Evaluate
\frac{157}{36}\approx 4.361111111
Factor
\frac{157}{2 ^ {2} \cdot 3 ^ {2}} = 4\frac{13}{36} = 4.361111111111111
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\begin{array}{l}\phantom{18000000)}\phantom{1}\\18000000\overline{)78500000}\\\end{array}
Use the 1^{st} digit 7 from dividend 78500000
\begin{array}{l}\phantom{18000000)}0\phantom{2}\\18000000\overline{)78500000}\\\end{array}
Since 7 is less than 18000000, use the next digit 8 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}0\phantom{3}\\18000000\overline{)78500000}\\\end{array}
Use the 2^{nd} digit 8 from dividend 78500000
\begin{array}{l}\phantom{18000000)}00\phantom{4}\\18000000\overline{)78500000}\\\end{array}
Since 78 is less than 18000000, use the next digit 5 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}00\phantom{5}\\18000000\overline{)78500000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 78500000
\begin{array}{l}\phantom{18000000)}000\phantom{6}\\18000000\overline{)78500000}\\\end{array}
Since 785 is less than 18000000, use the next digit 0 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}000\phantom{7}\\18000000\overline{)78500000}\\\end{array}
Use the 4^{th} digit 0 from dividend 78500000
\begin{array}{l}\phantom{18000000)}0000\phantom{8}\\18000000\overline{)78500000}\\\end{array}
Since 7850 is less than 18000000, use the next digit 0 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}0000\phantom{9}\\18000000\overline{)78500000}\\\end{array}
Use the 5^{th} digit 0 from dividend 78500000
\begin{array}{l}\phantom{18000000)}00000\phantom{10}\\18000000\overline{)78500000}\\\end{array}
Since 78500 is less than 18000000, use the next digit 0 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}00000\phantom{11}\\18000000\overline{)78500000}\\\end{array}
Use the 6^{th} digit 0 from dividend 78500000
\begin{array}{l}\phantom{18000000)}000000\phantom{12}\\18000000\overline{)78500000}\\\end{array}
Since 785000 is less than 18000000, use the next digit 0 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}000000\phantom{13}\\18000000\overline{)78500000}\\\end{array}
Use the 7^{th} digit 0 from dividend 78500000
\begin{array}{l}\phantom{18000000)}0000000\phantom{14}\\18000000\overline{)78500000}\\\end{array}
Since 7850000 is less than 18000000, use the next digit 0 from dividend 78500000 and add 0 to the quotient
\begin{array}{l}\phantom{18000000)}0000000\phantom{15}\\18000000\overline{)78500000}\\\end{array}
Use the 8^{th} digit 0 from dividend 78500000
\begin{array}{l}\phantom{18000000)}00000004\phantom{16}\\18000000\overline{)78500000}\\\phantom{18000000)}\underline{\phantom{}72000000\phantom{}}\\\phantom{18000000)9}6500000\\\end{array}
Find closest multiple of 18000000 to 78500000. We see that 4 \times 18000000 = 72000000 is the nearest. Now subtract 72000000 from 78500000 to get reminder 6500000. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }6500000
Since 6500000 is less than 18000000, stop the division. The reminder is 6500000. The topmost line 00000004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}