Solve 3/25*1/5+3/80:5frac{4/3}{(28+35*frac{603+37}{16}):364}+frac{frac{3}{25}:frac{9}{15}+frac{3}{84}*5frac{4}{14}}{frac{2}{7}:7*|-49|}*frac{3}{2}

$$\frac { \frac { 3 } { 25 } \times \frac { 1 } { 5 } + \frac { 3 } { 80 } : 5 \frac { 4 } { 3 } } { ( 28 + 35 \times \frac { 603 + 37 } { 16 } ) : 364 } + \frac { \frac { 3 } { 25 } : \frac { 9 } { 15 } + \frac { 3 } { 84 } \times 5 \frac { 4 } { 14 } } { \frac { 2 } { 7 } : 7 \times | - 49 | } \times \frac { 3 } { 2 }$$

Evaluate

$$\frac{2367787}{7913500}\approx 0.299208568$$

Solution Steps

Multiply \frac{3}{25} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 1}{25\times 5}+\frac{\frac{3}{80}}{\frac{5\times 3+4}{3}}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Do the multiplications in the fraction \frac{3\times 1}{25\times 5}.

$$\frac{\frac{3}{125}+\frac{\frac{3}{80}}{\frac{5\times 3+4}{3}}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Divide \frac{3}{80} by \frac{5\times 3+4}{3} by multiplying \frac{3}{80} by the reciprocal of \frac{5\times 3+4}{3}.

$$\frac{\frac{3}{125}+\frac{3\times 3}{80\left(5\times 3+4\right)}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{3}{125}+\frac{9}{80\left(5\times 3+4\right)}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{3}{125}+\frac{9}{80\left(15+4\right)}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 15 and 4 to get 19.

$$\frac{\frac{3}{125}+\frac{9}{80\times 19}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply 80 and 19 to get 1520.

$$\frac{\frac{3}{125}+\frac{9}{1520}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Least common multiple of 125 and 1520 is 38000. Convert \frac{3}{125} and \frac{9}{1520} to fractions with denominator 38000.

$$\frac{\frac{912}{38000}+\frac{225}{38000}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Since \frac{912}{38000} and \frac{225}{38000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{912+225}{38000}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 912 and 225 to get 1137.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times \frac{603+37}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 603 and 37 to get 640.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times \frac{640}{16}}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Divide 640 by 16 to get 40.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times 40}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply 35 and 40 to get 1400.

$$\frac{\frac{1137}{38000}}{\frac{28+1400}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 28 and 1400 to get 1428.

$$\frac{\frac{1137}{38000}}{\frac{1428}{364}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Reduce the fraction \frac{1428}{364} to lowest terms by extracting and canceling out 28.

$$\frac{\frac{1137}{38000}}{\frac{51}{13}}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Divide \frac{1137}{38000} by \frac{51}{13} by multiplying \frac{1137}{38000} by the reciprocal of \frac{51}{13}.

$$\frac{1137}{38000}\times \frac{13}{51}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply \frac{1137}{38000} times \frac{13}{51} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1137\times 13}{38000\times 51}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Do the multiplications in the fraction \frac{1137\times 13}{38000\times 51}.

$$\frac{14781}{1938000}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Reduce the fraction \frac{14781}{1938000} to lowest terms by extracting and canceling out 3.

$$\frac{4927}{646000}+\frac{\frac{\frac{3}{25}}{\frac{9}{15}}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Divide \frac{3}{25} by \frac{9}{15} by multiplying \frac{3}{25} by the reciprocal of \frac{9}{15}.

$$\frac{4927}{646000}+\frac{\frac{3\times 15}{25\times 9}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Cancel out 3\times 3\times 5 in both numerator and denominator.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{3}{84}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Reduce the fraction \frac{3}{84} to lowest terms by extracting and canceling out 3.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{1}{28}\times \frac{5\times 14+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply 5 and 14 to get 70.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{1}{28}\times \frac{70+4}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 70 and 4 to get 74.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{1}{28}\times \frac{74}{14}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Reduce the fraction \frac{74}{14} to lowest terms by extracting and canceling out 2.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{1}{28}\times \frac{37}{7}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Multiply \frac{1}{28} times \frac{37}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{1\times 37}{28\times 7}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Do the multiplications in the fraction \frac{1\times 37}{28\times 7}.

$$\frac{4927}{646000}+\frac{\frac{1}{5}+\frac{37}{196}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Least common multiple of 5 and 196 is 980. Convert \frac{1}{5} and \frac{37}{196} to fractions with denominator 980.

$$\frac{4927}{646000}+\frac{\frac{196}{980}+\frac{185}{980}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Since \frac{196}{980} and \frac{185}{980} have the same denominator, add them by adding their numerators.

$$\frac{4927}{646000}+\frac{\frac{196+185}{980}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Add 196 and 185 to get 381.

$$\frac{4927}{646000}+\frac{\frac{381}{980}}{\frac{\frac{2}{7}}{7}|-49|}\times \frac{3}{2}$$

Express \frac{\frac{2}{7}}{7} as a single fraction.

$$\frac{4927}{646000}+\frac{\frac{381}{980}}{\frac{2}{7\times 7}|-49|}\times \frac{3}{2}$$

Multiply 7 and 7 to get 49.

$$\frac{4927}{646000}+\frac{\frac{381}{980}}{\frac{2}{49}|-49|}\times \frac{3}{2}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -49 is 49.

$$\frac{4927}{646000}+\frac{\frac{381}{980}}{\frac{2}{49}\times 49}\times \frac{3}{2}$$

Cancel out 49 and 49.

$$\frac{4927}{646000}+\frac{\frac{381}{980}}{2}\times \frac{3}{2}$$

Express \frac{\frac{381}{980}}{2} as a single fraction.

$$\frac{4927}{646000}+\frac{381}{980\times 2}\times \frac{3}{2}$$

Multiply 980 and 2 to get 1960.

$$\frac{4927}{646000}+\frac{381}{1960}\times \frac{3}{2}$$

Multiply \frac{381}{1960} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4927}{646000}+\frac{381\times 3}{1960\times 2}$$

Do the multiplications in the fraction \frac{381\times 3}{1960\times 2}.

$$\frac{4927}{646000}+\frac{1143}{3920}$$

Least common multiple of 646000 and 3920 is 31654000. Convert \frac{4927}{646000} and \frac{1143}{3920} to fractions with denominator 31654000.

$$\frac{241423}{31654000}+\frac{9229725}{31654000}$$

Since \frac{241423}{31654000} and \frac{9229725}{31654000} have the same denominator, add them by adding their numerators.

$$\frac{241423+9229725}{31654000}$$

Add 241423 and 9229725 to get 9471148.

$$\frac{9471148}{31654000}$$

Reduce the fraction \frac{9471148}{31654000} to lowest terms by extracting and canceling out 4.

$$\frac{2367787}{7913500}$$

Factor

$$\frac{659 \cdot 3593}{2 ^ {2} \cdot 5 ^ {3} \cdot 7 ^ {2} \cdot 17 \cdot 19} = 0.29920856763758136$$