Evaluate
55
Factor
5\times 11
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)4125}\\\end{array}
Use the 1^{st} digit 4 from dividend 4125
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)4125}\\\end{array}
Since 4 is less than 75, use the next digit 1 from dividend 4125 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)4125}\\\end{array}
Use the 2^{nd} digit 1 from dividend 4125
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)4125}\\\end{array}
Since 41 is less than 75, use the next digit 2 from dividend 4125 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)4125}\\\end{array}
Use the 3^{rd} digit 2 from dividend 4125
\begin{array}{l}\phantom{75)}005\phantom{6}\\75\overline{)4125}\\\phantom{75)}\underline{\phantom{}375\phantom{9}}\\\phantom{75)9}37\\\end{array}
Find closest multiple of 75 to 412. We see that 5 \times 75 = 375 is the nearest. Now subtract 375 from 412 to get reminder 37. Add 5 to quotient.
\begin{array}{l}\phantom{75)}005\phantom{7}\\75\overline{)4125}\\\phantom{75)}\underline{\phantom{}375\phantom{9}}\\\phantom{75)9}375\\\end{array}
Use the 4^{th} digit 5 from dividend 4125
\begin{array}{l}\phantom{75)}0055\phantom{8}\\75\overline{)4125}\\\phantom{75)}\underline{\phantom{}375\phantom{9}}\\\phantom{75)9}375\\\phantom{75)}\underline{\phantom{9}375\phantom{}}\\\phantom{75)9999}0\\\end{array}
Find closest multiple of 75 to 375. We see that 5 \times 75 = 375 is the nearest. Now subtract 375 from 375 to get reminder 0. Add 5 to quotient.
\text{Quotient: }55 \text{Reminder: }0
Since 0 is less than 75, stop the division. The reminder is 0. The topmost line 0055 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 55.
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}