Evaluate
\frac{53}{7}\approx 7.571428571
Factor
\frac{53}{7} = 7\frac{4}{7} = 7.571428571428571
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)318}\\\end{array}
Use the 1^{st} digit 3 from dividend 318
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)318}\\\end{array}
Since 3 is less than 42, use the next digit 1 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)318}\\\end{array}
Use the 2^{nd} digit 1 from dividend 318
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)318}\\\end{array}
Since 31 is less than 42, use the next digit 8 from dividend 318 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)318}\\\end{array}
Use the 3^{rd} digit 8 from dividend 318
\begin{array}{l}\phantom{42)}007\phantom{6}\\42\overline{)318}\\\phantom{42)}\underline{\phantom{}294\phantom{}}\\\phantom{42)9}24\\\end{array}
Find closest multiple of 42 to 318. We see that 7 \times 42 = 294 is the nearest. Now subtract 294 from 318 to get reminder 24. Add 7 to quotient.
\text{Quotient: }7 \text{Reminder: }24
Since 24 is less than 42, stop the division. The reminder is 24. The topmost line 007 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7.
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}