Evaluate
\frac{91}{37}\approx 2.459459459
Factor
\frac{7 \cdot 13}{37} = 2\frac{17}{37} = 2.4594594594594597
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\begin{array}{l}\phantom{74)}\phantom{1}\\74\overline{)182}\\\end{array}
Use the 1^{st} digit 1 from dividend 182
\begin{array}{l}\phantom{74)}0\phantom{2}\\74\overline{)182}\\\end{array}
Since 1 is less than 74, use the next digit 8 from dividend 182 and add 0 to the quotient
\begin{array}{l}\phantom{74)}0\phantom{3}\\74\overline{)182}\\\end{array}
Use the 2^{nd} digit 8 from dividend 182
\begin{array}{l}\phantom{74)}00\phantom{4}\\74\overline{)182}\\\end{array}
Since 18 is less than 74, use the next digit 2 from dividend 182 and add 0 to the quotient
\begin{array}{l}\phantom{74)}00\phantom{5}\\74\overline{)182}\\\end{array}
Use the 3^{rd} digit 2 from dividend 182
\begin{array}{l}\phantom{74)}002\phantom{6}\\74\overline{)182}\\\phantom{74)}\underline{\phantom{}148\phantom{}}\\\phantom{74)9}34\\\end{array}
Find closest multiple of 74 to 182. We see that 2 \times 74 = 148 is the nearest. Now subtract 148 from 182 to get reminder 34. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }34
Since 34 is less than 74, stop the division. The reminder is 34. 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}