Solve M=1/8+7/12/frac{5{6}-4/15}

$$M = \frac { \frac { 1 } { 8 } + \frac { 7 } { 12 } } { \frac { 5 } { 6 } - \frac { 4 } { 15 } }$$

Solve for M

$$M = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Least common multiple of 8 and 12 is 24. Convert \frac{1}{8} and \frac{7}{12} to fractions with denominator 24.

$$M=\frac{\frac{3}{24}+\frac{14}{24}}{\frac{5}{6}-\frac{4}{15}}$$

Since \frac{3}{24} and \frac{14}{24} have the same denominator, add them by adding their numerators.

$$M=\frac{\frac{3+14}{24}}{\frac{5}{6}-\frac{4}{15}}$$

Add 3 and 14 to get 17.

$$M=\frac{\frac{17}{24}}{\frac{5}{6}-\frac{4}{15}}$$

Least common multiple of 6 and 15 is 30. Convert \frac{5}{6} and \frac{4}{15} to fractions with denominator 30.

$$M=\frac{\frac{17}{24}}{\frac{25}{30}-\frac{8}{30}}$$

Since \frac{25}{30} and \frac{8}{30} have the same denominator, subtract them by subtracting their numerators.

$$M=\frac{\frac{17}{24}}{\frac{25-8}{30}}$$

Subtract 8 from 25 to get 17.

$$M=\frac{\frac{17}{24}}{\frac{17}{30}}$$

Divide \frac{17}{24} by \frac{17}{30} by multiplying \frac{17}{24} by the reciprocal of \frac{17}{30}.

$$M=\frac{17}{24}\times \frac{30}{17}$$

Multiply \frac{17}{24} times \frac{30}{17} by multiplying numerator times numerator and denominator times denominator.

$$M=\frac{17\times 30}{24\times 17}$$

Cancel out 17 in both numerator and denominator.

$$M=\frac{30}{24}$$

Reduce the fraction \frac{30}{24} to lowest terms by extracting and canceling out 6.

$$M=\frac{5}{4}$$

Assign M

$$M≔\frac{5}{4}$$