Evaluate
\frac{4516}{4135}\approx 1.092140266
Factor
\frac{2 ^ {2} \cdot 1129}{5 \cdot 827} = 1\frac{381}{4135} = 1.0921402660217654
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\begin{array}{l}\phantom{12405)}\phantom{1}\\12405\overline{)13548}\\\end{array}
Use the 1^{st} digit 1 from dividend 13548
\begin{array}{l}\phantom{12405)}0\phantom{2}\\12405\overline{)13548}\\\end{array}
Since 1 is less than 12405, use the next digit 3 from dividend 13548 and add 0 to the quotient
\begin{array}{l}\phantom{12405)}0\phantom{3}\\12405\overline{)13548}\\\end{array}
Use the 2^{nd} digit 3 from dividend 13548
\begin{array}{l}\phantom{12405)}00\phantom{4}\\12405\overline{)13548}\\\end{array}
Since 13 is less than 12405, use the next digit 5 from dividend 13548 and add 0 to the quotient
\begin{array}{l}\phantom{12405)}00\phantom{5}\\12405\overline{)13548}\\\end{array}
Use the 3^{rd} digit 5 from dividend 13548
\begin{array}{l}\phantom{12405)}000\phantom{6}\\12405\overline{)13548}\\\end{array}
Since 135 is less than 12405, use the next digit 4 from dividend 13548 and add 0 to the quotient
\begin{array}{l}\phantom{12405)}000\phantom{7}\\12405\overline{)13548}\\\end{array}
Use the 4^{th} digit 4 from dividend 13548
\begin{array}{l}\phantom{12405)}0000\phantom{8}\\12405\overline{)13548}\\\end{array}
Since 1354 is less than 12405, use the next digit 8 from dividend 13548 and add 0 to the quotient
\begin{array}{l}\phantom{12405)}0000\phantom{9}\\12405\overline{)13548}\\\end{array}
Use the 5^{th} digit 8 from dividend 13548
\begin{array}{l}\phantom{12405)}00001\phantom{10}\\12405\overline{)13548}\\\phantom{12405)}\underline{\phantom{}12405\phantom{}}\\\phantom{12405)9}1143\\\end{array}
Find closest multiple of 12405 to 13548. We see that 1 \times 12405 = 12405 is the nearest. Now subtract 12405 from 13548 to get reminder 1143. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }1143
Since 1143 is less than 12405, stop the division. The reminder is 1143. The topmost line 00001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}