Evaluate
\frac{113}{13}\approx 8.692307692
Factor
\frac{113}{13} = 8\frac{9}{13} = 8.692307692307692
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\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)452}\\\end{array}
Use the 1^{st} digit 4 from dividend 452
\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)452}\\\end{array}
Since 4 is less than 52, use the next digit 5 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)452}\\\end{array}
Use the 2^{nd} digit 5 from dividend 452
\begin{array}{l}\phantom{52)}00\phantom{4}\\52\overline{)452}\\\end{array}
Since 45 is less than 52, use the next digit 2 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{52)}00\phantom{5}\\52\overline{)452}\\\end{array}
Use the 3^{rd} digit 2 from dividend 452
\begin{array}{l}\phantom{52)}008\phantom{6}\\52\overline{)452}\\\phantom{52)}\underline{\phantom{}416\phantom{}}\\\phantom{52)9}36\\\end{array}
Find closest multiple of 52 to 452. We see that 8 \times 52 = 416 is the nearest. Now subtract 416 from 452 to get reminder 36. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }36
Since 36 is less than 52, stop the division. The reminder is 36. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}