Evaluate
\frac{137}{90}\approx 1.522222222
Factor
\frac{137}{2 \cdot 3 ^ {2} \cdot 5} = 1\frac{47}{90} = 1.5222222222222221
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)137}\\\end{array}
Use the 1^{st} digit 1 from dividend 137
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)137}\\\end{array}
Since 1 is less than 90, use the next digit 3 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)137}\\\end{array}
Use the 2^{nd} digit 3 from dividend 137
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)137}\\\end{array}
Since 13 is less than 90, use the next digit 7 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)137}\\\end{array}
Use the 3^{rd} digit 7 from dividend 137
\begin{array}{l}\phantom{90)}001\phantom{6}\\90\overline{)137}\\\phantom{90)}\underline{\phantom{9}90\phantom{}}\\\phantom{90)9}47\\\end{array}
Find closest multiple of 90 to 137. We see that 1 \times 90 = 90 is the nearest. Now subtract 90 from 137 to get reminder 47. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }47
Since 47 is less than 90, stop the division. The reminder is 47. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}