Evaluate
\frac{27}{20}=1.35
Factor
\frac{3 ^ {3}}{2 ^ {2} \cdot 5} = 1\frac{7}{20} = 1.35
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)27}\\\end{array}
Use the 1^{st} digit 2 from dividend 27
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)27}\\\end{array}
Since 2 is less than 20, use the next digit 7 from dividend 27 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)27}\\\end{array}
Use the 2^{nd} digit 7 from dividend 27
\begin{array}{l}\phantom{20)}01\phantom{4}\\20\overline{)27}\\\phantom{20)}\underline{\phantom{}20\phantom{}}\\\phantom{20)9}7\\\end{array}
Find closest multiple of 20 to 27. We see that 1 \times 20 = 20 is the nearest. Now subtract 20 from 27 to get reminder 7. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }7
Since 7 is less than 20, stop the division. The reminder is 7. 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}