Evaluate
\frac{43}{30}\approx 1.433333333
Factor
\frac{43}{2 \cdot 3 \cdot 5} = 1\frac{13}{30} = 1.4333333333333333
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)43}\\\end{array}
Use the 1^{st} digit 4 from dividend 43
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)43}\\\end{array}
Since 4 is less than 30, use the next digit 3 from dividend 43 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)43}\\\end{array}
Use the 2^{nd} digit 3 from dividend 43
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)43}\\\phantom{30)}\underline{\phantom{}30\phantom{}}\\\phantom{30)}13\\\end{array}
Find closest multiple of 30 to 43. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 43 to get reminder 13. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }13
Since 13 is less than 30, stop the division. The reminder is 13. 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}