Evaluate
\frac{90}{7}\approx 12.857142857
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5}{7} = 12\frac{6}{7} = 12.857142857142858
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)900}\\\end{array}
Use the 1^{st} digit 9 from dividend 900
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)900}\\\end{array}
Since 9 is less than 70, use the next digit 0 from dividend 900 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)900}\\\end{array}
Use the 2^{nd} digit 0 from dividend 900
\begin{array}{l}\phantom{70)}01\phantom{4}\\70\overline{)900}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}20\\\end{array}
Find closest multiple of 70 to 90. We see that 1 \times 70 = 70 is the nearest. Now subtract 70 from 90 to get reminder 20. Add 1 to quotient.
\begin{array}{l}\phantom{70)}01\phantom{5}\\70\overline{)900}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}200\\\end{array}
Use the 3^{rd} digit 0 from dividend 900
\begin{array}{l}\phantom{70)}012\phantom{6}\\70\overline{)900}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}200\\\phantom{70)}\underline{\phantom{}140\phantom{}}\\\phantom{70)9}60\\\end{array}
Find closest multiple of 70 to 200. We see that 2 \times 70 = 140 is the nearest. Now subtract 140 from 200 to get reminder 60. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }60
Since 60 is less than 70, stop the division. The reminder is 60. The topmost line 012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}