a lower numerator.
2. Make the time units agree
A solution contains 0.50 mg/mL of a compound and flows at 120 mL/hour. Find the delivery rate in mg/min.
- 120 mL/hour × 1 hour/60 min = 2 mL/min.
- 0.50 mg/mL × 2 mL/min = 1 mg/min.
Carry this forward: The mL units cancel and the remaining units match the requested rate.
03 · TRY IT IN DIFFERENT FORMS
Practice in different forms
For each question, identify the requested quantity and write the setup before calculating. Use a hint if needed, then choose an answer to see the explanation.
Untimed learning practice. These responses stay on this page and reset when you leave or reload; they do not change your test results.
QUESTION 1 / 4 · Across subjects
Concentration to rate
Fluid containing 0.40 mg/mL of X flows at 90 mL/hour. What is the delivery rate in mg/min?
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TAKE INTO A FRESH PASSAGE
Your setup checklist
- Name the requested quantity and write its units.
- Translate “per” into division and rate into amount per time.
- Normalize each changing factor to its own control.
- Check whether the question asks for the final value, a fold change, or a percentage decrease.
Before calculating, explain what each term represents and what the requested answer would mean.
Concept references
All scenarios and questions here are original learning exercises. These references support the underlying concepts; the simplified assumptions are stated within each example.