Evaluate
\frac{159}{46}\approx 3.456521739
Factor
\frac{3 \cdot 53}{2 \cdot 23} = 3\frac{21}{46} = 3.4565217391304346
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\begin{array}{l}\phantom{92)}\phantom{1}\\92\overline{)318}\\\end{array}
Use the 1^{st} digit 3 from dividend 318
\begin{array}{l}\phantom{92)}0\phantom{2}\\92\overline{)318}\\\end{array}
Since 3 is less than 92, use the next digit 1 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{92)}0\phantom{3}\\92\overline{)318}\\\end{array}
Use the 2^{nd} digit 1 from dividend 318
\begin{array}{l}\phantom{92)}00\phantom{4}\\92\overline{)318}\\\end{array}
Since 31 is less than 92, use the next digit 8 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{92)}00\phantom{5}\\92\overline{)318}\\\end{array}
Use the 3^{rd} digit 8 from dividend 318
\begin{array}{l}\phantom{92)}003\phantom{6}\\92\overline{)318}\\\phantom{92)}\underline{\phantom{}276\phantom{}}\\\phantom{92)9}42\\\end{array}
Find closest multiple of 92 to 318. We see that 3 \times 92 = 276 is the nearest. Now subtract 276 from 318 to get reminder 42. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }42
Since 42 is less than 92, stop the division. The reminder is 42. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}