LEMMA

Applied arithmetic

Doses, rates, and conversions

TEAS math

Set up doses and rates as proportions, and let the units tell you whether to multiply or divide.

What this covers

2.2 lb≈1 kg,dose=kgmg​⋅kg
  • Write what one unit is worth, then scale to how many units there are.
  • Converting to a larger unit makes the number smaller — divide.
  • A per-kilogram dose repeats once for every kilogram — multiply.
  • For supplies, find the total needed first, then divide by the container size.

Worked example

Worked example

An arithmetic exercise specifies 3 mg per kg and a weight of 110 lb. Using the exercise's conversion factor 2.2 lb per kg, find the dose.

  1. 110÷2.2=50 kgKilograms are bigger than pounds, so the number shrinks.
  2. 3⋅50=150 mgThe 3 mg repeats once per kilogram, fifty times.
Another worked example

A liquid medication contains 250 mg in 5 mL. How many milliliters contain a 125 mg dose?

  1. 125mg⋅250mg5mL​Put mg in the factor's denominator so the original mg cancels.
  2. 250625​mL=2.5mLThe resulting unit is a volume. This calculation uses the concentration stated in the exercise.

A common mistake

A mistake Lemma catches

From

w=110⋅2.2w=110÷2.2

“Every kilogram is 2.2 pounds, so the same body is fewer kilograms than pounds: divide, 110 ÷ 2.2 = 50 kg. Multiplying gives 242 — more kilograms than pounds, which cannot be.”

Try one

Sample problem

A patient weighs 22 pounds. Using 2.2 lb = 1 kg, what is the weight in kilograms? Enter the number.

22 lb⋅2.2 lb1 kg​

Practice doses & rates free

No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.

Where this fits

Before this