Evaluate
\frac{127}{49}\approx 2.591836735
Factor
\frac{127}{7 ^ {2}} = 2\frac{29}{49} = 2.5918367346938775
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\begin{array}{l}\phantom{49)}\phantom{1}\\49\overline{)127}\\\end{array}
Use the 1^{st} digit 1 from dividend 127
\begin{array}{l}\phantom{49)}0\phantom{2}\\49\overline{)127}\\\end{array}
Since 1 is less than 49, use the next digit 2 from dividend 127 and add 0 to the quotient
\begin{array}{l}\phantom{49)}0\phantom{3}\\49\overline{)127}\\\end{array}
Use the 2^{nd} digit 2 from dividend 127
\begin{array}{l}\phantom{49)}00\phantom{4}\\49\overline{)127}\\\end{array}
Since 12 is less than 49, use the next digit 7 from dividend 127 and add 0 to the quotient
\begin{array}{l}\phantom{49)}00\phantom{5}\\49\overline{)127}\\\end{array}
Use the 3^{rd} digit 7 from dividend 127
\begin{array}{l}\phantom{49)}002\phantom{6}\\49\overline{)127}\\\phantom{49)}\underline{\phantom{9}98\phantom{}}\\\phantom{49)9}29\\\end{array}
Find closest multiple of 49 to 127. We see that 2 \times 49 = 98 is the nearest. Now subtract 98 from 127 to get reminder 29. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }29
Since 29 is less than 49, stop the division. The reminder is 29. 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}