Solve 3/25*1/5+3/80:5frac{4/3}{(28+35*frac{283+37}{16}):364}

$$\frac { \frac { 3 } { 25 } \times \frac { 1 } { 5 } + \frac { 3 } { 80 } : 5 \frac { 4 } { 3 } } { ( 28 + 35 \times \frac { 283 + 37 } { 16 } ) : 364 }$$

Evaluate

$$\frac{1137}{76000}\approx 0.014960526$$

Solution Steps

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

$$\frac{\frac{3\times 1}{25\times 5}+\frac{\frac{3}{80}}{\frac{5\times 3+4}{3}}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

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

$$\frac{\frac{3}{125}+\frac{\frac{3}{80}}{\frac{5\times 3+4}{3}}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

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}.

$$\frac{\frac{3}{125}+\frac{3\times 3}{80\left(5\times 3+4\right)}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{3}{125}+\frac{9}{80\left(5\times 3+4\right)}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{3}{125}+\frac{9}{80\left(15+4\right)}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Add 15 and 4 to get 19.

$$\frac{\frac{3}{125}+\frac{9}{80\times 19}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Multiply 80 and 19 to get 1520.

$$\frac{\frac{3}{125}+\frac{9}{1520}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

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

$$\frac{\frac{912}{38000}+\frac{225}{38000}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

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

$$\frac{\frac{912+225}{38000}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Add 912 and 225 to get 1137.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times \frac{283+37}{16}}{364}}$$

Add 283 and 37 to get 320.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times \frac{320}{16}}{364}}$$

Divide 320 by 16 to get 20.

$$\frac{\frac{1137}{38000}}{\frac{28+35\times 20}{364}}$$

Multiply 35 and 20 to get 700.

$$\frac{\frac{1137}{38000}}{\frac{28+700}{364}}$$

Add 28 and 700 to get 728.

$$\frac{\frac{1137}{38000}}{\frac{728}{364}}$$

Divide 728 by 364 to get 2.

$$\frac{\frac{1137}{38000}}{2}$$

Express \frac{\frac{1137}{38000}}{2} as a single fraction.

$$\frac{1137}{38000\times 2}$$

Multiply 38000 and 2 to get 76000.

$$\frac{1137}{76000}$$

Factor

$$\frac{3 \cdot 379}{2 ^ {5} \cdot 5 ^ {3} \cdot 19} = 0.014960526315789474$$