Solve 5/7*1/3+5/7*8/9-frac{2}{9}*frac{5}{7}+frac{5}{7}*1frac{2}{3}

$$\frac { 5 } { 7 } \times \frac { 1 } { 3 } + \frac { 5 } { 7 } \times \frac { 8 } { 9 } - \frac { 2 } { 9 } \times \frac { 5 } { 7 } + \frac { 5 } { 7 } \times 1 \frac { 2 } { 3 }$$

Evaluate

$$\frac{40}{21}\approx 1.904761905$$

Solution Steps

Multiply \frac{5}{7} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 1}{7\times 3}+\frac{5}{7}\times \frac{8}{9}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Do the multiplications in the fraction \frac{5\times 1}{7\times 3}.

$$\frac{5}{21}+\frac{5}{7}\times \frac{8}{9}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Multiply \frac{5}{7} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{21}+\frac{5\times 8}{7\times 9}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Do the multiplications in the fraction \frac{5\times 8}{7\times 9}.

$$\frac{5}{21}+\frac{40}{63}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Least common multiple of 21 and 63 is 63. Convert \frac{5}{21} and \frac{40}{63} to fractions with denominator 63.

$$\frac{15}{63}+\frac{40}{63}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Since \frac{15}{63} and \frac{40}{63} have the same denominator, add them by adding their numerators.

$$\frac{15+40}{63}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Add 15 and 40 to get 55.

$$\frac{55}{63}-\frac{2}{9}\times \frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Multiply \frac{2}{9} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{55}{63}-\frac{2\times 5}{9\times 7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Do the multiplications in the fraction \frac{2\times 5}{9\times 7}.

$$\frac{55}{63}-\frac{10}{63}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Since \frac{55}{63} and \frac{10}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-10}{63}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Subtract 10 from 55 to get 45.

$$\frac{45}{63}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Reduce the fraction \frac{45}{63} to lowest terms by extracting and canceling out 9.

$$\frac{5}{7}+\frac{5}{7}\times \frac{1\times 3+2}{3}$$

Multiply 1 and 3 to get 3.

$$\frac{5}{7}+\frac{5}{7}\times \frac{3+2}{3}$$

Add 3 and 2 to get 5.

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

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

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

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

$$\frac{5}{7}+\frac{25}{21}$$

Least common multiple of 7 and 21 is 21. Convert \frac{5}{7} and \frac{25}{21} to fractions with denominator 21.

$$\frac{15}{21}+\frac{25}{21}$$

Since \frac{15}{21} and \frac{25}{21} have the same denominator, add them by adding their numerators.

$$\frac{15+25}{21}$$

Add 15 and 25 to get 40.

$$\frac{40}{21}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3 \cdot 7} = 1\frac{19}{21} = 1.9047619047619047$$