Evaluate
\frac{555}{22}\approx 25.227272727
Factor
\frac{3 \cdot 5 \cdot 37}{2 \cdot 11} = 25\frac{5}{22} = 25.227272727272727
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)555}\\\end{array}
Use the 1^{st} digit 5 from dividend 555
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)555}\\\end{array}
Since 5 is less than 22, use the next digit 5 from dividend 555 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)555}\\\end{array}
Use the 2^{nd} digit 5 from dividend 555
\begin{array}{l}\phantom{22)}02\phantom{4}\\22\overline{)555}\\\phantom{22)}\underline{\phantom{}44\phantom{9}}\\\phantom{22)}11\\\end{array}
Find closest multiple of 22 to 55. We see that 2 \times 22 = 44 is the nearest. Now subtract 44 from 55 to get reminder 11. Add 2 to quotient.
\begin{array}{l}\phantom{22)}02\phantom{5}\\22\overline{)555}\\\phantom{22)}\underline{\phantom{}44\phantom{9}}\\\phantom{22)}115\\\end{array}
Use the 3^{rd} digit 5 from dividend 555
\begin{array}{l}\phantom{22)}025\phantom{6}\\22\overline{)555}\\\phantom{22)}\underline{\phantom{}44\phantom{9}}\\\phantom{22)}115\\\phantom{22)}\underline{\phantom{}110\phantom{}}\\\phantom{22)99}5\\\end{array}
Find closest multiple of 22 to 115. We see that 5 \times 22 = 110 is the nearest. Now subtract 110 from 115 to get reminder 5. Add 5 to quotient.
\text{Quotient: }25 \text{Reminder: }5
Since 5 is less than 22, stop the division. The reminder is 5. The topmost line 025 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 25.
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}