( ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 0,6 : 3 \frac { 3 } { 4 } ) 2 \frac { 1 } { 2 } + 3,75 : 1 \frac { 1 } { 2 } ) : 2,2
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\frac{\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply 1 and 7 to get 7.
\frac{\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Add 7 and 1 to get 8.
\frac{\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Least common multiple of 7 and 49 is 49. Convert \frac{8}{7} and \frac{23}{49} to fractions with denominator 49.
\frac{\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Since \frac{56}{49} and \frac{23}{49} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Subtract 23 from 56 to get 33.
\frac{\frac{33}{49}\times \frac{147}{22}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Divide \frac{33}{49} by \frac{22}{147} by multiplying \frac{33}{49} by the reciprocal of \frac{22}{147}.
\frac{\frac{33\times 147}{49\times 22}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply \frac{33}{49} times \frac{147}{22} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{4851}{1078}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Do the multiplications in the fraction \frac{33\times 147}{49\times 22}.
\frac{\frac{9}{2}-\frac{0,6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Reduce the fraction \frac{4851}{1078} to lowest terms by extracting and canceling out 539.
\frac{\frac{9}{2}-\frac{0,6\times 4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Divide 0,6 by \frac{3\times 4+3}{4} by multiplying 0,6 by the reciprocal of \frac{3\times 4+3}{4}.
\frac{\frac{9}{2}-\frac{2,4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply 0,6 and 4 to get 2,4.
\frac{\frac{9}{2}-\frac{2,4}{12+3}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply 3 and 4 to get 12.
\frac{\frac{9}{2}-\frac{2,4}{15}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Add 12 and 3 to get 15.
\frac{\frac{9}{2}-\frac{24}{150}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Expand \frac{2,4}{15} by multiplying both numerator and the denominator by 10.
\frac{\frac{9}{2}-\frac{4}{25}\times \frac{2\times 2+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Reduce the fraction \frac{24}{150} to lowest terms by extracting and canceling out 6.
\frac{\frac{9}{2}-\frac{4}{25}\times \frac{4+1}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply 2 and 2 to get 4.
\frac{\frac{9}{2}-\frac{4}{25}\times \frac{5}{2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Add 4 and 1 to get 5.
\frac{\frac{9}{2}-\frac{4\times 5}{25\times 2}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Multiply \frac{4}{25} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{9}{2}-\frac{20}{50}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Do the multiplications in the fraction \frac{4\times 5}{25\times 2}.
\frac{\frac{9}{2}-\frac{2}{5}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.
\frac{\frac{45}{10}-\frac{4}{10}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{2}{5} to fractions with denominator 10.
\frac{\frac{45-4}{10}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Since \frac{45}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{41}{10}+\frac{3,75}{\frac{1\times 2+1}{2}}}{2,2}
Subtract 4 from 45 to get 41.
\frac{\frac{41}{10}+\frac{3,75\times 2}{1\times 2+1}}{2,2}
Divide 3,75 by \frac{1\times 2+1}{2} by multiplying 3,75 by the reciprocal of \frac{1\times 2+1}{2}.
\frac{\frac{41}{10}+\frac{7,5}{1\times 2+1}}{2,2}
Multiply 3,75 and 2 to get 7,5.
\frac{\frac{41}{10}+\frac{7,5}{2+1}}{2,2}
Multiply 1 and 2 to get 2.
\frac{\frac{41}{10}+\frac{7,5}{3}}{2,2}
Add 2 and 1 to get 3.
\frac{\frac{41}{10}+\frac{75}{30}}{2,2}
Expand \frac{7,5}{3} by multiplying both numerator and the denominator by 10.
\frac{\frac{41}{10}+\frac{5}{2}}{2,2}
Reduce the fraction \frac{75}{30} to lowest terms by extracting and canceling out 15.
\frac{\frac{41}{10}+\frac{25}{10}}{2,2}
Least common multiple of 10 and 2 is 10. Convert \frac{41}{10} and \frac{5}{2} to fractions with denominator 10.
\frac{\frac{41+25}{10}}{2,2}
Since \frac{41}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.
\frac{\frac{66}{10}}{2,2}
Add 41 and 25 to get 66.
\frac{\frac{33}{5}}{2,2}
Reduce the fraction \frac{66}{10} to lowest terms by extracting and canceling out 2.
\frac{33}{5\times 2,2}
Express \frac{\frac{33}{5}}{2,2} as a single fraction.
\frac{33}{11}
Multiply 5 and 2,2 to get 11.
3
Divide 33 by 11 to get 3.
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}