Evaluate
\frac{69}{7}\approx 9.857142857
Factor
\frac{3 \cdot 23}{7} = 9\frac{6}{7} = 9.857142857142858
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)138}\\\end{array}
Use the 1^{st} digit 1 from dividend 138
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)138}\\\end{array}
Since 1 is less than 14, use the next digit 3 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)138}\\\end{array}
Use the 2^{nd} digit 3 from dividend 138
\begin{array}{l}\phantom{14)}00\phantom{4}\\14\overline{)138}\\\end{array}
Since 13 is less than 14, use the next digit 8 from dividend 138 and add 0 to the quotient
\begin{array}{l}\phantom{14)}00\phantom{5}\\14\overline{)138}\\\end{array}
Use the 3^{rd} digit 8 from dividend 138
\begin{array}{l}\phantom{14)}009\phantom{6}\\14\overline{)138}\\\phantom{14)}\underline{\phantom{}126\phantom{}}\\\phantom{14)9}12\\\end{array}
Find closest multiple of 14 to 138. We see that 9 \times 14 = 126 is the nearest. Now subtract 126 from 138 to get reminder 12. Add 9 to quotient.
\text{Quotient: }9 \text{Reminder: }12
Since 12 is less than 14, stop the division. The reminder is 12. The topmost line 009 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 9.
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}