Evaluate
\frac{477}{35}\approx 13.628571429
Factor
\frac{3 ^ {2} \cdot 53}{5 \cdot 7} = 13\frac{22}{35} = 13.628571428571428
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)954}\\\end{array}
Use the 1^{st} digit 9 from dividend 954
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)954}\\\end{array}
Since 9 is less than 70, use the next digit 5 from dividend 954 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)954}\\\end{array}
Use the 2^{nd} digit 5 from dividend 954
\begin{array}{l}\phantom{70)}01\phantom{4}\\70\overline{)954}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}25\\\end{array}
Find closest multiple of 70 to 95. We see that 1 \times 70 = 70 is the nearest. Now subtract 70 from 95 to get reminder 25. Add 1 to quotient.
\begin{array}{l}\phantom{70)}01\phantom{5}\\70\overline{)954}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}254\\\end{array}
Use the 3^{rd} digit 4 from dividend 954
\begin{array}{l}\phantom{70)}013\phantom{6}\\70\overline{)954}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}254\\\phantom{70)}\underline{\phantom{}210\phantom{}}\\\phantom{70)9}44\\\end{array}
Find closest multiple of 70 to 254. We see that 3 \times 70 = 210 is the nearest. Now subtract 210 from 254 to get reminder 44. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }44
Since 44 is less than 70, stop the division. The reminder is 44. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}