Evaluate
\frac{43}{37}\approx 1.162162162
Factor
\frac{43}{37} = 1\frac{6}{37} = 1.162162162162162
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\begin{array}{l}\phantom{74)}\phantom{1}\\74\overline{)86}\\\end{array}
Use the 1^{st} digit 8 from dividend 86
\begin{array}{l}\phantom{74)}0\phantom{2}\\74\overline{)86}\\\end{array}
Since 8 is less than 74, use the next digit 6 from dividend 86 and add 0 to the quotient
\begin{array}{l}\phantom{74)}0\phantom{3}\\74\overline{)86}\\\end{array}
Use the 2^{nd} digit 6 from dividend 86
\begin{array}{l}\phantom{74)}01\phantom{4}\\74\overline{)86}\\\phantom{74)}\underline{\phantom{}74\phantom{}}\\\phantom{74)}12\\\end{array}
Find closest multiple of 74 to 86. We see that 1 \times 74 = 74 is the nearest. Now subtract 74 from 86 to get reminder 12. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }12
Since 12 is less than 74, 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}