Evaluate
\frac{452}{121}\approx 3.73553719
Factor
\frac{2 ^ {2} \cdot 113}{11 ^ {2}} = 3\frac{89}{121} = 3.7355371900826446
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\begin{array}{l}\phantom{121)}\phantom{1}\\121\overline{)452}\\\end{array}
Use the 1^{st} digit 4 from dividend 452
\begin{array}{l}\phantom{121)}0\phantom{2}\\121\overline{)452}\\\end{array}
Since 4 is less than 121, use the next digit 5 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{121)}0\phantom{3}\\121\overline{)452}\\\end{array}
Use the 2^{nd} digit 5 from dividend 452
\begin{array}{l}\phantom{121)}00\phantom{4}\\121\overline{)452}\\\end{array}
Since 45 is less than 121, use the next digit 2 from dividend 452 and add 0 to the quotient
\begin{array}{l}\phantom{121)}00\phantom{5}\\121\overline{)452}\\\end{array}
Use the 3^{rd} digit 2 from dividend 452
\begin{array}{l}\phantom{121)}003\phantom{6}\\121\overline{)452}\\\phantom{121)}\underline{\phantom{}363\phantom{}}\\\phantom{121)9}89\\\end{array}
Find closest multiple of 121 to 452. We see that 3 \times 121 = 363 is the nearest. Now subtract 363 from 452 to get reminder 89. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }89
Since 89 is less than 121, stop the division. The reminder is 89. 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}