Evaluate
\frac{3}{2}=1.5
Factor
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\begin{array}{l}\phantom{38)}\phantom{1}\\38\overline{)57}\\\end{array}
Use the 1^{st} digit 5 from dividend 57
\begin{array}{l}\phantom{38)}0\phantom{2}\\38\overline{)57}\\\end{array}
Since 5 is less than 38, use the next digit 7 from dividend 57 and add 0 to the quotient
\begin{array}{l}\phantom{38)}0\phantom{3}\\38\overline{)57}\\\end{array}
Use the 2^{nd} digit 7 from dividend 57
\begin{array}{l}\phantom{38)}01\phantom{4}\\38\overline{)57}\\\phantom{38)}\underline{\phantom{}38\phantom{}}\\\phantom{38)}19\\\end{array}
Find closest multiple of 38 to 57. We see that 1 \times 38 = 38 is the nearest. Now subtract 38 from 57 to get reminder 19. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }19
Since 19 is less than 38, stop the division. The reminder is 19. 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}