Evaluate
\frac{23}{15}\approx 1.533333333
Factor
\frac{23}{3 \cdot 5} = 1\frac{8}{15} = 1.5333333333333334
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\begin{array}{l}\phantom{150)}\phantom{1}\\150\overline{)230}\\\end{array}
Use the 1^{st} digit 2 from dividend 230
\begin{array}{l}\phantom{150)}0\phantom{2}\\150\overline{)230}\\\end{array}
Since 2 is less than 150, use the next digit 3 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{150)}0\phantom{3}\\150\overline{)230}\\\end{array}
Use the 2^{nd} digit 3 from dividend 230
\begin{array}{l}\phantom{150)}00\phantom{4}\\150\overline{)230}\\\end{array}
Since 23 is less than 150, use the next digit 0 from dividend 230 and add 0 to the quotient
\begin{array}{l}\phantom{150)}00\phantom{5}\\150\overline{)230}\\\end{array}
Use the 3^{rd} digit 0 from dividend 230
\begin{array}{l}\phantom{150)}001\phantom{6}\\150\overline{)230}\\\phantom{150)}\underline{\phantom{}150\phantom{}}\\\phantom{150)9}80\\\end{array}
Find closest multiple of 150 to 230. We see that 1 \times 150 = 150 is the nearest. Now subtract 150 from 230 to get reminder 80. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }80
Since 80 is less than 150, stop the division. The reminder is 80. 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}