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{400)}\phantom{1}\\400\overline{)420}\\\end{array}
Use the 1^{st} digit 4 from dividend 420
\begin{array}{l}\phantom{400)}0\phantom{2}\\400\overline{)420}\\\end{array}
Since 4 is less than 400, use the next digit 2 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{400)}0\phantom{3}\\400\overline{)420}\\\end{array}
Use the 2^{nd} digit 2 from dividend 420
\begin{array}{l}\phantom{400)}00\phantom{4}\\400\overline{)420}\\\end{array}
Since 42 is less than 400, use the next digit 0 from dividend 420 and add 0 to the quotient
\begin{array}{l}\phantom{400)}00\phantom{5}\\400\overline{)420}\\\end{array}
Use the 3^{rd} digit 0 from dividend 420
\begin{array}{l}\phantom{400)}001\phantom{6}\\400\overline{)420}\\\phantom{400)}\underline{\phantom{}400\phantom{}}\\\phantom{400)9}20\\\end{array}
Find closest multiple of 400 to 420. We see that 1 \times 400 = 400 is the nearest. Now subtract 400 from 420 to get reminder 20. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }20
Since 20 is less than 400, stop the division. The reminder is 20. 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}