Evaluate
\frac{45}{32}=1.40625
Factor
\frac{3 ^ {2} \cdot 5}{2 ^ {5}} = 1\frac{13}{32} = 1.40625
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\begin{array}{l}\phantom{32)}\phantom{1}\\32\overline{)45}\\\end{array}
Use the 1^{st} digit 4 from dividend 45
\begin{array}{l}\phantom{32)}0\phantom{2}\\32\overline{)45}\\\end{array}
Since 4 is less than 32, use the next digit 5 from dividend 45 and add 0 to the quotient
\begin{array}{l}\phantom{32)}0\phantom{3}\\32\overline{)45}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45
\begin{array}{l}\phantom{32)}01\phantom{4}\\32\overline{)45}\\\phantom{32)}\underline{\phantom{}32\phantom{}}\\\phantom{32)}13\\\end{array}
Find closest multiple of 32 to 45. We see that 1 \times 32 = 32 is the nearest. Now subtract 32 from 45 to get reminder 13. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }13
Since 13 is less than 32, stop the division. The reminder is 13. The topmost line 01 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}