Evaluate
\frac{2053}{20}=102.65
Factor
\frac{2053}{2 ^ {2} \cdot 5} = 102\frac{13}{20} = 102.65
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)6159}\\\end{array}
Use the 1^{st} digit 6 from dividend 6159
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)6159}\\\end{array}
Since 6 is less than 60, use the next digit 1 from dividend 6159 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)6159}\\\end{array}
Use the 2^{nd} digit 1 from dividend 6159
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)6159}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)9}1\\\end{array}
Find closest multiple of 60 to 61. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 61 to get reminder 1. Add 1 to quotient.
\begin{array}{l}\phantom{60)}01\phantom{5}\\60\overline{)6159}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)9}15\\\end{array}
Use the 3^{rd} digit 5 from dividend 6159
\begin{array}{l}\phantom{60)}010\phantom{6}\\60\overline{)6159}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)9}15\\\end{array}
Since 15 is less than 60, use the next digit 9 from dividend 6159 and add 0 to the quotient
\begin{array}{l}\phantom{60)}010\phantom{7}\\60\overline{)6159}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)9}159\\\end{array}
Use the 4^{th} digit 9 from dividend 6159
\begin{array}{l}\phantom{60)}0102\phantom{8}\\60\overline{)6159}\\\phantom{60)}\underline{\phantom{}60\phantom{99}}\\\phantom{60)9}159\\\phantom{60)}\underline{\phantom{9}120\phantom{}}\\\phantom{60)99}39\\\end{array}
Find closest multiple of 60 to 159. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 159 to get reminder 39. Add 2 to quotient.
\text{Quotient: }102 \text{Reminder: }39
Since 39 is less than 60, stop the division. The reminder is 39. The topmost line 0102 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 102.
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}