Evaluate
\frac{21}{20}=1.05
Factor
\frac{3 \cdot 7}{2 ^ {2} \cdot 5} = 1\frac{1}{20} = 1.05
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\begin{array}{l}\phantom{100)}\phantom{1}\\100\overline{)105}\\\end{array}
Use the 1^{st} digit 1 from dividend 105
\begin{array}{l}\phantom{100)}0\phantom{2}\\100\overline{)105}\\\end{array}
Since 1 is less than 100, use the next digit 0 from dividend 105 and add 0 to the quotient
\begin{array}{l}\phantom{100)}0\phantom{3}\\100\overline{)105}\\\end{array}
Use the 2^{nd} digit 0 from dividend 105
\begin{array}{l}\phantom{100)}00\phantom{4}\\100\overline{)105}\\\end{array}
Since 10 is less than 100, use the next digit 5 from dividend 105 and add 0 to the quotient
\begin{array}{l}\phantom{100)}00\phantom{5}\\100\overline{)105}\\\end{array}
Use the 3^{rd} digit 5 from dividend 105
\begin{array}{l}\phantom{100)}001\phantom{6}\\100\overline{)105}\\\phantom{100)}\underline{\phantom{}100\phantom{}}\\\phantom{100)99}5\\\end{array}
Find closest multiple of 100 to 105. We see that 1 \times 100 = 100 is the nearest. Now subtract 100 from 105 to get reminder 5. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }5
Since 5 is less than 100, stop the division. The reminder is 5. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}