Evaluate
\frac{456}{23}\approx 19.826086957
Factor
\frac{2 ^ {3} \cdot 3 \cdot 19}{23} = 19\frac{19}{23} = 19.82608695652174
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)456}\\\end{array}
Use the 1^{st} digit 4 from dividend 456
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)456}\\\end{array}
Since 4 is less than 23, use the next digit 5 from dividend 456 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)456}\\\end{array}
Use the 2^{nd} digit 5 from dividend 456
\begin{array}{l}\phantom{23)}01\phantom{4}\\23\overline{)456}\\\phantom{23)}\underline{\phantom{}23\phantom{9}}\\\phantom{23)}22\\\end{array}
Find closest multiple of 23 to 45. We see that 1 \times 23 = 23 is the nearest. Now subtract 23 from 45 to get reminder 22. Add 1 to quotient.
\begin{array}{l}\phantom{23)}01\phantom{5}\\23\overline{)456}\\\phantom{23)}\underline{\phantom{}23\phantom{9}}\\\phantom{23)}226\\\end{array}
Use the 3^{rd} digit 6 from dividend 456
\begin{array}{l}\phantom{23)}019\phantom{6}\\23\overline{)456}\\\phantom{23)}\underline{\phantom{}23\phantom{9}}\\\phantom{23)}226\\\phantom{23)}\underline{\phantom{}207\phantom{}}\\\phantom{23)9}19\\\end{array}
Find closest multiple of 23 to 226. We see that 9 \times 23 = 207 is the nearest. Now subtract 207 from 226 to get reminder 19. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }19
Since 19 is less than 23, stop the division. The reminder is 19. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}