Solve 5/7*3/8+5/8*5/7quadfrac{3}{5}*6*5

$$\frac { 5 } { 7 } \times \frac { 3 } { 8 } + \frac { 5 } { 8 } \times \frac { 5 } { 7 } \quad \frac { 3 } { 5 } \times 6 \times 5$$

Evaluate

$$\frac{465}{56}\approx 8.303571429$$

Solution Steps

Multiply \frac{5}{7} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 3}{7\times 8}+\frac{5}{8}\times \frac{5}{7}\times \frac{3}{5}\times 6\times 5$$

Do the multiplications in the fraction \frac{5\times 3}{7\times 8}.

$$\frac{15}{56}+\frac{5}{8}\times \frac{5}{7}\times \frac{3}{5}\times 6\times 5$$

Multiply \frac{5}{8} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{56}+\frac{5\times 5}{8\times 7}\times \frac{3}{5}\times 6\times 5$$

Do the multiplications in the fraction \frac{5\times 5}{8\times 7}.

$$\frac{15}{56}+\frac{25}{56}\times \frac{3}{5}\times 6\times 5$$

Multiply \frac{25}{56} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15}{56}+\frac{25\times 3}{56\times 5}\times 6\times 5$$

Do the multiplications in the fraction \frac{25\times 3}{56\times 5}.

$$\frac{15}{56}+\frac{75}{280}\times 6\times 5$$

Reduce the fraction \frac{75}{280} to lowest terms by extracting and canceling out 5.

$$\frac{15}{56}+\frac{15}{56}\times 6\times 5$$

Express \frac{15}{56}\times 6 as a single fraction.

$$\frac{15}{56}+\frac{15\times 6}{56}\times 5$$

Multiply 15 and 6 to get 90.

$$\frac{15}{56}+\frac{90}{56}\times 5$$

Reduce the fraction \frac{90}{56} to lowest terms by extracting and canceling out 2.

$$\frac{15}{56}+\frac{45}{28}\times 5$$

Express \frac{45}{28}\times 5 as a single fraction.

$$\frac{15}{56}+\frac{45\times 5}{28}$$

Multiply 45 and 5 to get 225.

$$\frac{15}{56}+\frac{225}{28}$$

Least common multiple of 56 and 28 is 56. Convert \frac{15}{56} and \frac{225}{28} to fractions with denominator 56.

$$\frac{15}{56}+\frac{450}{56}$$

Since \frac{15}{56} and \frac{450}{56} have the same denominator, add them by adding their numerators.

$$\frac{15+450}{56}$$

Add 15 and 450 to get 465.

$$\frac{465}{56}$$

Factor

$$\frac{3 \cdot 5 \cdot 31}{2 ^ {3} \cdot 7} = 8\frac{17}{56} = 8.303571428571429$$