Evaluate
\frac{274}{135}\approx 2.02962963
Factor
\frac{2 \cdot 137}{3 ^ {3} \cdot 5} = 2\frac{4}{135} = 2.0296296296296297
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\begin{array}{l}\phantom{270)}\phantom{1}\\270\overline{)548}\\\end{array}
Use the 1^{st} digit 5 from dividend 548
\begin{array}{l}\phantom{270)}0\phantom{2}\\270\overline{)548}\\\end{array}
Since 5 is less than 270, use the next digit 4 from dividend 548 and add 0 to the quotient
\begin{array}{l}\phantom{270)}0\phantom{3}\\270\overline{)548}\\\end{array}
Use the 2^{nd} digit 4 from dividend 548
\begin{array}{l}\phantom{270)}00\phantom{4}\\270\overline{)548}\\\end{array}
Since 54 is less than 270, use the next digit 8 from dividend 548 and add 0 to the quotient
\begin{array}{l}\phantom{270)}00\phantom{5}\\270\overline{)548}\\\end{array}
Use the 3^{rd} digit 8 from dividend 548
\begin{array}{l}\phantom{270)}002\phantom{6}\\270\overline{)548}\\\phantom{270)}\underline{\phantom{}540\phantom{}}\\\phantom{270)99}8\\\end{array}
Find closest multiple of 270 to 548. We see that 2 \times 270 = 540 is the nearest. Now subtract 540 from 548 to get reminder 8. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }8
Since 8 is less than 270, stop the division. The reminder is 8. The topmost line 002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}