Evaluate
\frac{455}{62}\approx 7.338709677
Factor
\frac{5 \cdot 7 \cdot 13}{2 \cdot 31} = 7\frac{21}{62} = 7.338709677419355
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\begin{array}{l}\phantom{62)}\phantom{1}\\62\overline{)455}\\\end{array}
Use the 1^{st} digit 4 from dividend 455
\begin{array}{l}\phantom{62)}0\phantom{2}\\62\overline{)455}\\\end{array}
Since 4 is less than 62, use the next digit 5 from dividend 455 and add 0 to the quotient
\begin{array}{l}\phantom{62)}0\phantom{3}\\62\overline{)455}\\\end{array}
Use the 2^{nd} digit 5 from dividend 455
\begin{array}{l}\phantom{62)}00\phantom{4}\\62\overline{)455}\\\end{array}
Since 45 is less than 62, use the next digit 5 from dividend 455 and add 0 to the quotient
\begin{array}{l}\phantom{62)}00\phantom{5}\\62\overline{)455}\\\end{array}
Use the 3^{rd} digit 5 from dividend 455
\begin{array}{l}\phantom{62)}007\phantom{6}\\62\overline{)455}\\\phantom{62)}\underline{\phantom{}434\phantom{}}\\\phantom{62)9}21\\\end{array}
Find closest multiple of 62 to 455. We see that 7 \times 62 = 434 is the nearest. Now subtract 434 from 455 to get reminder 21. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }21
Since 21 is less than 62, stop the division. The reminder is 21. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}