Evaluate
\frac{423}{70}\approx 6.042857143
Factor
\frac{3 ^ {2} \cdot 47}{2 \cdot 5 \cdot 7} = 6\frac{3}{70} = 6.042857142857143
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)423}\\\end{array}
Use the 1^{st} digit 4 from dividend 423
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)423}\\\end{array}
Since 4 is less than 70, use the next digit 2 from dividend 423 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)423}\\\end{array}
Use the 2^{nd} digit 2 from dividend 423
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)423}\\\end{array}
Since 42 is less than 70, use the next digit 3 from dividend 423 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)423}\\\end{array}
Use the 3^{rd} digit 3 from dividend 423
\begin{array}{l}\phantom{70)}006\phantom{6}\\70\overline{)423}\\\phantom{70)}\underline{\phantom{}420\phantom{}}\\\phantom{70)99}3\\\end{array}
Find closest multiple of 70 to 423. We see that 6 \times 70 = 420 is the nearest. Now subtract 420 from 423 to get reminder 3. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }3
Since 3 is less than 70, stop the division. The reminder is 3. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}