Evaluate
\frac{5}{3}\approx 1.666666667
Factor
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\begin{array}{l}\phantom{135)}\phantom{1}\\135\overline{)225}\\\end{array}
Use the 1^{st} digit 2 from dividend 225
\begin{array}{l}\phantom{135)}0\phantom{2}\\135\overline{)225}\\\end{array}
Since 2 is less than 135, use the next digit 2 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{135)}0\phantom{3}\\135\overline{)225}\\\end{array}
Use the 2^{nd} digit 2 from dividend 225
\begin{array}{l}\phantom{135)}00\phantom{4}\\135\overline{)225}\\\end{array}
Since 22 is less than 135, use the next digit 5 from dividend 225 and add 0 to the quotient
\begin{array}{l}\phantom{135)}00\phantom{5}\\135\overline{)225}\\\end{array}
Use the 3^{rd} digit 5 from dividend 225
\begin{array}{l}\phantom{135)}001\phantom{6}\\135\overline{)225}\\\phantom{135)}\underline{\phantom{}135\phantom{}}\\\phantom{135)9}90\\\end{array}
Find closest multiple of 135 to 225. We see that 1 \times 135 = 135 is the nearest. Now subtract 135 from 225 to get reminder 90. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }90
Since 90 is less than 135, stop the division. The reminder is 90. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}