# Fractions Part 9 – Fraction Problems

OK, let’s now use the skills in my previous posts to solve some example problems. I will show the problems first so you can try them on your own, then further down the post, you can see the solutions:

$\begin{array}{l} {{1}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}\div\hspace{0.33em}{2}\frac{7}{8}}\\ {{2}{.}\hspace{0.33em}\hspace{0.33em}\frac{7}{9}\hspace{0.33em}{+}\hspace{0.33em}\frac{11}{12}}\\ {{3}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}{+}\hspace{0.33em}{2}\frac{7}{8}}\\ {{4}{.}\hspace{0.33em}\hspace{0.33em}\frac{11}{12}\hspace{0.33em}{-}\hspace{0.33em}\frac{7}{9}}\\ {{5}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}\times\hspace{0.33em}{2}\frac{7}{8}} \end{array}$

SOLUTIONS:

${1}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}\div\hspace{0.33em}{2}\frac{7}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{25}{4}\hspace{0.33em}\div\hspace{0.33em}\frac{23}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{25}{4}\hspace{0.33em}\times\hspace{0.33em}\frac{8}{23}\hspace{0.33em}{=}\hspace{0.33em}\frac{{25}\hspace{0.33em}\times\hspace{0.33em}{8}}{{4}\hspace{0.33em}\times\hspace{0.33em}{23}}$

Now I will simplify this as much as possible now before I multiply to keep the numbers as small as possible:

$\frac{{25}\hspace{0.33em}\times\hspace{0.33em}{8}}{{4}\hspace{0.33em}\times\hspace{0.33em}{23}}\hspace{0.33em}{=}\hspace{0.33em}\frac{{25}\hspace{0.33em}\times\hspace{0.33em}\rlap{/}{4}\hspace{0.33em}\times\hspace{0.33em}{2}}{\rlap{/}{4}\hspace{0.33em}\times\hspace{0.33em}{23}}\hspace{0.33em}{=}\hspace{0.33em}\frac{{25}\hspace{0.33em}\times\hspace{0.33em}{2}}{23}\hspace{0.33em}{=}\hspace{0.33em}\frac{50}{23}\hspace{0.33em}{=}\hspace{0.33em}{2}\frac{4}{23}$

${2}{.}\hspace{0.33em}\hspace{0.33em}\frac{7}{9}\hspace{0.33em}{+}\hspace{0.33em}\frac{11}{12}$.  Since these fractions are being added and they have different denominators, we need to find a common denominator. To find the Least Common Denominator (LCD):

9 = 3 × 3,   12 = 2 × 2 × 3

LCD = 2 × 2 × 3 × 3 = 36

So now convert each of the fractions into equivalent ones with 36 as the denominator. So I will multiply the top and bottom of the first fraction by 4 and the other one by 3:

$\frac{7}{9}\hspace{0.33em}{+}\hspace{0.33em}\frac{11}{12}\hspace{0.33em}{=}\hspace{0.33em}\frac{{7}\hspace{0.33em}\times\hspace{0.33em}{4}}{{9}\hspace{0.33em}\times\hspace{0.33em}{4}}\hspace{0.33em}{+}\hspace{0.33em}\frac{{11}\hspace{0.33em}\times\hspace{0.33em}{3}}{{12}\hspace{0.33em}\times\hspace{0.33em}{3}}\hspace{0.33em}{=}\hspace{0.33em}\frac{28}{36}\hspace{0.33em}{+}\hspace{0.33em}\frac{33}{36}\hspace{0.33em}{=}\hspace{0.33em}\frac{61}{36}\hspace{0.33em}{=}\hspace{0.33em}{1}\frac{25}{36}$

${3}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}{+}\hspace{0.33em}{2}\frac{7}{8}$. First, the fractions need to be converted to improper ones. Then since 4 evenly divides into 8, we just need to convert the first fraction to an equivalent one with 8 as the denominator:

${6}\frac{1}{4}\hspace{0.33em}{+}\hspace{0.33em}{2}\frac{7}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{25}{4}\hspace{0.33em}{+}\hspace{0.33em}\frac{23}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{{25}\hspace{0.33em}\times\hspace{0.33em}{2}}{{4}\hspace{0.33em}\times\hspace{0.33em}{2}}\hspace{0.33em}{+}\hspace{0.33em}\frac{23}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{50}{8}\hspace{0.33em}{+}\hspace{0.33em}\frac{23}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{73}{8}\hspace{0.33em}{=}\hspace{0.33em}{9}\frac{1}{8}$

${4}{.}\hspace{0.33em}\hspace{0.33em}\frac{11}{12}\hspace{0.33em}{-}\hspace{0.33em}\frac{7}{9}$. These are the same fractions as in the second problem, but now it’s a subtraction problem. We have already converted these two fractions into equivalent fractions with the same denominator, so we will use that result here:

$\frac{11}{12}\hspace{0.33em}{-}\hspace{0.33em}\frac{7}{9}\hspace{0.33em}{=}\hspace{0.33em}\frac{33}{36}\hspace{0.33em}{-}\hspace{0.33em}\frac{28}{36}\hspace{0.33em}{=}\hspace{0.33em}\frac{5}{36}$

${5}{.}\hspace{0.33em}\hspace{0.33em}{6}\frac{1}{4}\hspace{0.33em}\times\hspace{0.33em}{2}\frac{7}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{25}{4}\hspace{0.33em}\times\hspace{0.33em}\frac{23}{8}\hspace{0.33em}{=}\hspace{0.33em}\frac{575}{8}\hspace{0.33em}{=}\hspace{0.33em}{71}\frac{7}{8}$

How did you do?