Solve 5/6+4/9-25/32+5/8*frac{2}{15}

$$\frac { 5 } { 6 } + \frac { 4 } { 9 } - \frac { 25 } { 32 } + \frac { 5 } { 8 } \times \frac { 2 } { 15 }$$

Evaluate

$$\frac{167}{288}\approx 0.579861111$$

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{4}{9} to fractions with denominator 18.

$$\frac{15}{18}+\frac{8}{18}-\frac{25}{32}+\frac{5}{8}\times \frac{2}{15}$$

Since \frac{15}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{15+8}{18}-\frac{25}{32}+\frac{5}{8}\times \frac{2}{15}$$

Add 15 and 8 to get 23.

$$\frac{23}{18}-\frac{25}{32}+\frac{5}{8}\times \frac{2}{15}$$

Least common multiple of 18 and 32 is 288. Convert \frac{23}{18} and \frac{25}{32} to fractions with denominator 288.

$$\frac{368}{288}-\frac{225}{288}+\frac{5}{8}\times \frac{2}{15}$$

Since \frac{368}{288} and \frac{225}{288} have the same denominator, subtract them by subtracting their numerators.

$$\frac{368-225}{288}+\frac{5}{8}\times \frac{2}{15}$$

Subtract 225 from 368 to get 143.

$$\frac{143}{288}+\frac{5}{8}\times \frac{2}{15}$$

Multiply \frac{5}{8} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{143}{288}+\frac{5\times 2}{8\times 15}$$

Do the multiplications in the fraction \frac{5\times 2}{8\times 15}.

$$\frac{143}{288}+\frac{10}{120}$$

Reduce the fraction \frac{10}{120} to lowest terms by extracting and canceling out 10.

$$\frac{143}{288}+\frac{1}{12}$$

Least common multiple of 288 and 12 is 288. Convert \frac{143}{288} and \frac{1}{12} to fractions with denominator 288.

$$\frac{143}{288}+\frac{24}{288}$$

Since \frac{143}{288} and \frac{24}{288} have the same denominator, add them by adding their numerators.

$$\frac{143+24}{288}$$

Add 143 and 24 to get 167.

$$\frac{167}{288}$$

Factor

$$\frac{167}{2 ^ {5} \cdot 3 ^ {2}} = 0.5798611111111112$$