Evaluate
\frac{13}{10}=1.3
Factor
\frac{13}{2 \cdot 5} = 1\frac{3}{10} = 1.3
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)52}\\\end{array}
Use the 1^{st} digit 5 from dividend 52
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)52}\\\end{array}
Since 5 is less than 40, use the next digit 2 from dividend 52 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)52}\\\end{array}
Use the 2^{nd} digit 2 from dividend 52
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)52}\\\phantom{40)}\underline{\phantom{}40\phantom{}}\\\phantom{40)}12\\\end{array}
Find closest multiple of 40 to 52. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 52 to get reminder 12. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }12
Since 12 is less than 40, stop the division. The reminder is 12. 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}