Solve (5/6+7/8)*36/41+16/25(frac{3}{4}-frac{5}{8})*frac{5}{4}

$$( \frac { 5 } { 6 } + \frac { 7 } { 8 } ) \cdot \frac { 36 } { 41 } + \frac { 16 } { 25 } ( \frac { 3 } { 4 } - \frac { 5 } { 8 } ) \cdot \frac { 5 } { 4 }$$

Evaluate

$$\frac{8}{5}=1.6$$

Solution Steps

Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{7}{8} to fractions with denominator 24.

$$\left(\frac{20}{24}+\frac{21}{24}\right)\times \frac{36}{41}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Since \frac{20}{24} and \frac{21}{24} have the same denominator, add them by adding their numerators.

$$\frac{20+21}{24}\times \frac{36}{41}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Add 20 and 21 to get 41.

$$\frac{41}{24}\times \frac{36}{41}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Multiply \frac{41}{24} times \frac{36}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 36}{24\times 41}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Cancel out 41 in both numerator and denominator.

$$\frac{36}{24}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$\frac{3}{2}+\frac{16}{25}\left(\frac{3}{4}-\frac{5}{8}\right)\times \frac{5}{4}$$

Least common multiple of 4 and 8 is 8. Convert \frac{3}{4} and \frac{5}{8} to fractions with denominator 8.

$$\frac{3}{2}+\frac{16}{25}\left(\frac{6}{8}-\frac{5}{8}\right)\times \frac{5}{4}$$

Since \frac{6}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}+\frac{16}{25}\times \frac{6-5}{8}\times \frac{5}{4}$$

Subtract 5 from 6 to get 1.

$$\frac{3}{2}+\frac{16}{25}\times \frac{1}{8}\times \frac{5}{4}$$

Multiply \frac{16}{25} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{16\times 1}{25\times 8}\times \frac{5}{4}$$

Do the multiplications in the fraction \frac{16\times 1}{25\times 8}.

$$\frac{3}{2}+\frac{16}{200}\times \frac{5}{4}$$

Reduce the fraction \frac{16}{200} to lowest terms by extracting and canceling out 8.

$$\frac{3}{2}+\frac{2}{25}\times \frac{5}{4}$$

Multiply \frac{2}{25} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{2\times 5}{25\times 4}$$

Do the multiplications in the fraction \frac{2\times 5}{25\times 4}.

$$\frac{3}{2}+\frac{10}{100}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\frac{3}{2}+\frac{1}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{3}{2} and \frac{1}{10} to fractions with denominator 10.

$$\frac{15}{10}+\frac{1}{10}$$

Since \frac{15}{10} and \frac{1}{10} have the same denominator, add them by adding their numerators.

$$\frac{15+1}{10}$$

Add 15 and 1 to get 16.

$$\frac{16}{10}$$

Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{8}{5}$$

Factor

$$\frac{2 ^ {3}}{5} = 1\frac{3}{5} = 1.6$$