Evaluate
\frac{174}{85}\approx 2.047058824
Factor
\frac{2 \cdot 3 \cdot 29}{5 \cdot 17} = 2\frac{4}{85} = 2.0470588235294116
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)174}\\\end{array}
Use the 1^{st} digit 1 from dividend 174
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)174}\\\end{array}
Since 1 is less than 85, use the next digit 7 from dividend 174 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)174}\\\end{array}
Use the 2^{nd} digit 7 from dividend 174
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)174}\\\end{array}
Since 17 is less than 85, use the next digit 4 from dividend 174 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)174}\\\end{array}
Use the 3^{rd} digit 4 from dividend 174
\begin{array}{l}\phantom{85)}002\phantom{6}\\85\overline{)174}\\\phantom{85)}\underline{\phantom{}170\phantom{}}\\\phantom{85)99}4\\\end{array}
Find closest multiple of 85 to 174. We see that 2 \times 85 = 170 is the nearest. Now subtract 170 from 174 to get reminder 4. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }4
Since 4 is less than 85, stop the division. The reminder is 4. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}