Evaluate
\frac{43}{15}\approx 2.866666667
Factor
\frac{43}{3 \cdot 5} = 2\frac{13}{15} = 2.8666666666666667
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)43}\\\end{array}
Use the 1^{st} digit 4 from dividend 43
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)43}\\\end{array}
Since 4 is less than 15, use the next digit 3 from dividend 43 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)43}\\\end{array}
Use the 2^{nd} digit 3 from dividend 43
\begin{array}{l}\phantom{15)}02\phantom{4}\\15\overline{)43}\\\phantom{15)}\underline{\phantom{}30\phantom{}}\\\phantom{15)}13\\\end{array}
Find closest multiple of 15 to 43. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 43 to get reminder 13. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }13
Since 13 is less than 15, stop the division. The reminder is 13. 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}