Evaluate
\frac{137}{37}\approx 3.702702703
Factor
\frac{137}{37} = 3\frac{26}{37} = 3.7027027027027026
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)137}\\\end{array}
Use the 1^{st} digit 1 from dividend 137
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)137}\\\end{array}
Since 1 is less than 37, use the next digit 3 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)137}\\\end{array}
Use the 2^{nd} digit 3 from dividend 137
\begin{array}{l}\phantom{37)}00\phantom{4}\\37\overline{)137}\\\end{array}
Since 13 is less than 37, use the next digit 7 from dividend 137 and add 0 to the quotient
\begin{array}{l}\phantom{37)}00\phantom{5}\\37\overline{)137}\\\end{array}
Use the 3^{rd} digit 7 from dividend 137
\begin{array}{l}\phantom{37)}003\phantom{6}\\37\overline{)137}\\\phantom{37)}\underline{\phantom{}111\phantom{}}\\\phantom{37)9}26\\\end{array}
Find closest multiple of 37 to 137. We see that 3 \times 37 = 111 is the nearest. Now subtract 111 from 137 to get reminder 26. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }26
Since 26 is less than 37, stop the division. The reminder is 26. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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Matrix
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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}