Evaluate
\frac{153}{124}\approx 1.233870968
Factor
\frac{3 ^ {2} \cdot 17}{2 ^ {2} \cdot 31} = 1\frac{29}{124} = 1.2338709677419355
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\begin{array}{l}\phantom{992)}\phantom{1}\\992\overline{)1224}\\\end{array}
Use the 1^{st} digit 1 from dividend 1224
\begin{array}{l}\phantom{992)}0\phantom{2}\\992\overline{)1224}\\\end{array}
Since 1 is less than 992, use the next digit 2 from dividend 1224 and add 0 to the quotient
\begin{array}{l}\phantom{992)}0\phantom{3}\\992\overline{)1224}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1224
\begin{array}{l}\phantom{992)}00\phantom{4}\\992\overline{)1224}\\\end{array}
Since 12 is less than 992, use the next digit 2 from dividend 1224 and add 0 to the quotient
\begin{array}{l}\phantom{992)}00\phantom{5}\\992\overline{)1224}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1224
\begin{array}{l}\phantom{992)}000\phantom{6}\\992\overline{)1224}\\\end{array}
Since 122 is less than 992, use the next digit 4 from dividend 1224 and add 0 to the quotient
\begin{array}{l}\phantom{992)}000\phantom{7}\\992\overline{)1224}\\\end{array}
Use the 4^{th} digit 4 from dividend 1224
\begin{array}{l}\phantom{992)}0001\phantom{8}\\992\overline{)1224}\\\phantom{992)}\underline{\phantom{9}992\phantom{}}\\\phantom{992)9}232\\\end{array}
Find closest multiple of 992 to 1224. We see that 1 \times 992 = 992 is the nearest. Now subtract 992 from 1224 to get reminder 232. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }232
Since 232 is less than 992, stop the division. The reminder is 232. The topmost line 0001 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}