Evaluate
5
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\begin{array}{l}\phantom{2435)}\phantom{1}\\2435\overline{)12175}\\\end{array}
Use the 1^{st} digit 1 from dividend 12175
\begin{array}{l}\phantom{2435)}0\phantom{2}\\2435\overline{)12175}\\\end{array}
Since 1 is less than 2435, use the next digit 2 from dividend 12175 and add 0 to the quotient
\begin{array}{l}\phantom{2435)}0\phantom{3}\\2435\overline{)12175}\\\end{array}
Use the 2^{nd} digit 2 from dividend 12175
\begin{array}{l}\phantom{2435)}00\phantom{4}\\2435\overline{)12175}\\\end{array}
Since 12 is less than 2435, use the next digit 1 from dividend 12175 and add 0 to the quotient
\begin{array}{l}\phantom{2435)}00\phantom{5}\\2435\overline{)12175}\\\end{array}
Use the 3^{rd} digit 1 from dividend 12175
\begin{array}{l}\phantom{2435)}000\phantom{6}\\2435\overline{)12175}\\\end{array}
Since 121 is less than 2435, use the next digit 7 from dividend 12175 and add 0 to the quotient
\begin{array}{l}\phantom{2435)}000\phantom{7}\\2435\overline{)12175}\\\end{array}
Use the 4^{th} digit 7 from dividend 12175
\begin{array}{l}\phantom{2435)}0000\phantom{8}\\2435\overline{)12175}\\\end{array}
Since 1217 is less than 2435, use the next digit 5 from dividend 12175 and add 0 to the quotient
\begin{array}{l}\phantom{2435)}0000\phantom{9}\\2435\overline{)12175}\\\end{array}
Use the 5^{th} digit 5 from dividend 12175
\begin{array}{l}\phantom{2435)}00005\phantom{10}\\2435\overline{)12175}\\\phantom{2435)}\underline{\phantom{}12175\phantom{}}\\\phantom{2435)99999}0\\\end{array}
Find closest multiple of 2435 to 12175. We see that 5 \times 2435 = 12175 is the nearest. Now subtract 12175 from 12175 to get reminder 0. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }0
Since 0 is less than 2435, stop the division. The reminder is 0. The topmost line 00005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}