Solve 15.8-(8/5+1/8div4/5)

$$15.8-( \frac{ 8 }{ 5 } + \frac{ 1 }{ 8 } \div \frac{ 4 }{ 5 } )$$

Evaluate

$$14.04375$$

Solution Steps

Divide \frac{1}{8} by \frac{4}{5} by multiplying \frac{1}{8} by the reciprocal of \frac{4}{5}.

$$15.8-\left(\frac{8}{5}+\frac{1}{8}\times \frac{5}{4}\right)$$

Multiply \frac{1}{8} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$15.8-\left(\frac{8}{5}+\frac{1\times 5}{8\times 4}\right)$$

Do the multiplications in the fraction \frac{1\times 5}{8\times 4}.

$$15.8-\left(\frac{8}{5}+\frac{5}{32}\right)$$

Least common multiple of 5 and 32 is 160. Convert \frac{8}{5} and \frac{5}{32} to fractions with denominator 160.

$$15.8-\left(\frac{256}{160}+\frac{25}{160}\right)$$

Since \frac{256}{160} and \frac{25}{160} have the same denominator, add them by adding their numerators.

$$15.8-\frac{256+25}{160}$$

Add 256 and 25 to get 281.

$$15.8-\frac{281}{160}$$

Convert decimal number 15.8 to fraction \frac{158}{10}. Reduce the fraction \frac{158}{10} to lowest terms by extracting and canceling out 2.

$$\frac{79}{5}-\frac{281}{160}$$

Least common multiple of 5 and 160 is 160. Convert \frac{79}{5} and \frac{281}{160} to fractions with denominator 160.

$$\frac{2528}{160}-\frac{281}{160}$$

Since \frac{2528}{160} and \frac{281}{160} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2528-281}{160}$$

Subtract 281 from 2528 to get 2247.

$$\frac{2247}{160}$$

Factor

$$\frac{3 \cdot 7 \cdot 107}{5 \cdot 2 ^ {5}} = 14\frac{7}{160} = 14.04375$$