Evaluate
\frac{3845}{37}\approx 103.918918919
Factor
\frac{5 \cdot 769}{37} = 103\frac{34}{37} = 103.91891891891892
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)3845}\\\end{array}
Use the 1^{st} digit 3 from dividend 3845
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)3845}\\\end{array}
Since 3 is less than 37, use the next digit 8 from dividend 3845 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)3845}\\\end{array}
Use the 2^{nd} digit 8 from dividend 3845
\begin{array}{l}\phantom{37)}01\phantom{4}\\37\overline{)3845}\\\phantom{37)}\underline{\phantom{}37\phantom{99}}\\\phantom{37)9}1\\\end{array}
Find closest multiple of 37 to 38. We see that 1 \times 37 = 37 is the nearest. Now subtract 37 from 38 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{37)}01\phantom{5}\\37\overline{)3845}\\\phantom{37)}\underline{\phantom{}37\phantom{99}}\\\phantom{37)9}14\\\end{array}
Use the 3^{rd} digit 4 from dividend 3845
\begin{array}{l}\phantom{37)}010\phantom{6}\\37\overline{)3845}\\\phantom{37)}\underline{\phantom{}37\phantom{99}}\\\phantom{37)9}14\\\end{array}
Since 14 is less than 37, use the next digit 5 from dividend 3845 and add 0 to the quotient
\begin{array}{l}\phantom{37)}010\phantom{7}\\37\overline{)3845}\\\phantom{37)}\underline{\phantom{}37\phantom{99}}\\\phantom{37)9}145\\\end{array}
Use the 4^{th} digit 5 from dividend 3845
\begin{array}{l}\phantom{37)}0103\phantom{8}\\37\overline{)3845}\\\phantom{37)}\underline{\phantom{}37\phantom{99}}\\\phantom{37)9}145\\\phantom{37)}\underline{\phantom{9}111\phantom{}}\\\phantom{37)99}34\\\end{array}
Find closest multiple of 37 to 145. We see that 3 \times 37 = 111 is the nearest. Now subtract 111 from 145 to get reminder 34. Add 3 to quotient.
\text{Quotient: }103 \text{Reminder: }34
Since 34 is less than 37, stop the division. The reminder is 34. The topmost line 0103 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 103.
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}