Evaluate
\frac{40}{21}\approx 1.904761905
Factor
\frac{2 ^ {3} \cdot 5}{3 \cdot 7} = 1\frac{19}{21} = 1.9047619047619047
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)40}\\\end{array}
Use the 1^{st} digit 4 from dividend 40
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)40}\\\end{array}
Since 4 is less than 21, use the next digit 0 from dividend 40 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)40}\\\end{array}
Use the 2^{nd} digit 0 from dividend 40
\begin{array}{l}\phantom{21)}01\phantom{4}\\21\overline{)40}\\\phantom{21)}\underline{\phantom{}21\phantom{}}\\\phantom{21)}19\\\end{array}
Find closest multiple of 21 to 40. We see that 1 \times 21 = 21 is the nearest. Now subtract 21 from 40 to get reminder 19. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }19
Since 19 is less than 21, stop the division. The reminder is 19. The topmost line 01 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}