Solve (4/9*5-5/8):5/36

$$( \frac { 4 } { 9 } \cdot 5 - \frac { 5 } { 8 } ) : \frac { 5 } { 36 }$$

Evaluate

$$\frac{23}{2}=11.5$$

Solution Steps

Express \frac{4}{9}\times 5 as a single fraction.

$$\frac{\frac{4\times 5}{9}-\frac{5}{8}}{\frac{5}{36}}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{20}{9}-\frac{5}{8}}{\frac{5}{36}}$$

Least common multiple of 9 and 8 is 72. Convert \frac{20}{9} and \frac{5}{8} to fractions with denominator 72.

$$\frac{\frac{160}{72}-\frac{45}{72}}{\frac{5}{36}}$$

Since \frac{160}{72} and \frac{45}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{160-45}{72}}{\frac{5}{36}}$$

Subtract 45 from 160 to get 115.

$$\frac{\frac{115}{72}}{\frac{5}{36}}$$

Divide \frac{115}{72} by \frac{5}{36} by multiplying \frac{115}{72} by the reciprocal of \frac{5}{36}.

$$\frac{115}{72}\times \frac{36}{5}$$

Multiply \frac{115}{72} times \frac{36}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{115\times 36}{72\times 5}$$

Do the multiplications in the fraction \frac{115\times 36}{72\times 5}.

$$\frac{4140}{360}$$

Reduce the fraction \frac{4140}{360} to lowest terms by extracting and canceling out 180.

$$\frac{23}{2}$$

Factor

$$\frac{23}{2} = 11\frac{1}{2} = 11.5$$