Evaluate
85
Factor
5\times 17
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)850}\\\end{array}
Use the 1^{st} digit 8 from dividend 850
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)850}\\\end{array}
Since 8 is less than 10, use the next digit 5 from dividend 850 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)850}\\\end{array}
Use the 2^{nd} digit 5 from dividend 850
\begin{array}{l}\phantom{10)}08\phantom{4}\\10\overline{)850}\\\phantom{10)}\underline{\phantom{}80\phantom{9}}\\\phantom{10)9}5\\\end{array}
Find closest multiple of 10 to 85. We see that 8 \times 10 = 80 is the nearest. Now subtract 80 from 85 to get reminder 5. Add 8 to quotient.
\begin{array}{l}\phantom{10)}08\phantom{5}\\10\overline{)850}\\\phantom{10)}\underline{\phantom{}80\phantom{9}}\\\phantom{10)9}50\\\end{array}
Use the 3^{rd} digit 0 from dividend 850
\begin{array}{l}\phantom{10)}085\phantom{6}\\10\overline{)850}\\\phantom{10)}\underline{\phantom{}80\phantom{9}}\\\phantom{10)9}50\\\phantom{10)}\underline{\phantom{9}50\phantom{}}\\\phantom{10)999}0\\\end{array}
Find closest multiple of 10 to 50. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 50 to get reminder 0. Add 5 to quotient.
\text{Quotient: }85 \text{Reminder: }0
Since 0 is less than 10, stop the division. The reminder is 0. The topmost line 085 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 85.
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}