Evaluate
\frac{55}{38}\approx 1.447368421
Factor
\frac{5 \cdot 11}{2 \cdot 19} = 1\frac{17}{38} = 1.4473684210526316
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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)55}\\\end{array}
Use the 1^{st} digit 5 from dividend 55
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)55}\\\end{array}
Since 5 is less than 38, use the next digit 5 from dividend 55 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)55}\\\end{array}
Use the 2^{nd} digit 5 from dividend 55
\begin{array}{l}\phantom{38)}01\phantom{4}\\38\overline{)55}\\\phantom{38)}\underline{\phantom{}38\phantom{}}\\\phantom{38)}17\\\end{array}
Find closest multiple of 38 to 55. We see that 1 \times 38 = 38 is the nearest. Now subtract 38 from 55 to get reminder 17. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }17
Since 17 is less than 38, stop the division. The reminder is 17. The topmost line 01 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}