Evaluate
101
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101
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\begin{array}{l}\phantom{52)}\phantom{1}\\52\overline{)5252}\\\end{array}
Use the 1^{st} digit 5 from dividend 5252
\begin{array}{l}\phantom{52)}0\phantom{2}\\52\overline{)5252}\\\end{array}
Since 5 is less than 52, use the next digit 2 from dividend 5252 and add 0 to the quotient
\begin{array}{l}\phantom{52)}0\phantom{3}\\52\overline{)5252}\\\end{array}
Use the 2^{nd} digit 2 from dividend 5252
\begin{array}{l}\phantom{52)}01\phantom{4}\\52\overline{)5252}\\\phantom{52)}\underline{\phantom{}52\phantom{99}}\\\phantom{52)99}0\\\end{array}
Find closest multiple of 52 to 52. We see that 1 \times 52 = 52 is the nearest. Now subtract 52 from 52 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{52)}01\phantom{5}\\52\overline{)5252}\\\phantom{52)}\underline{\phantom{}52\phantom{99}}\\\phantom{52)99}5\\\end{array}
Use the 3^{rd} digit 5 from dividend 5252
\begin{array}{l}\phantom{52)}010\phantom{6}\\52\overline{)5252}\\\phantom{52)}\underline{\phantom{}52\phantom{99}}\\\phantom{52)99}5\\\end{array}
Since 5 is less than 52, use the next digit 2 from dividend 5252 and add 0 to the quotient
\begin{array}{l}\phantom{52)}010\phantom{7}\\52\overline{)5252}\\\phantom{52)}\underline{\phantom{}52\phantom{99}}\\\phantom{52)99}52\\\end{array}
Use the 4^{th} digit 2 from dividend 5252
\begin{array}{l}\phantom{52)}0101\phantom{8}\\52\overline{)5252}\\\phantom{52)}\underline{\phantom{}52\phantom{99}}\\\phantom{52)99}52\\\phantom{52)}\underline{\phantom{99}52\phantom{}}\\\phantom{52)9999}0\\\end{array}
Find closest multiple of 52 to 52. We see that 1 \times 52 = 52 is the nearest. Now subtract 52 from 52 to get reminder 0. Add 1 to quotient.
\text{Quotient: }101 \text{Reminder: }0
Since 0 is less than 52, stop the division. The reminder is 0. The topmost line 0101 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 101.
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}