Evaluate
\frac{85}{7}\approx 12.142857143
Factor
\frac{5 \cdot 17}{7} = 12\frac{1}{7} = 12.142857142857142
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)850}\\\end{array}
Use the 1^{st} digit 8 from dividend 850
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)850}\\\end{array}
Since 8 is less than 70, use the next digit 5 from dividend 850 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)850}\\\end{array}
Use the 2^{nd} digit 5 from dividend 850
\begin{array}{l}\phantom{70)}01\phantom{4}\\70\overline{)850}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}15\\\end{array}
Find closest multiple of 70 to 85. We see that 1 \times 70 = 70 is the nearest. Now subtract 70 from 85 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{70)}01\phantom{5}\\70\overline{)850}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}150\\\end{array}
Use the 3^{rd} digit 0 from dividend 850
\begin{array}{l}\phantom{70)}012\phantom{6}\\70\overline{)850}\\\phantom{70)}\underline{\phantom{}70\phantom{9}}\\\phantom{70)}150\\\phantom{70)}\underline{\phantom{}140\phantom{}}\\\phantom{70)9}10\\\end{array}
Find closest multiple of 70 to 150. We see that 2 \times 70 = 140 is the nearest. Now subtract 140 from 150 to get reminder 10. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }10
Since 10 is less than 70, stop the division. The reminder is 10. 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}