Ratios, proportions & percents · Topic 6 of 15

Ratios, Proportions & Unit Rates

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Math · ratios & proportions

Set two ratios equal with matching units, cross-multiply and divide; a unit rate is the amount for one unit.

01 · Solve a proportionCross-multiply: a/b = c/d → a × d = b × c

02 · Dose problemsLine up the units: mg/tab = mg/tab

03 · Unit rateUnit rate = top ÷ bottom (per 1)

A ratio compares two amounts: a to b = a:b = a/b must know

Proportion = two equal ratios: a/b = c/d must know

Unit rate = top ÷ bottom (the amount per 1 unit) must know

Cross-multiply: a/b = c/d means a × d = b × c, then divide must know

Match the units: mg over tablets = mg over tablets must know

Simplify a ratio but keep both parts: 12:3 = 4:1, not 4

Part-to-part → add the parts for the whole: 3:2 of 25 → 3/5 × 25 = 15

Distance = rate × time; rate = d ÷ t, time = d ÷ r

Write the known ratio with units (250 mg / 1 tab)

Write the second ratio, units in the same spots, x for the unknown

Cross-multiply, divide, then check the answer makes sense

125 mg in 5 mL, need 375 mg: 125x = 1,875 → x = 15 mL

10 mg/kg for a 22-kg patient: x = 10 × 22 = 220 mg

150 miles in 2.5 hours = 150 ÷ 2.5 = 60 mph

Commonly confused

	Ratio	Rate
Compares	Two amounts in the same unit	Two amounts in different units
Written as	3:12, 3 to 12 or 3/12	150 miles / 2.5 hours
Simplify to	Lowest terms, keep both parts (1:4)	A unit rate, per 1 (60 mph)
Before comparing	Convert to one unit first	Divide top by bottom

Keep the order of the words: 1 nurse to 4 patients = 1:4, not 4:1

mg/kg with weight in lb: change lb to kg first (see Household ↔ Metric)

Show 2 more facts

Same unit before you compare: 2 in to 1 ft = 2:12 = 1:6

x on top? Multiply both sides by its denominator instead

Pearl

Units face units: if mg is on top of one ratio, mg goes on top of the other.

Practice this topic, then test the whole section.

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