Solve 4/9*12/5+7/8div5/6-frac{11}{30}

$$\frac { 4 } { 9 } \cdot \frac { 12 } { 5 } + \frac { 7 } { 8 } \div \frac { 5 } { 6 } - \frac { 11 } { 30 }$$

Evaluate

$$\frac{7}{4}=1.75$$

Solution Steps

Multiply \frac{4}{9} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 12}{9\times 5}+\frac{\frac{7}{8}}{\frac{5}{6}}-\frac{11}{30}$$

Do the multiplications in the fraction \frac{4\times 12}{9\times 5}.

$$\frac{48}{45}+\frac{\frac{7}{8}}{\frac{5}{6}}-\frac{11}{30}$$

Reduce the fraction \frac{48}{45} to lowest terms by extracting and canceling out 3.

$$\frac{16}{15}+\frac{\frac{7}{8}}{\frac{5}{6}}-\frac{11}{30}$$

Divide \frac{7}{8} by \frac{5}{6} by multiplying \frac{7}{8} by the reciprocal of \frac{5}{6}.

$$\frac{16}{15}+\frac{7}{8}\times \frac{6}{5}-\frac{11}{30}$$

Multiply \frac{7}{8} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16}{15}+\frac{7\times 6}{8\times 5}-\frac{11}{30}$$

Do the multiplications in the fraction \frac{7\times 6}{8\times 5}.

$$\frac{16}{15}+\frac{42}{40}-\frac{11}{30}$$

Reduce the fraction \frac{42}{40} to lowest terms by extracting and canceling out 2.

$$\frac{16}{15}+\frac{21}{20}-\frac{11}{30}$$

Least common multiple of 15 and 20 is 60. Convert \frac{16}{15} and \frac{21}{20} to fractions with denominator 60.

$$\frac{64}{60}+\frac{63}{60}-\frac{11}{30}$$

Since \frac{64}{60} and \frac{63}{60} have the same denominator, add them by adding their numerators.

$$\frac{64+63}{60}-\frac{11}{30}$$

Add 64 and 63 to get 127.

$$\frac{127}{60}-\frac{11}{30}$$

Least common multiple of 60 and 30 is 60. Convert \frac{127}{60} and \frac{11}{30} to fractions with denominator 60.

$$\frac{127}{60}-\frac{22}{60}$$

Since \frac{127}{60} and \frac{22}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{127-22}{60}$$

Subtract 22 from 127 to get 105.

$$\frac{105}{60}$$

Reduce the fraction \frac{105}{60} to lowest terms by extracting and canceling out 15.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$