Evaluate
\frac{1205}{4}=301.25
Factor
\frac{5 \cdot 241}{2 ^ {2}} = 301\frac{1}{4} = 301.25
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\begin{array}{l}\phantom{12)}\phantom{1}\\12\overline{)3615}\\\end{array}
Use the 1^{st} digit 3 from dividend 3615
\begin{array}{l}\phantom{12)}0\phantom{2}\\12\overline{)3615}\\\end{array}
Since 3 is less than 12, use the next digit 6 from dividend 3615 and add 0 to the quotient
\begin{array}{l}\phantom{12)}0\phantom{3}\\12\overline{)3615}\\\end{array}
Use the 2^{nd} digit 6 from dividend 3615
\begin{array}{l}\phantom{12)}03\phantom{4}\\12\overline{)3615}\\\phantom{12)}\underline{\phantom{}36\phantom{99}}\\\phantom{12)99}0\\\end{array}
Find closest multiple of 12 to 36. We see that 3 \times 12 = 36 is the nearest. Now subtract 36 from 36 to get reminder 0. Add 3 to quotient.
\begin{array}{l}\phantom{12)}03\phantom{5}\\12\overline{)3615}\\\phantom{12)}\underline{\phantom{}36\phantom{99}}\\\phantom{12)99}1\\\end{array}
Use the 3^{rd} digit 1 from dividend 3615
\begin{array}{l}\phantom{12)}030\phantom{6}\\12\overline{)3615}\\\phantom{12)}\underline{\phantom{}36\phantom{99}}\\\phantom{12)99}1\\\end{array}
Since 1 is less than 12, use the next digit 5 from dividend 3615 and add 0 to the quotient
\begin{array}{l}\phantom{12)}030\phantom{7}\\12\overline{)3615}\\\phantom{12)}\underline{\phantom{}36\phantom{99}}\\\phantom{12)99}15\\\end{array}
Use the 4^{th} digit 5 from dividend 3615
\begin{array}{l}\phantom{12)}0301\phantom{8}\\12\overline{)3615}\\\phantom{12)}\underline{\phantom{}36\phantom{99}}\\\phantom{12)99}15\\\phantom{12)}\underline{\phantom{99}12\phantom{}}\\\phantom{12)999}3\\\end{array}
Find closest multiple of 12 to 15. We see that 1 \times 12 = 12 is the nearest. Now subtract 12 from 15 to get reminder 3. Add 1 to quotient.
\text{Quotient: }301 \text{Reminder: }3
Since 3 is less than 12, stop the division. The reminder is 3. The topmost line 0301 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 301.
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}