Evaluate
\frac{45}{2}=22.5
Factor
\frac{3 ^ {2} \cdot 5}{2} = 22\frac{1}{2} = 22.5
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)900}\\\end{array}
Use the 1^{st} digit 9 from dividend 900
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)900}\\\end{array}
Since 9 is less than 40, use the next digit 0 from dividend 900 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)900}\\\end{array}
Use the 2^{nd} digit 0 from dividend 900
\begin{array}{l}\phantom{40)}02\phantom{4}\\40\overline{)900}\\\phantom{40)}\underline{\phantom{}80\phantom{9}}\\\phantom{40)}10\\\end{array}
Find closest multiple of 40 to 90. We see that 2 \times 40 = 80 is the nearest. Now subtract 80 from 90 to get reminder 10. Add 2 to quotient.
\begin{array}{l}\phantom{40)}02\phantom{5}\\40\overline{)900}\\\phantom{40)}\underline{\phantom{}80\phantom{9}}\\\phantom{40)}100\\\end{array}
Use the 3^{rd} digit 0 from dividend 900
\begin{array}{l}\phantom{40)}022\phantom{6}\\40\overline{)900}\\\phantom{40)}\underline{\phantom{}80\phantom{9}}\\\phantom{40)}100\\\phantom{40)}\underline{\phantom{9}80\phantom{}}\\\phantom{40)9}20\\\end{array}
Find closest multiple of 40 to 100. We see that 2 \times 40 = 80 is the nearest. Now subtract 80 from 100 to get reminder 20. Add 2 to quotient.
\text{Quotient: }22 \text{Reminder: }20
Since 20 is less than 40, stop the division. The reminder is 20. The topmost line 022 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 22.
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}