FractionSteps - Maple Help
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Student[Basics]

 FractionSteps
 show steps in the simplification of a specified expression

 Calling Sequence FractionSteps(ex, opts)

Parameters

 ex - expression or string opts - options of the form keyword=value where keyword is one of displaystyle, output

Description

 • The FractionSteps command is used to show the steps of adding fractions.
 • If expr is a string, then it is parsed into an expression using InertForm:-Parse so that no automatic simplifications are applied, and thus no steps are missed.
 • The displaystyle and output options can be used to change the output format.  See OutputStepsRecord for details.
 • This function is part of the Student:-Basics package.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{Basics}\right):$
 > $\mathrm{FractionSteps}\left("1/2+1/3"\right)$
 $\begin{array}{lll}{}& {}& \text{Let's Simplify Fractions}\\ {}& {}& \frac{{1}}{{2}}{+}\frac{{1}}{{3}}\\ \text{•}& {}& \text{Find fractions to get lowest common denominator of}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}6\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}{\cdot }\left(\frac{{1}}{{2}}\right){+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}{\cdot }\left(\frac{{1}}{{3}}\right)\\ \text{•}& {}& \text{Multiply}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}}{+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}}\\ \text{•}& {}& \text{Add numerators}\\ {}& {}& \frac{\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{1}}\right)}{{6}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}3\cdot 1\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}{+}{2}{\cdot }{1}}{{6}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}2\cdot 1\\ {}& {}& \frac{{3}{+}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{2}}}{{6}}\\ \text{•}& {}& \text{Add}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}3+2\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{5}}}{{6}}\\ \text{•}& {}& \text{Solution}\\ {}& {}& \frac{{5}}{{6}}\end{array}$ (1)
 > $\mathrm{FractionSteps}\left("a/2+a/3+a/4"\right)$
 $\begin{array}{lll}{}& {}& \text{Let's Simplify Fractions}\\ {}& {}& \frac{{a}}{{2}}{+}\frac{{a}}{{3}}{+}\frac{{a}}{{4}}\\ \text{•}& {}& \text{Find fractions to get lowest common denominator of}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}12\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}}{\cdot }\left(\frac{{a}}{{2}}\right){+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}}{\cdot }\left(\frac{{a}}{{3}}\right){+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}{\cdot }\left(\frac{{a}}{{4}}\right)\\ \text{•}& {}& \text{Multiply}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{12}}}{+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{12}}}{+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{12}}}\\ \text{•}& {}& \text{Add numerators}\\ {}& {}& \frac{\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{6}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{4}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\right)}{{12}}\\ \text{•}& {}& \text{Add}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}6a+4a+3a\\ {}& {}& \frac{\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{13}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{a}}\right)}{{12}}\\ \text{•}& {}& \text{Solution}\\ {}& {}& \frac{{13}{a}}{{12}}\end{array}$ (2)
 > $\mathrm{FractionSteps}\left("3/11+13/29",\mathrm{output}=\mathrm{typeset}\right)$
 $\begin{array}{lll}{}& {}& \text{Let's Simplify Fractions}\\ {}& {}& \frac{{3}}{{11}}{+}\frac{{13}}{{29}}\\ \text{•}& {}& \text{Find fractions to get lowest common denominator of}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}319\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{29}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{29}}}{\cdot }\left(\frac{{3}}{{11}}\right){+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{11}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{11}}}{\cdot }\left(\frac{{13}}{{29}}\right)\\ \text{•}& {}& \text{Multiply}\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{29}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{319}}}{+}\frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{11}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{13}}}{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{319}}}\\ \text{•}& {}& \text{Add numerators}\\ {}& {}& \frac{\left(\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{29}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{3}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{+}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{11}}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{\cdot }}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{13}}\right)}{{319}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}29\cdot 3\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{87}}{+}{11}{\cdot }{13}}{{319}}\\ \text{•}& {}& \text{Multiply}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}11\cdot 13\\ {}& {}& \frac{{87}{+}\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{143}}}{{319}}\\ \text{•}& {}& \text{Add}\phantom{\rule[-0.0ex]{1.0thickmathspace}{0.0ex}}87+143\\ {}& {}& \frac{\colorbox[rgb]{0.886274509803922,0.964705882352941,0.996078431372549}{{230}}}{{319}}\\ \text{•}& {}& \text{Solution}\\ {}& {}& \frac{{230}}{{319}}\end{array}$ (3)

Compatibility

 • The Student[Basics][FractionSteps] command was introduced in Maple 2022.
 • For more information on Maple 2022 changes, see Updates in Maple 2022.