How to calculate proportions

If there are about 100 E. coli (a bacterium) in a 20 mL water sample, about how many E. coli would be found in 1000 mL of this water?

There are two ways we can solve this equation:

Method 1: solving a proportion equation

Step 1: 100 E. coli / 20 mL = ? / 1000 mL. This can also be written as:

$$ \frac{100\;E.coli}{20\; mL} = \frac{?}{1000\; mL} $$

Aside: We usually let x be the number of E.coli that we are looking for. Hence the equation above can be written as:

$$ \frac{100\;E.coli}{20\; mL} = \frac{x}{1000\; mL} $$

Step 2 Now we can solve for x

$$ 100\; E.coli \times 1000\; mL = 20\; mL \times x $$

Step 3: Solve the equation for x, where x is the number of E.coli we are looking for:

$$ \begin{align*} x &= \frac{100\; E. coli \times 1000\; mL}{20\; mL} \cr &= 5000\; E. coli \end{align*} $$

Therefore, about 5000 E. coli can be found in 1000 mL of this water.

Method 2: solving how many E. coli are in each mL

Step 1: 100 E. coli / 20 mL = ? / 1 mL

Step 2: To determine how many E.coli are present in 1 mL, we divide by 20 which gives:

100E. coli / 20 mL = 5 E.coli per 1 mL

Step 3: Now to determine how many E.coli are present in 1000 mL, we multiply by 1000 as:

If there are 5 E. coli per 1 mL of water, multiple 5 by 1000 to find out how many E. coli there are in total.

Therefore, there are 5000 E. coli in 1000 mL of this water.

Reference: Basic Laboratory Calculations for Biotechnology by Lisa A. Seidman