Evaluate
\frac{1511}{101}\approx 14.96039604
Factor
\frac{1511}{101} = 14\frac{97}{101} = 14.96039603960396
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\begin{array}{l}\phantom{505)}\phantom{1}\\505\overline{)7555}\\\end{array}
Use the 1^{st} digit 7 from dividend 7555
\begin{array}{l}\phantom{505)}0\phantom{2}\\505\overline{)7555}\\\end{array}
Since 7 is less than 505, use the next digit 5 from dividend 7555 and add 0 to the quotient
\begin{array}{l}\phantom{505)}0\phantom{3}\\505\overline{)7555}\\\end{array}
Use the 2^{nd} digit 5 from dividend 7555
\begin{array}{l}\phantom{505)}00\phantom{4}\\505\overline{)7555}\\\end{array}
Since 75 is less than 505, use the next digit 5 from dividend 7555 and add 0 to the quotient
\begin{array}{l}\phantom{505)}00\phantom{5}\\505\overline{)7555}\\\end{array}
Use the 3^{rd} digit 5 from dividend 7555
\begin{array}{l}\phantom{505)}001\phantom{6}\\505\overline{)7555}\\\phantom{505)}\underline{\phantom{}505\phantom{9}}\\\phantom{505)}250\\\end{array}
Find closest multiple of 505 to 755. We see that 1 \times 505 = 505 is the nearest. Now subtract 505 from 755 to get reminder 250. Add 1 to quotient.
\begin{array}{l}\phantom{505)}001\phantom{7}\\505\overline{)7555}\\\phantom{505)}\underline{\phantom{}505\phantom{9}}\\\phantom{505)}2505\\\end{array}
Use the 4^{th} digit 5 from dividend 7555
\begin{array}{l}\phantom{505)}0014\phantom{8}\\505\overline{)7555}\\\phantom{505)}\underline{\phantom{}505\phantom{9}}\\\phantom{505)}2505\\\phantom{505)}\underline{\phantom{}2020\phantom{}}\\\phantom{505)9}485\\\end{array}
Find closest multiple of 505 to 2505. We see that 4 \times 505 = 2020 is the nearest. Now subtract 2020 from 2505 to get reminder 485. Add 4 to quotient.
\text{Quotient: }14 \text{Reminder: }485
Since 485 is less than 505, stop the division. The reminder is 485. The topmost line 0014 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 14.
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}