Evaluate
\frac{403}{25}=16.12
Factor
\frac{13 \cdot 31}{5 ^ {2}} = 16\frac{3}{25} = 16.12
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)1612}\\\end{array}
Use the 1^{st} digit 1 from dividend 1612
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)1612}\\\end{array}
Since 1 is less than 100, use the next digit 6 from dividend 1612 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)1612}\\\end{array}
Use the 2^{nd} digit 6 from dividend 1612
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)1612}\\\end{array}
Since 16 is less than 100, use the next digit 1 from dividend 1612 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)1612}\\\end{array}
Use the 3^{rd} digit 1 from dividend 1612
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)1612}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}61\\\end{array}
Find closest multiple of 100 to 161. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 161 to get reminder 61. Add 1 to quotient.
\begin{array}{l}\phantom{100)}001\phantom{7}\\100\overline{)1612}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}612\\\end{array}
Use the 4^{th} digit 2 from dividend 1612
\begin{array}{l}\phantom{100)}0016\phantom{8}\\100\overline{)1612}\\\phantom{100)}\underline{\phantom{}100\phantom{9}}\\\phantom{100)9}612\\\phantom{100)}\underline{\phantom{9}600\phantom{}}\\\phantom{100)99}12\\\end{array}
Find closest multiple of 100 to 612. We see that 6 \times 100 = 600 is the nearest. Now subtract 600 from 612 to get reminder 12. Add 6 to quotient.
\text{Quotient: }16 \text{Reminder: }12
Since 12 is less than 100, stop the division. The reminder is 12. The topmost line 0016 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 16.
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}