Evaluate
\frac{455}{88}\approx 5.170454545
Factor
\frac{5 \cdot 7 \cdot 13}{2 ^ {3} \cdot 11} = 5\frac{15}{88} = 5.170454545454546
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\begin{array}{l}\phantom{88)}\phantom{1}\\88\overline{)455}\\\end{array}
Use the 1^{st} digit 4 from dividend 455
\begin{array}{l}\phantom{88)}0\phantom{2}\\88\overline{)455}\\\end{array}
Since 4 is less than 88, use the next digit 5 from dividend 455 and add 0 to the quotient
\begin{array}{l}\phantom{88)}0\phantom{3}\\88\overline{)455}\\\end{array}
Use the 2^{nd} digit 5 from dividend 455
\begin{array}{l}\phantom{88)}00\phantom{4}\\88\overline{)455}\\\end{array}
Since 45 is less than 88, use the next digit 5 from dividend 455 and add 0 to the quotient
\begin{array}{l}\phantom{88)}00\phantom{5}\\88\overline{)455}\\\end{array}
Use the 3^{rd} digit 5 from dividend 455
\begin{array}{l}\phantom{88)}005\phantom{6}\\88\overline{)455}\\\phantom{88)}\underline{\phantom{}440\phantom{}}\\\phantom{88)9}15\\\end{array}
Find closest multiple of 88 to 455. We see that 5 \times 88 = 440 is the nearest. Now subtract 440 from 455 to get reminder 15. Add 5 to quotient.
\text{Quotient: }5 \text{Reminder: }15
Since 15 is less than 88, stop the division. The reminder is 15. 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}