Solve 425/16+25(9/16:125/64:-27/8)=

$$4 \frac { 25 } { 16 } + 25 ( \frac { 9 } { 16 } : \frac { 125 } { 64 } : \frac { - 27 } { 8 } ) =$$

Evaluate

$$\frac{823}{240}\approx 3.429166667$$

Solution Steps

Multiply 4 and 16 to get 64.

$$\frac{64+25}{16}+25\times \frac{\frac{\frac{9}{16}}{\frac{125}{64}}}{\frac{-27}{8}}$$

Add 64 and 25 to get 89.

$$\frac{89}{16}+25\times \frac{\frac{\frac{9}{16}}{\frac{125}{64}}}{\frac{-27}{8}}$$

Divide \frac{\frac{9}{16}}{\frac{125}{64}} by \frac{-27}{8} by multiplying \frac{\frac{9}{16}}{\frac{125}{64}} by the reciprocal of \frac{-27}{8}.

$$\frac{89}{16}+25\times \frac{\frac{9}{16}\times 8}{\frac{125}{64}\left(-27\right)}$$

Express \frac{9}{16}\times 8 as a single fraction.

$$\frac{89}{16}+25\times \frac{\frac{9\times 8}{16}}{\frac{125}{64}\left(-27\right)}$$

Multiply 9 and 8 to get 72.

$$\frac{89}{16}+25\times \frac{\frac{72}{16}}{\frac{125}{64}\left(-27\right)}$$

Reduce the fraction \frac{72}{16} to lowest terms by extracting and canceling out 8.

$$\frac{89}{16}+25\times \frac{\frac{9}{2}}{\frac{125}{64}\left(-27\right)}$$

Express \frac{125}{64}\left(-27\right) as a single fraction.

$$\frac{89}{16}+25\times \frac{\frac{9}{2}}{\frac{125\left(-27\right)}{64}}$$

Multiply 125 and -27 to get -3375.

$$\frac{89}{16}+25\times \frac{\frac{9}{2}}{\frac{-3375}{64}}$$

Fraction \frac{-3375}{64} can be rewritten as -\frac{3375}{64} by extracting the negative sign.

$$\frac{89}{16}+25\times \frac{\frac{9}{2}}{-\frac{3375}{64}}$$

Divide \frac{9}{2} by -\frac{3375}{64} by multiplying \frac{9}{2} by the reciprocal of -\frac{3375}{64}.

$$\frac{89}{16}+25\times \frac{9}{2}\left(-\frac{64}{3375}\right)$$

Multiply \frac{9}{2} times -\frac{64}{3375} by multiplying numerator times numerator and denominator times denominator.

$$\frac{89}{16}+25\times \frac{9\left(-64\right)}{2\times 3375}$$

Do the multiplications in the fraction \frac{9\left(-64\right)}{2\times 3375}.

$$\frac{89}{16}+25\times \frac{-576}{6750}$$

Reduce the fraction \frac{-576}{6750} to lowest terms by extracting and canceling out 18.

$$\frac{89}{16}+25\left(-\frac{32}{375}\right)$$

Express 25\left(-\frac{32}{375}\right) as a single fraction.

$$\frac{89}{16}+\frac{25\left(-32\right)}{375}$$

Multiply 25 and -32 to get -800.

$$\frac{89}{16}+\frac{-800}{375}$$

Reduce the fraction \frac{-800}{375} to lowest terms by extracting and canceling out 25.

$$\frac{89}{16}-\frac{32}{15}$$

Least common multiple of 16 and 15 is 240. Convert \frac{89}{16} and \frac{32}{15} to fractions with denominator 240.

$$\frac{1335}{240}-\frac{512}{240}$$

Since \frac{1335}{240} and \frac{512}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1335-512}{240}$$

Subtract 512 from 1335 to get 823.

$$\frac{823}{240}$$

Factor

$$\frac{823}{2 ^ {4} \cdot 3 \cdot 5} = 3\frac{103}{240} = 3.4291666666666667$$