Lesson 3: Imperial Units and Conversion - Use a Proportion

   Constructing Knowledge

Recall from the previous Lesson that you can set up a proportion to solve for an unkown measurement.

To convert from one imperial unit to another, follow the steps below.

  1. Determine a conversion ratio for the two units, using the Imperial Conversion Table.
  2. Assign a variable for the unknown and create a second ratio using the information provided.
  3. Write a proportion with both ratios and solve for the unknown (the variable).

EXAMPLE 1

How many pounds are there in 12 tons?

Solution


Step 1: Determine a conversion ratio for the two units.

A conversion ratio for pounds and tons is 2000 lbs = 1 t, which can also be written as \(\frac{1\,\text{t}}{2000\,\text{lbs}}=1\) or \(\frac{2000\,\text{lbs}}{1\,\text{t}}=1\).

Step 2: Assign a variable for the unknown and create a second ratio using the information from the question.

Letting x represent the unknown number of pounds gives the equation y lbs = 12 ton, which can be rewritten as \(\frac{x\,\,\text{lbs}}{12\,\text{t}}=1\).

Step 3: Write an equation with both ratios and solve.

You now have multiple expressions that are equal to 1, so they must be equal to each other. Choose the conversion ratio format that has the same unit location as the expression with the variable.



Now solve the equation to determine the value of x.

\(\begin{align} \frac{x\,\,\text{lbs}}{12\,\text{t}}&=\frac{2000\,\text{lbs}}{1\,\text{t}} \\ \\ \frac{x}{12\,\text{t}}\times {\color{red}{12\,\text{t}}}&=\frac{2000\,\text{lbs}}{1\,\text{t}}\times {\color{red}{12\,\text{t}}} \\ \\ \frac{x}{\cancel{12\,\text{t}}}\times \cancel{12\,\text{t}}&=\frac{2000\,\text{lbs}}{1\cancel{\text{t}}}\times 12\cancel{\text{t}} \\ \\ x&=24\,000\,\text{lbs} \\ \end{align}\)

There are 24 000 pounds in 12 tons.


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