Solve a=1-0,125*1/2/frac{7{8}-8/7}

$$a = \frac { 1 - 0,125 \cdot \frac { 1 } { 2 } } { \frac { 7 } { 8 } - \frac { 8 } { 7 } }$$

Solve for a

$$a=-3,5$$

Steps for Solving Linear Equation

Convert decimal number 0,125 to fraction \frac{125}{1000}. Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$a=\frac{1-\frac{1}{8}\times \frac{1}{2}}{\frac{7}{8}-\frac{8}{7}}$$

Multiply \frac{1}{8} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{1-\frac{1\times 1}{8\times 2}}{\frac{7}{8}-\frac{8}{7}}$$

Do the multiplications in the fraction \frac{1\times 1}{8\times 2}.

$$a=\frac{1-\frac{1}{16}}{\frac{7}{8}-\frac{8}{7}}$$

Convert 1 to fraction \frac{16}{16}.

$$a=\frac{\frac{16}{16}-\frac{1}{16}}{\frac{7}{8}-\frac{8}{7}}$$

Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{\frac{16-1}{16}}{\frac{7}{8}-\frac{8}{7}}$$

Subtract 1 from 16 to get 15.

$$a=\frac{\frac{15}{16}}{\frac{7}{8}-\frac{8}{7}}$$

Least common multiple of 8 and 7 is 56. Convert \frac{7}{8} and \frac{8}{7} to fractions with denominator 56.

$$a=\frac{\frac{15}{16}}{\frac{49}{56}-\frac{64}{56}}$$

Since \frac{49}{56} and \frac{64}{56} have the same denominator, subtract them by subtracting their numerators.

$$a=\frac{\frac{15}{16}}{\frac{49-64}{56}}$$

Subtract 64 from 49 to get -15.

$$a=\frac{\frac{15}{16}}{-\frac{15}{56}}$$

Divide \frac{15}{16} by -\frac{15}{56} by multiplying \frac{15}{16} by the reciprocal of -\frac{15}{56}.

$$a=\frac{15}{16}\left(-\frac{56}{15}\right)$$

Multiply \frac{15}{16} times -\frac{56}{15} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{15\left(-56\right)}{16\times 15}$$

Cancel out 15 in both numerator and denominator.

$$a=\frac{-56}{16}$$

Reduce the fraction \frac{-56}{16} to lowest terms by extracting and canceling out 8.

$$a=-\frac{7}{2}$$

Assign a

$$a≔-3,5$$