Evaluate
\frac{6}{5}=1.2
Factor
\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2
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\begin{array}{l}\phantom{105)}\phantom{1}\\105\overline{)126}\\\end{array}
Use the 1^{st} digit 1 from dividend 126
\begin{array}{l}\phantom{105)}0\phantom{2}\\105\overline{)126}\\\end{array}
Since 1 is less than 105, use the next digit 2 from dividend 126 and add 0 to the quotient
\begin{array}{l}\phantom{105)}0\phantom{3}\\105\overline{)126}\\\end{array}
Use the 2^{nd} digit 2 from dividend 126
\begin{array}{l}\phantom{105)}00\phantom{4}\\105\overline{)126}\\\end{array}
Since 12 is less than 105, use the next digit 6 from dividend 126 and add 0 to the quotient
\begin{array}{l}\phantom{105)}00\phantom{5}\\105\overline{)126}\\\end{array}
Use the 3^{rd} digit 6 from dividend 126
\begin{array}{l}\phantom{105)}001\phantom{6}\\105\overline{)126}\\\phantom{105)}\underline{\phantom{}105\phantom{}}\\\phantom{105)9}21\\\end{array}
Find closest multiple of 105 to 126. We see that 1 \times 105 = 105 is the nearest. Now subtract 105 from 126 to get reminder 21. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }21
Since 21 is less than 105, stop the division. The reminder is 21. The topmost line 001 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}