Evaluate
\frac{175}{27}\approx 6.481481481
Factor
\frac{5 ^ {2} \cdot 7}{3 ^ {3}} = 6\frac{13}{27} = 6.481481481481482
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)350}\\\end{array}
Use the 1^{st} digit 3 from dividend 350
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)350}\\\end{array}
Since 3 is less than 54, use the next digit 5 from dividend 350 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)350}\\\end{array}
Use the 2^{nd} digit 5 from dividend 350
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)350}\\\end{array}
Since 35 is less than 54, use the next digit 0 from dividend 350 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)350}\\\end{array}
Use the 3^{rd} digit 0 from dividend 350
\begin{array}{l}\phantom{54)}006\phantom{6}\\54\overline{)350}\\\phantom{54)}\underline{\phantom{}324\phantom{}}\\\phantom{54)9}26\\\end{array}
Find closest multiple of 54 to 350. We see that 6 \times 54 = 324 is the nearest. Now subtract 324 from 350 to get reminder 26. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }26
Since 26 is less than 54, stop the division. The reminder is 26. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}