Evaluate
\frac{33}{20}=1.65
Factor
\frac{3 \cdot 11}{2 ^ {2} \cdot 5} = 1\frac{13}{20} = 1.65
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)99}\\\end{array}
Use the 1^{st} digit 9 from dividend 99
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)99}\\\end{array}
Since 9 is less than 60, use the next digit 9 from dividend 99 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)99}\\\end{array}
Use the 2^{nd} digit 9 from dividend 99
\begin{array}{l}\phantom{60)}01\phantom{4}\\60\overline{)99}\\\phantom{60)}\underline{\phantom{}60\phantom{}}\\\phantom{60)}39\\\end{array}
Find closest multiple of 60 to 99. We see that 1 \times 60 = 60 is the nearest. Now subtract 60 from 99 to get reminder 39. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }39
Since 39 is less than 60, stop the division. The reminder is 39. 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}