Solve 55/48:(11/16+3/32)-14/15*frac{5}{7}

$$\frac { 55 } { 48 } : ( \frac { 11 } { 16 } + \frac { 3 } { 32 } ) - \frac { 14 } { 15 } \cdot \frac { 5 } { 7 }$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Least common multiple of 16 and 32 is 32. Convert \frac{11}{16} and \frac{3}{32} to fractions with denominator 32.

$$\frac{\frac{55}{48}}{\frac{22}{32}+\frac{3}{32}}-\frac{14}{15}\times \frac{5}{7}$$

Since \frac{22}{32} and \frac{3}{32} have the same denominator, add them by adding their numerators.

$$\frac{\frac{55}{48}}{\frac{22+3}{32}}-\frac{14}{15}\times \frac{5}{7}$$

Add 22 and 3 to get 25.

$$\frac{\frac{55}{48}}{\frac{25}{32}}-\frac{14}{15}\times \frac{5}{7}$$

Divide \frac{55}{48} by \frac{25}{32} by multiplying \frac{55}{48} by the reciprocal of \frac{25}{32}.

$$\frac{55}{48}\times \frac{32}{25}-\frac{14}{15}\times \frac{5}{7}$$

Multiply \frac{55}{48} times \frac{32}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55\times 32}{48\times 25}-\frac{14}{15}\times \frac{5}{7}$$

Do the multiplications in the fraction \frac{55\times 32}{48\times 25}.

$$\frac{1760}{1200}-\frac{14}{15}\times \frac{5}{7}$$

Reduce the fraction \frac{1760}{1200} to lowest terms by extracting and canceling out 80.

$$\frac{22}{15}-\frac{14}{15}\times \frac{5}{7}$$

Multiply \frac{14}{15} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22}{15}-\frac{14\times 5}{15\times 7}$$

Do the multiplications in the fraction \frac{14\times 5}{15\times 7}.

$$\frac{22}{15}-\frac{70}{105}$$

Reduce the fraction \frac{70}{105} to lowest terms by extracting and canceling out 35.

$$\frac{22}{15}-\frac{2}{3}$$

Least common multiple of 15 and 3 is 15. Convert \frac{22}{15} and \frac{2}{3} to fractions with denominator 15.

$$\frac{22}{15}-\frac{10}{15}$$

Since \frac{22}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-10}{15}$$

Subtract 10 from 22 to get 12.

$$\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$