Evaluate
\frac{38}{25}=1.52
Factor
\frac{2 \cdot 19}{5 ^ {2}} = 1\frac{13}{25} = 1.52
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)152}\\\end{array}
Use the 1^{st} digit 1 from dividend 152
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)152}\\\end{array}
Since 1 is less than 100, use the next digit 5 from dividend 152 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)152}\\\end{array}
Use the 2^{nd} digit 5 from dividend 152
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)152}\\\end{array}
Since 15 is less than 100, use the next digit 2 from dividend 152 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)152}\\\end{array}
Use the 3^{rd} digit 2 from dividend 152
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)152}\\\phantom{100)}\underline{\phantom{}100\phantom{}}\\\phantom{100)9}52\\\end{array}
Find closest multiple of 100 to 152. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 152 to get reminder 52. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }52
Since 52 is less than 100, stop the division. The reminder is 52. The topmost line 001 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}