Evaluate
\frac{25}{16}=1.5625
Factor
\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625
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\begin{array}{l}\phantom{80)}\phantom{1}\\80\overline{)125}\\\end{array}
Use the 1^{st} digit 1 from dividend 125
\begin{array}{l}\phantom{80)}0\phantom{2}\\80\overline{)125}\\\end{array}
Since 1 is less than 80, use the next digit 2 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{80)}0\phantom{3}\\80\overline{)125}\\\end{array}
Use the 2^{nd} digit 2 from dividend 125
\begin{array}{l}\phantom{80)}00\phantom{4}\\80\overline{)125}\\\end{array}
Since 12 is less than 80, use the next digit 5 from dividend 125 and add 0 to the quotient
\begin{array}{l}\phantom{80)}00\phantom{5}\\80\overline{)125}\\\end{array}
Use the 3^{rd} digit 5 from dividend 125
\begin{array}{l}\phantom{80)}001\phantom{6}\\80\overline{)125}\\\phantom{80)}\underline{\phantom{9}80\phantom{}}\\\phantom{80)9}45\\\end{array}
Find closest multiple of 80 to 125. We see that 1 \times 80 = 80 is the nearest. Now subtract 80 from 125 to get reminder 45. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }45
Since 45 is less than 80, stop the division. The reminder is 45. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}