Evaluate
\frac{2435}{24}\approx 101.458333333
Factor
\frac{5 \cdot 487}{2 ^ {3} \cdot 3} = 101\frac{11}{24} = 101.45833333333333
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\begin{array}{l}\phantom{360)}\phantom{1}\\360\overline{)36525}\\\end{array}
Use the 1^{st} digit 3 from dividend 36525
\begin{array}{l}\phantom{360)}0\phantom{2}\\360\overline{)36525}\\\end{array}
Since 3 is less than 360, use the next digit 6 from dividend 36525 and add 0 to the quotient
\begin{array}{l}\phantom{360)}0\phantom{3}\\360\overline{)36525}\\\end{array}
Use the 2^{nd} digit 6 from dividend 36525
\begin{array}{l}\phantom{360)}00\phantom{4}\\360\overline{)36525}\\\end{array}
Since 36 is less than 360, use the next digit 5 from dividend 36525 and add 0 to the quotient
\begin{array}{l}\phantom{360)}00\phantom{5}\\360\overline{)36525}\\\end{array}
Use the 3^{rd} digit 5 from dividend 36525
\begin{array}{l}\phantom{360)}001\phantom{6}\\360\overline{)36525}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)99}5\\\end{array}
Find closest multiple of 360 to 365. We see that 1 \times 360 = 360 is the nearest. Now subtract 360 from 365 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{360)}001\phantom{7}\\360\overline{)36525}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)99}52\\\end{array}
Use the 4^{th} digit 2 from dividend 36525
\begin{array}{l}\phantom{360)}0010\phantom{8}\\360\overline{)36525}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)99}52\\\end{array}
Since 52 is less than 360, use the next digit 5 from dividend 36525 and add 0 to the quotient
\begin{array}{l}\phantom{360)}0010\phantom{9}\\360\overline{)36525}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)99}525\\\end{array}
Use the 5^{th} digit 5 from dividend 36525
\begin{array}{l}\phantom{360)}00101\phantom{10}\\360\overline{)36525}\\\phantom{360)}\underline{\phantom{}360\phantom{99}}\\\phantom{360)99}525\\\phantom{360)}\underline{\phantom{99}360\phantom{}}\\\phantom{360)99}165\\\end{array}
Find closest multiple of 360 to 525. We see that 1 \times 360 = 360 is the nearest. Now subtract 360 from 525 to get reminder 165. Add 1 to quotient.
\text{Quotient: }101 \text{Reminder: }165
Since 165 is less than 360, stop the division. The reminder is 165. The topmost line 00101 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 101.
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}