Evaluate
\frac{56}{45}\approx 1.244444444
Factor
\frac{2 ^ {3} \cdot 7}{3 ^ {2} \cdot 5} = 1\frac{11}{45} = 1.2444444444444445
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\begin{array}{l}\phantom{2025)}\phantom{1}\\2025\overline{)2520}\\\end{array}
Use the 1^{st} digit 2 from dividend 2520
\begin{array}{l}\phantom{2025)}0\phantom{2}\\2025\overline{)2520}\\\end{array}
Since 2 is less than 2025, use the next digit 5 from dividend 2520 and add 0 to the quotient
\begin{array}{l}\phantom{2025)}0\phantom{3}\\2025\overline{)2520}\\\end{array}
Use the 2^{nd} digit 5 from dividend 2520
\begin{array}{l}\phantom{2025)}00\phantom{4}\\2025\overline{)2520}\\\end{array}
Since 25 is less than 2025, use the next digit 2 from dividend 2520 and add 0 to the quotient
\begin{array}{l}\phantom{2025)}00\phantom{5}\\2025\overline{)2520}\\\end{array}
Use the 3^{rd} digit 2 from dividend 2520
\begin{array}{l}\phantom{2025)}000\phantom{6}\\2025\overline{)2520}\\\end{array}
Since 252 is less than 2025, use the next digit 0 from dividend 2520 and add 0 to the quotient
\begin{array}{l}\phantom{2025)}000\phantom{7}\\2025\overline{)2520}\\\end{array}
Use the 4^{th} digit 0 from dividend 2520
\begin{array}{l}\phantom{2025)}0001\phantom{8}\\2025\overline{)2520}\\\phantom{2025)}\underline{\phantom{}2025\phantom{}}\\\phantom{2025)9}495\\\end{array}
Find closest multiple of 2025 to 2520. We see that 1 \times 2025 = 2025 is the nearest. Now subtract 2025 from 2520 to get reminder 495. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }495
Since 495 is less than 2025, stop the division. The reminder is 495. The topmost line 0001 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}