Evaluate
\frac{325}{63}\approx 5.158730159
Factor
\frac{5 ^ {2} \cdot 13}{3 ^ {2} \cdot 7} = 5\frac{10}{63} = 5.158730158730159
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\begin{array}{l}\phantom{63)}\phantom{1}\\63\overline{)325}\\\end{array}
Use the 1^{st} digit 3 from dividend 325
\begin{array}{l}\phantom{63)}0\phantom{2}\\63\overline{)325}\\\end{array}
Since 3 is less than 63, use the next digit 2 from dividend 325 and add 0 to the quotient
\begin{array}{l}\phantom{63)}0\phantom{3}\\63\overline{)325}\\\end{array}
Use the 2^{nd} digit 2 from dividend 325
\begin{array}{l}\phantom{63)}00\phantom{4}\\63\overline{)325}\\\end{array}
Since 32 is less than 63, use the next digit 5 from dividend 325 and add 0 to the quotient
\begin{array}{l}\phantom{63)}00\phantom{5}\\63\overline{)325}\\\end{array}
Use the 3^{rd} digit 5 from dividend 325
\begin{array}{l}\phantom{63)}005\phantom{6}\\63\overline{)325}\\\phantom{63)}\underline{\phantom{}315\phantom{}}\\\phantom{63)9}10\\\end{array}
Find closest multiple of 63 to 325. We see that 5 \times 63 = 315 is the nearest. Now subtract 315 from 325 to get reminder 10. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }10
Since 10 is less than 63, stop the division. The reminder is 10. The topmost line 005 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5.
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}