Using Fractions Example 2

Lesson 3: Imperial Units and Conversion - Using Fractions Example 2

   Constructing Knowledge

Adding fractions requires a common denominator. You can change the denominator in a fraction by multiplying by a second fraction with the same value in the numerator and denominator.

\(\begin{align} \frac{5}{8}+\frac{3}{4}&=\frac{5}{8}+\frac{3}{4}\times {\color{red}{\frac{2}{2}}} \\ \\ &=\frac{5}{8}+\frac{3\times 2}{4\times 2} \\ \\ &=\frac{5}{8}+\frac{6}{8} \\ \\ &=\frac{5+6}{8} \\ \\ &=\frac{11}{8} \\ \end{align}\)

A video demonstration of the solution for Example 2 is provided.

EXAMPLE 2

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Darwin needs two pieces of plastic border edging for a garden that is in the corner of his yard. If one side of the garden is \(\text{12' 7}\frac{5}{8}"\) and the other is \(\text{5' 9}\frac{3}{4}"\), how much border edging is required?

Solution

To determine the total length of border edging, the individual side measurements will need to be added. This addition can be completed by converting every measurement to inches and then adding them or by adding the different units separately. This example shows adding the different units separately.

Start by adding the smallest unit, the inches.

\(\begin{align} 7\frac{5}{8}"+\,9\frac{3}{4}"&=7\frac{5}{8}"+\,9\frac{6}{8}" \\ \\ &=16\frac{11}{8}" \\ \\ &=17\frac{3}{8}" \\ \end{align}\)

There are 12 inches in a foot, so this measurement can be written as \(\text{1' 5}\frac{3}{8}"\).

Now add this measurement to the amount of feet.

\(\text{12' + 5" + 1' 5}\frac{3}{8}"\,=\text{18' 5}\frac{3}{8}"\)

So \(\text{18' 5}\frac{3}{8}"\) of border edging is required.




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