Lesson 3: Imperial Units and Conversion - Using Fractions with the Imperial System

   Constructing Knowledge

Measurements in the imperial system often involve fractions, instead of decimals. When fractions are given in a measurement, it is expected that they will also be used in the solution to a problem involving that measurement.

When performing an operation on a mixed fraction such as \(1\frac{3}{4}\), it is often best to convert it to an improper fraction. Recall that you can multiply the denominator by the whole number, and add the product to the numerator to get the new numerator.

\(\begin{align} {\color{red}{1}}\frac{\color{green}{3}}{\color{blue}{4}}&=\frac{\left({\color{blue}{4}}\times {\color{red}{1}}\right)+{\color{green}{3}}}{4} \\ \\ &=\frac{7}{4} \\ \end{align}\)

EXAMPLE 1

Convert \(1\frac{3}{4}\) miles into yards.

Solution


\(\begin{align} \frac{1\frac{3}{4}}{z\,\,\text{yards}}&=\frac{1\,\text{mile}}{1760\,\text{yards}} \\ \\ \\ \text{Cross Multiply} \\ \\ 1\frac{3}{4}\times 1760&=1\times z \\ \\ \frac{7}{4}\times \frac{1760}{1}&=z \\ \\ \frac{7\times1760}{4\times1}&=z \\ \\ \frac{12\,320}{4}&=z \\ \\ 3080&=z \\ \end{align}\)

There are 3080 yards in \(1\frac{3}{4}\) miles.


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