Evaluate
\frac{110}{9}\approx 12.222222222
Factor
\frac{2 \cdot 5 \cdot 11}{3 ^ {2}} = 12\frac{2}{9} = 12.222222222222221
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\begin{array}{l}\phantom{288)}\phantom{1}\\288\overline{)3520}\\\end{array}
Use the 1^{st} digit 3 from dividend 3520
\begin{array}{l}\phantom{288)}0\phantom{2}\\288\overline{)3520}\\\end{array}
Since 3 is less than 288, use the next digit 5 from dividend 3520 and add 0 to the quotient
\begin{array}{l}\phantom{288)}0\phantom{3}\\288\overline{)3520}\\\end{array}
Use the 2^{nd} digit 5 from dividend 3520
\begin{array}{l}\phantom{288)}00\phantom{4}\\288\overline{)3520}\\\end{array}
Since 35 is less than 288, use the next digit 2 from dividend 3520 and add 0 to the quotient
\begin{array}{l}\phantom{288)}00\phantom{5}\\288\overline{)3520}\\\end{array}
Use the 3^{rd} digit 2 from dividend 3520
\begin{array}{l}\phantom{288)}001\phantom{6}\\288\overline{)3520}\\\phantom{288)}\underline{\phantom{}288\phantom{9}}\\\phantom{288)9}64\\\end{array}
Find closest multiple of 288 to 352. We see that 1 \times 288 = 288 is the nearest. Now subtract 288 from 352 to get reminder 64. Add 1 to quotient.
\begin{array}{l}\phantom{288)}001\phantom{7}\\288\overline{)3520}\\\phantom{288)}\underline{\phantom{}288\phantom{9}}\\\phantom{288)9}640\\\end{array}
Use the 4^{th} digit 0 from dividend 3520
\begin{array}{l}\phantom{288)}0012\phantom{8}\\288\overline{)3520}\\\phantom{288)}\underline{\phantom{}288\phantom{9}}\\\phantom{288)9}640\\\phantom{288)}\underline{\phantom{9}576\phantom{}}\\\phantom{288)99}64\\\end{array}
Find closest multiple of 288 to 640. We see that 2 \times 288 = 576 is the nearest. Now subtract 576 from 640 to get reminder 64. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }64
Since 64 is less than 288, stop the division. The reminder is 64. The topmost line 0012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}