Mixed Numbers and Long Division

A number written in the form 14${\frac{{5}}{{9}}}$ is interpreted as the mixed number 14 + ${\frac{{5}}{{9}}}$. Most commands applied to a mixed number return a fraction. For example, applying Evaluate or Simplify to 14${\frac{{5}}{{9}}}$ gives the result ${\frac{{131}}{{9}}}$. The reverse is accomplished by Expand, which converts a fraction to a mixed number. These commands are also available directly on the Compute Toolbar. Click itbpF0.3035in0.3035in0.0701inevaluate.wmffor Evaluate, itbpF0.3035in0.3035in0.0701insimplify.wmf for Simplify, and itbpF0.3001in0.3001in0.0701incxpand.wmf for Expand.

$\blacktriangleright$ Evaluate

1${\frac{{2}}{{3}}}$ = ${\frac{{5}}{{3}}}$


193${\frac{{87}}{{94}}}$ = ${\frac{{18229}}{{94}}}$


1${\frac{{2}}{{3}}}$ +2${\frac{{3}}{{4}}}$ = ${\frac{{53}}{{12}}}$

$\blacktriangleright$ Expand

${\frac{{18229}}{{94}}}$ = 193${\frac{{87}}{{94}}}$


${\frac{{53}}{{12}}}$ = 4${\frac{{5}}{{12}}}$

The expansion of a fraction into a mixed number uses the familiar long-division algorithm. In the preceding example, 18229 divided by 94 is equal to 193 with remainder 87.