Evaluate
55
Factor
5\times 11
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)1485}\\\end{array}
Use the 1^{st} digit 1 from dividend 1485
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)1485}\\\end{array}
Since 1 is less than 27, use the next digit 4 from dividend 1485 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)1485}\\\end{array}
Use the 2^{nd} digit 4 from dividend 1485
\begin{array}{l}\phantom{27)}00\phantom{4}\\27\overline{)1485}\\\end{array}
Since 14 is less than 27, use the next digit 8 from dividend 1485 and add 0 to the quotient
\begin{array}{l}\phantom{27)}00\phantom{5}\\27\overline{)1485}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1485
\begin{array}{l}\phantom{27)}005\phantom{6}\\27\overline{)1485}\\\phantom{27)}\underline{\phantom{}135\phantom{9}}\\\phantom{27)9}13\\\end{array}
Find closest multiple of 27 to 148. We see that 5 \times 27 = 135 is the nearest. Now subtract 135 from 148 to get reminder 13. Add 5 to quotient.
\begin{array}{l}\phantom{27)}005\phantom{7}\\27\overline{)1485}\\\phantom{27)}\underline{\phantom{}135\phantom{9}}\\\phantom{27)9}135\\\end{array}
Use the 4^{th} digit 5 from dividend 1485
\begin{array}{l}\phantom{27)}0055\phantom{8}\\27\overline{)1485}\\\phantom{27)}\underline{\phantom{}135\phantom{9}}\\\phantom{27)9}135\\\phantom{27)}\underline{\phantom{9}135\phantom{}}\\\phantom{27)9999}0\\\end{array}
Find closest multiple of 27 to 135. We see that 5 \times 27 = 135 is the nearest. Now subtract 135 from 135 to get reminder 0. Add 5 to quotient.
\text{Quotient: }55 \text{Reminder: }0
Since 0 is less than 27, 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}