Evaluate
\frac{53}{4}=13.25
Factor
\frac{53}{2 ^ {2}} = 13\frac{1}{4} = 13.25
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\begin{array}{l}\phantom{8000000)}\phantom{1}\\8000000\overline{)106000000}\\\end{array}
Use the 1^{st} digit 1 from dividend 106000000
\begin{array}{l}\phantom{8000000)}0\phantom{2}\\8000000\overline{)106000000}\\\end{array}
Since 1 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}0\phantom{3}\\8000000\overline{)106000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}00\phantom{4}\\8000000\overline{)106000000}\\\end{array}
Since 10 is less than 8000000, use the next digit 6 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}00\phantom{5}\\8000000\overline{)106000000}\\\end{array}
Use the 3^{rd} digit 6 from dividend 106000000
\begin{array}{l}\phantom{8000000)}000\phantom{6}\\8000000\overline{)106000000}\\\end{array}
Since 106 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}000\phantom{7}\\8000000\overline{)106000000}\\\end{array}
Use the 4^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}0000\phantom{8}\\8000000\overline{)106000000}\\\end{array}
Since 1060 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}0000\phantom{9}\\8000000\overline{)106000000}\\\end{array}
Use the 5^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}00000\phantom{10}\\8000000\overline{)106000000}\\\end{array}
Since 10600 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}00000\phantom{11}\\8000000\overline{)106000000}\\\end{array}
Use the 6^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}000000\phantom{12}\\8000000\overline{)106000000}\\\end{array}
Since 106000 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}000000\phantom{13}\\8000000\overline{)106000000}\\\end{array}
Use the 7^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}0000000\phantom{14}\\8000000\overline{)106000000}\\\end{array}
Since 1060000 is less than 8000000, use the next digit 0 from dividend 106000000 and add 0 to the quotient
\begin{array}{l}\phantom{8000000)}0000000\phantom{15}\\8000000\overline{)106000000}\\\end{array}
Use the 8^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}00000001\phantom{16}\\8000000\overline{)106000000}\\\phantom{8000000)}\underline{\phantom{9}8000000\phantom{9}}\\\phantom{8000000)9}2600000\\\end{array}
Find closest multiple of 8000000 to 10600000. We see that 1 \times 8000000 = 8000000 is the nearest. Now subtract 8000000 from 10600000 to get reminder 2600000. Add 1 to quotient.
\begin{array}{l}\phantom{8000000)}00000001\phantom{17}\\8000000\overline{)106000000}\\\phantom{8000000)}\underline{\phantom{9}8000000\phantom{9}}\\\phantom{8000000)9}26000000\\\end{array}
Use the 9^{th} digit 0 from dividend 106000000
\begin{array}{l}\phantom{8000000)}000000013\phantom{18}\\8000000\overline{)106000000}\\\phantom{8000000)}\underline{\phantom{9}8000000\phantom{9}}\\\phantom{8000000)9}26000000\\\phantom{8000000)}\underline{\phantom{9}24000000\phantom{}}\\\phantom{8000000)99}2000000\\\end{array}
Find closest multiple of 8000000 to 26000000. We see that 3 \times 8000000 = 24000000 is the nearest. Now subtract 24000000 from 26000000 to get reminder 2000000. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }2000000
Since 2000000 is less than 8000000, stop the division. The reminder is 2000000. The topmost line 000000013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}