Solve (19/16-1/32):11/21

$$( \frac { 19 } { 16 } - \frac { 1 } { 32 } ) : \frac { 11 } { 21 }$$

Evaluate

$$\frac{777}{352}\approx 2.207386364$$

Solution Steps

Least common multiple of 16 and 32 is 32. Convert \frac{19}{16} and \frac{1}{32} to fractions with denominator 32.

$$\frac{\frac{38}{32}-\frac{1}{32}}{\frac{11}{21}}$$

Since \frac{38}{32} and \frac{1}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{38-1}{32}}{\frac{11}{21}}$$

Subtract 1 from 38 to get 37.

$$\frac{\frac{37}{32}}{\frac{11}{21}}$$

Divide \frac{37}{32} by \frac{11}{21} by multiplying \frac{37}{32} by the reciprocal of \frac{11}{21}.

$$\frac{37}{32}\times \frac{21}{11}$$

Multiply \frac{37}{32} times \frac{21}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{37\times 21}{32\times 11}$$

Do the multiplications in the fraction \frac{37\times 21}{32\times 11}.

$$\frac{777}{352}$$

Factor

$$\frac{3 \cdot 7 \cdot 37}{2 ^ {5} \cdot 11} = 2\frac{73}{352} = 2.2073863636363638$$