Evaluate
52
Factor
2^{2}\times 13
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)520}\\\end{array}
Use the 1^{st} digit 5 from dividend 520
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)520}\\\end{array}
Since 5 is less than 10, use the next digit 2 from dividend 520 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)520}\\\end{array}
Use the 2^{nd} digit 2 from dividend 520
\begin{array}{l}\phantom{10)}05\phantom{4}\\10\overline{)520}\\\phantom{10)}\underline{\phantom{}50\phantom{9}}\\\phantom{10)9}2\\\end{array}
Find closest multiple of 10 to 52. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 52 to get reminder 2. Add 5 to quotient.
\begin{array}{l}\phantom{10)}05\phantom{5}\\10\overline{)520}\\\phantom{10)}\underline{\phantom{}50\phantom{9}}\\\phantom{10)9}20\\\end{array}
Use the 3^{rd} digit 0 from dividend 520
\begin{array}{l}\phantom{10)}052\phantom{6}\\10\overline{)520}\\\phantom{10)}\underline{\phantom{}50\phantom{9}}\\\phantom{10)9}20\\\phantom{10)}\underline{\phantom{9}20\phantom{}}\\\phantom{10)999}0\\\end{array}
Find closest multiple of 10 to 20. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 20 to get reminder 0. Add 2 to quotient.
\text{Quotient: }52 \text{Reminder: }0
Since 0 is less than 10, stop the division. The reminder is 0. The topmost line 052 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 52.
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}