Solve 32/25+16/34left(1-7*32/125right)

$$\frac{ 32 }{ 25 } + \frac{ 16 }{ 34 } \left( 1-7 \times \frac{ 32 }{ 125 } \right)$$

Evaluate

$$\frac{1928}{2125}\approx 0.907294118$$

Solution Steps

Reduce the fraction \frac{16}{34} to lowest terms by extracting and canceling out 2.

$$\frac{32}{25}+\frac{8}{17}\left(1-7\times \frac{32}{125}\right)$$

Express 7\times \frac{32}{125} as a single fraction.

$$\frac{32}{25}+\frac{8}{17}\left(1-\frac{7\times 32}{125}\right)$$

Multiply 7 and 32 to get 224.

$$\frac{32}{25}+\frac{8}{17}\left(1-\frac{224}{125}\right)$$

Convert 1 to fraction \frac{125}{125}.

$$\frac{32}{25}+\frac{8}{17}\left(\frac{125}{125}-\frac{224}{125}\right)$$

Since \frac{125}{125} and \frac{224}{125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32}{25}+\frac{8}{17}\times \frac{125-224}{125}$$

Subtract 224 from 125 to get -99.

$$\frac{32}{25}+\frac{8}{17}\left(-\frac{99}{125}\right)$$

Multiply \frac{8}{17} times -\frac{99}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32}{25}+\frac{8\left(-99\right)}{17\times 125}$$

Do the multiplications in the fraction \frac{8\left(-99\right)}{17\times 125}.

$$\frac{32}{25}+\frac{-792}{2125}$$

Fraction \frac{-792}{2125} can be rewritten as -\frac{792}{2125} by extracting the negative sign.

$$\frac{32}{25}-\frac{792}{2125}$$

Least common multiple of 25 and 2125 is 2125. Convert \frac{32}{25} and \frac{792}{2125} to fractions with denominator 2125.

$$\frac{2720}{2125}-\frac{792}{2125}$$

Since \frac{2720}{2125} and \frac{792}{2125} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2720-792}{2125}$$

Subtract 792 from 2720 to get 1928.

$$\frac{1928}{2125}$$

Factor

$$\frac{2 ^ {3} \cdot 241}{5 ^ {3} \cdot 17} = 0.9072941176470588$$