Evaluate
\frac{15}{2}=7.5
Factor
\frac{3 \cdot 5}{2} = 7\frac{1}{2} = 7.5
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)75}\\\end{array}
Use the 1^{st} digit 7 from dividend 75
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)75}\\\end{array}
Since 7 is less than 10, use the next digit 5 from dividend 75 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)75}\\\end{array}
Use the 2^{nd} digit 5 from dividend 75
\begin{array}{l}\phantom{10)}07\phantom{4}\\10\overline{)75}\\\phantom{10)}\underline{\phantom{}70\phantom{}}\\\phantom{10)9}5\\\end{array}
Find closest multiple of 10 to 75. We see that 7 \times 10 = 70 is the nearest. Now subtract 70 from 75 to get reminder 5. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }5
Since 5 is less than 10, stop the division. The reminder is 5. The topmost line 07 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}