Evaluate
\frac{76}{45}\approx 1.688888889
Factor
\frac{2 ^ {2} \cdot 19}{3 ^ {2} \cdot 5} = 1\frac{31}{45} = 1.6888888888888889
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)76}\\\end{array}
Use the 1^{st} digit 7 from dividend 76
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)76}\\\end{array}
Since 7 is less than 45, use the next digit 6 from dividend 76 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)76}\\\end{array}
Use the 2^{nd} digit 6 from dividend 76
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)76}\\\phantom{45)}\underline{\phantom{}45\phantom{}}\\\phantom{45)}31\\\end{array}
Find closest multiple of 45 to 76. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 76 to get reminder 31. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }31
Since 31 is less than 45, stop the division. The reminder is 31. 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}