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To find what that video's length must be, subtract the previous videos' lengths from the requirement, 5 hours. (x is the video length of her fourth video)
7/8 + 1 1/4 + 2 1/2 + x = 5
To make adding these fractions easier, find a common denominator.
[tex]\frac{7}{8} + 1\frac{1}{4} + 2\frac{1}{2}\\=\frac{7}{8} + \frac{5}{4} + \frac{5}{2}\\=\frac{7}{8} + \frac{5}{4} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{4}{4}\\=\frac{7}{8} + \frac{10}{8} + \frac{20}{8}\\=\frac{7+10+20}{8}\\=\frac{37}{8}[/tex]hours. To meet the [tex]5 = \frac{40}{8}[/tex] hour goal the shortest fouth video she can make is [tex]\frac{40}{8} - \frac{37}{8} = \frac{3}{8}[/tex] hours, because if the fourth video was any shorter, she'd end up with less than [tex]\frac{37}{8} + \frac{3}{8} = \frac{40}{8} = 5[/tex] hours in total (this is called a proof by contradiction). We are now done.
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