Evaluate
\frac{37}{7}\approx 5.285714286
Factor
\frac{37}{7} = 5\frac{2}{7} = 5.285714285714286
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)185}\\\end{array}
Use the 1^{st} digit 1 from dividend 185
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)185}\\\end{array}
Since 1 is less than 35, use the next digit 8 from dividend 185 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)185}\\\end{array}
Use the 2^{nd} digit 8 from dividend 185
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)185}\\\end{array}
Since 18 is less than 35, use the next digit 5 from dividend 185 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)185}\\\end{array}
Use the 3^{rd} digit 5 from dividend 185
\begin{array}{l}\phantom{35)}005\phantom{6}\\35\overline{)185}\\\phantom{35)}\underline{\phantom{}175\phantom{}}\\\phantom{35)9}10\\\end{array}
Find closest multiple of 35 to 185. We see that 5 \times 35 = 175 is the nearest. Now subtract 175 from 185 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 35, stop the division. The reminder is 10. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}