Evaluate
\frac{1225}{39}\approx 31.41025641
Factor
\frac{5 ^ {2} \cdot 7 ^ {2}}{3 \cdot 13} = 31\frac{16}{39} = 31.41025641025641
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\begin{array}{l}\phantom{39)}\phantom{1}\\39\overline{)1225}\\\end{array}
Use the 1^{st} digit 1 from dividend 1225
\begin{array}{l}\phantom{39)}0\phantom{2}\\39\overline{)1225}\\\end{array}
Since 1 is less than 39, use the next digit 2 from dividend 1225 and add 0 to the quotient
\begin{array}{l}\phantom{39)}0\phantom{3}\\39\overline{)1225}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1225
\begin{array}{l}\phantom{39)}00\phantom{4}\\39\overline{)1225}\\\end{array}
Since 12 is less than 39, use the next digit 2 from dividend 1225 and add 0 to the quotient
\begin{array}{l}\phantom{39)}00\phantom{5}\\39\overline{)1225}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1225
\begin{array}{l}\phantom{39)}003\phantom{6}\\39\overline{)1225}\\\phantom{39)}\underline{\phantom{}117\phantom{9}}\\\phantom{39)99}5\\\end{array}
Find closest multiple of 39 to 122. We see that 3 \times 39 = 117 is the nearest. Now subtract 117 from 122 to get reminder 5. Add 3 to quotient.
\begin{array}{l}\phantom{39)}003\phantom{7}\\39\overline{)1225}\\\phantom{39)}\underline{\phantom{}117\phantom{9}}\\\phantom{39)99}55\\\end{array}
Use the 4^{th} digit 5 from dividend 1225
\begin{array}{l}\phantom{39)}0031\phantom{8}\\39\overline{)1225}\\\phantom{39)}\underline{\phantom{}117\phantom{9}}\\\phantom{39)99}55\\\phantom{39)}\underline{\phantom{99}39\phantom{}}\\\phantom{39)99}16\\\end{array}
Find closest multiple of 39 to 55. We see that 1 \times 39 = 39 is the nearest. Now subtract 39 from 55 to get reminder 16. Add 1 to quotient.
\text{Quotient: }31 \text{Reminder: }16
Since 16 is less than 39, stop the division. The reminder is 16. The topmost line 0031 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 31.
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}