Solve 7/6-1/4/frac{4{15}+1/2}

$$\frac { \frac { 7 } { 6 } - \frac { 1 } { 4 } } { \frac { 4 } { 15 } + \frac { 1 } { 2 } }$$

Evaluate

$$\frac{55}{46}\approx 1.195652174$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{14}{12}-\frac{3}{12}}{\frac{4}{15}+\frac{1}{2}}$$

Since \frac{14}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-3}{12}}{\frac{4}{15}+\frac{1}{2}}$$

Subtract 3 from 14 to get 11.

$$\frac{\frac{11}{12}}{\frac{4}{15}+\frac{1}{2}}$$

Least common multiple of 15 and 2 is 30. Convert \frac{4}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{\frac{11}{12}}{\frac{8}{30}+\frac{15}{30}}$$

Since \frac{8}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{12}}{\frac{8+15}{30}}$$

Add 8 and 15 to get 23.

$$\frac{\frac{11}{12}}{\frac{23}{30}}$$

Divide \frac{11}{12} by \frac{23}{30} by multiplying \frac{11}{12} by the reciprocal of \frac{23}{30}.

$$\frac{11}{12}\times \frac{30}{23}$$

Multiply \frac{11}{12} times \frac{30}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 30}{12\times 23}$$

Do the multiplications in the fraction \frac{11\times 30}{12\times 23}.

$$\frac{330}{276}$$

Reduce the fraction \frac{330}{276} to lowest terms by extracting and canceling out 6.

$$\frac{55}{46}$$

Factor

$$\frac{5 \cdot 11}{2 \cdot 23} = 1\frac{9}{46} = 1.1956521739130435$$