Evaluate
\frac{7}{2}=3.5
Factor
\frac{7}{2} = 3\frac{1}{2} = 3.5
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\begin{array}{l}\phantom{150)}\phantom{1}\\150\overline{)525}\\\end{array}
Use the 1^{st} digit 5 from dividend 525
\begin{array}{l}\phantom{150)}0\phantom{2}\\150\overline{)525}\\\end{array}
Since 5 is less than 150, use the next digit 2 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{150)}0\phantom{3}\\150\overline{)525}\\\end{array}
Use the 2^{nd} digit 2 from dividend 525
\begin{array}{l}\phantom{150)}00\phantom{4}\\150\overline{)525}\\\end{array}
Since 52 is less than 150, use the next digit 5 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{150)}00\phantom{5}\\150\overline{)525}\\\end{array}
Use the 3^{rd} digit 5 from dividend 525
\begin{array}{l}\phantom{150)}003\phantom{6}\\150\overline{)525}\\\phantom{150)}\underline{\phantom{}450\phantom{}}\\\phantom{150)9}75\\\end{array}
Find closest multiple of 150 to 525. We see that 3 \times 150 = 450 is the nearest. Now subtract 450 from 525 to get reminder 75. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }75
Since 75 is less than 150, stop the division. The reminder is 75. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}