Solve 11/2[1/15*2+(1/15-1)1/60]

$$\frac { 11 } { 2 } [ \frac { 1 } { 15 } \times 2 + ( \frac { 1 } { 15 } - 1 ) \frac { 1 } { 60 } ]$$

Evaluate

$$\frac{583}{900}\approx 0.647777778$$

Solution Steps

Multiply \frac{1}{15} and 2 to get \frac{2}{15}.

$$\frac{11}{2}\left(\frac{2}{15}+\left(\frac{1}{15}-1\right)\times \frac{1}{60}\right)$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{11}{2}\left(\frac{2}{15}+\left(\frac{1}{15}-\frac{15}{15}\right)\times \frac{1}{60}\right)$$

Since \frac{1}{15} and \frac{15}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\left(\frac{2}{15}+\frac{1-15}{15}\times \frac{1}{60}\right)$$

Subtract 15 from 1 to get -14.

$$\frac{11}{2}\left(\frac{2}{15}-\frac{14}{15}\times \frac{1}{60}\right)$$

Multiply -\frac{14}{15} times \frac{1}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11}{2}\left(\frac{2}{15}+\frac{-14}{15\times 60}\right)$$

Do the multiplications in the fraction \frac{-14}{15\times 60}.

$$\frac{11}{2}\left(\frac{2}{15}+\frac{-14}{900}\right)$$

Reduce the fraction \frac{-14}{900} to lowest terms by extracting and canceling out 2.

$$\frac{11}{2}\left(\frac{2}{15}-\frac{7}{450}\right)$$

Least common multiple of 15 and 450 is 450. Convert \frac{2}{15} and \frac{7}{450} to fractions with denominator 450.

$$\frac{11}{2}\left(\frac{60}{450}-\frac{7}{450}\right)$$

Since \frac{60}{450} and \frac{7}{450} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{2}\times \frac{60-7}{450}$$

Subtract 7 from 60 to get 53.

$$\frac{11}{2}\times \frac{53}{450}$$

Multiply \frac{11}{2} times \frac{53}{450} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 53}{2\times 450}$$

Do the multiplications in the fraction \frac{11\times 53}{2\times 450}.

$$\frac{583}{900}$$

Factor

$$\frac{11 \cdot 53}{2 ^ {2} \cdot 3 ^ {2} \cdot 5 ^ {2}} = 0.6477777777777778$$