How to Calculate Proportions

If there are about 100 mg of Na in a 20 mL water sample, about how many mg of Na 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 mg / 20 mL = ? / 1000 mL. This can also be written as: $$\frac{100\; mg}{20\;mL}=\frac{?}{1000\;mL}$$

Aside: We usually let $x$ me the number of mg that we are looking for. Hence, the equation above can be written as: $$\frac{100\; mg}{20\;mL}=\frac{x}{1000\;mL}$$

Step 2: Now, we can solve for $x$ by cross multiplying:

$$100\;mg \times 1000\;mL = 20\; mL \times x$$

Step 3: Solve the equation for $x$, where $x$ is the number of mg we are looking for:

\begin{align*}x &= \frac{100\;mg \times 1000\; mL}{20\; mL} \cr &= 5000\;mg \end{align*}

Therefore, about 5000 mg of Na can be found in 1000 mL of this water.

Method 2: solving how many mg of Na are in each mL

Step 1: 100 mg / 20 mL = ? / 1 mL

Step 2: To determine how many mg of Na are present in 1 mL, we divide by 20 which gives:

100 mg of Na/ 20 mL = 5 mg of Na per 1 mL

Step 3: To now determine how many mg of Na are present in 1000 mL, we multiply by 1000 as:

If there are 5 mg of Na per 1 mL of water, multiply 5 by 1000 to find out how many mg of Na there are in total.

Therefore, there are 5000 mg of Na in 1000 mL of this water.