Evaluate
\frac{101}{3}\approx 33.666666667
Factor
\frac{101}{3} = 33\frac{2}{3} = 33.666666666666664
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\begin{array}{l}\phantom{135)}\phantom{1}\\135\overline{)4545}\\\end{array}
Use the 1^{st} digit 4 from dividend 4545
\begin{array}{l}\phantom{135)}0\phantom{2}\\135\overline{)4545}\\\end{array}
Since 4 is less than 135, use the next digit 5 from dividend 4545 and add 0 to the quotient
\begin{array}{l}\phantom{135)}0\phantom{3}\\135\overline{)4545}\\\end{array}
Use the 2^{nd} digit 5 from dividend 4545
\begin{array}{l}\phantom{135)}00\phantom{4}\\135\overline{)4545}\\\end{array}
Since 45 is less than 135, use the next digit 4 from dividend 4545 and add 0 to the quotient
\begin{array}{l}\phantom{135)}00\phantom{5}\\135\overline{)4545}\\\end{array}
Use the 3^{rd} digit 4 from dividend 4545
\begin{array}{l}\phantom{135)}003\phantom{6}\\135\overline{)4545}\\\phantom{135)}\underline{\phantom{}405\phantom{9}}\\\phantom{135)9}49\\\end{array}
Find closest multiple of 135 to 454. We see that 3 \times 135 = 405 is the nearest. Now subtract 405 from 454 to get reminder 49. Add 3 to quotient.
\begin{array}{l}\phantom{135)}003\phantom{7}\\135\overline{)4545}\\\phantom{135)}\underline{\phantom{}405\phantom{9}}\\\phantom{135)9}495\\\end{array}
Use the 4^{th} digit 5 from dividend 4545
\begin{array}{l}\phantom{135)}0033\phantom{8}\\135\overline{)4545}\\\phantom{135)}\underline{\phantom{}405\phantom{9}}\\\phantom{135)9}495\\\phantom{135)}\underline{\phantom{9}405\phantom{}}\\\phantom{135)99}90\\\end{array}
Find closest multiple of 135 to 495. We see that 3 \times 135 = 405 is the nearest. Now subtract 405 from 495 to get reminder 90. Add 3 to quotient.
\text{Quotient: }33 \text{Reminder: }90
Since 90 is less than 135, stop the division. The reminder is 90. The topmost line 0033 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 33.
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}