Evaluate
\frac{13}{5}=2.6
Factor
\frac{13}{5} = 2\frac{3}{5} = 2.6
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)52}\\\end{array}
Use the 1^{st} digit 5 from dividend 52
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)52}\\\end{array}
Since 5 is less than 20, use the next digit 2 from dividend 52 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)52}\\\end{array}
Use the 2^{nd} digit 2 from dividend 52
\begin{array}{l}\phantom{20)}02\phantom{4}\\20\overline{)52}\\\phantom{20)}\underline{\phantom{}40\phantom{}}\\\phantom{20)}12\\\end{array}
Find closest multiple of 20 to 52. We see that 2 \times 20 = 40 is the nearest. Now subtract 40 from 52 to get reminder 12. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }12
Since 12 is less than 20, stop the division. The reminder is 12. The topmost line 02 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}