Evaluate
\frac{33}{7}\approx 4.714285714
Factor
\frac{3 \cdot 11}{7} = 4\frac{5}{7} = 4.714285714285714
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\begin{array}{l}\phantom{525)}\phantom{1}\\525\overline{)2475}\\\end{array}
Use the 1^{st} digit 2 from dividend 2475
\begin{array}{l}\phantom{525)}0\phantom{2}\\525\overline{)2475}\\\end{array}
Since 2 is less than 525, use the next digit 4 from dividend 2475 and add 0 to the quotient
\begin{array}{l}\phantom{525)}0\phantom{3}\\525\overline{)2475}\\\end{array}
Use the 2^{nd} digit 4 from dividend 2475
\begin{array}{l}\phantom{525)}00\phantom{4}\\525\overline{)2475}\\\end{array}
Since 24 is less than 525, use the next digit 7 from dividend 2475 and add 0 to the quotient
\begin{array}{l}\phantom{525)}00\phantom{5}\\525\overline{)2475}\\\end{array}
Use the 3^{rd} digit 7 from dividend 2475
\begin{array}{l}\phantom{525)}000\phantom{6}\\525\overline{)2475}\\\end{array}
Since 247 is less than 525, use the next digit 5 from dividend 2475 and add 0 to the quotient
\begin{array}{l}\phantom{525)}000\phantom{7}\\525\overline{)2475}\\\end{array}
Use the 4^{th} digit 5 from dividend 2475
\begin{array}{l}\phantom{525)}0004\phantom{8}\\525\overline{)2475}\\\phantom{525)}\underline{\phantom{}2100\phantom{}}\\\phantom{525)9}375\\\end{array}
Find closest multiple of 525 to 2475. We see that 4 \times 525 = 2100 is the nearest. Now subtract 2100 from 2475 to get reminder 375. Add 4 to quotient.
\text{Quotient: }4 \text{Reminder: }375
Since 375 is less than 525, stop the division. The reminder is 375. The topmost line 0004 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4.
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}