Evaluate
\frac{4108}{85}\approx 48.329411765
Factor
\frac{2 ^ {2} \cdot 13 \cdot 79}{5 \cdot 17} = 48\frac{28}{85} = 48.32941176470588
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)4108}\\\end{array}
Use the 1^{st} digit 4 from dividend 4108
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)4108}\\\end{array}
Since 4 is less than 85, use the next digit 1 from dividend 4108 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)4108}\\\end{array}
Use the 2^{nd} digit 1 from dividend 4108
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)4108}\\\end{array}
Since 41 is less than 85, use the next digit 0 from dividend 4108 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)4108}\\\end{array}
Use the 3^{rd} digit 0 from dividend 4108
\begin{array}{l}\phantom{85)}004\phantom{6}\\85\overline{)4108}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}70\\\end{array}
Find closest multiple of 85 to 410. We see that 4 \times 85 = 340 is the nearest. Now subtract 340 from 410 to get reminder 70. Add 4 to quotient.
\begin{array}{l}\phantom{85)}004\phantom{7}\\85\overline{)4108}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}708\\\end{array}
Use the 4^{th} digit 8 from dividend 4108
\begin{array}{l}\phantom{85)}0048\phantom{8}\\85\overline{)4108}\\\phantom{85)}\underline{\phantom{}340\phantom{9}}\\\phantom{85)9}708\\\phantom{85)}\underline{\phantom{9}680\phantom{}}\\\phantom{85)99}28\\\end{array}
Find closest multiple of 85 to 708. We see that 8 \times 85 = 680 is the nearest. Now subtract 680 from 708 to get reminder 28. Add 8 to quotient.
\text{Quotient: }48 \text{Reminder: }28
Since 28 is less than 85, stop the division. The reminder is 28. The topmost line 0048 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 48.
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}