Solve 13/7*15/14+5/7*14/15

$$1 \frac { 3 } { 7 } \times \frac { 15 } { 14 } + \frac { 5 } { 7 } \times \frac { 14 } { 15 }$$

Evaluate

$$\frac{323}{147}\approx 2.197278912$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{7+3}{7}\times \frac{15}{14}+\frac{5}{7}\times \frac{14}{15}$$

Add 7 and 3 to get 10.

$$\frac{10}{7}\times \frac{15}{14}+\frac{5}{7}\times \frac{14}{15}$$

Multiply \frac{10}{7} times \frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 15}{7\times 14}+\frac{5}{7}\times \frac{14}{15}$$

Do the multiplications in the fraction \frac{10\times 15}{7\times 14}.

$$\frac{150}{98}+\frac{5}{7}\times \frac{14}{15}$$

Reduce the fraction \frac{150}{98} to lowest terms by extracting and canceling out 2.

$$\frac{75}{49}+\frac{5}{7}\times \frac{14}{15}$$

Multiply \frac{5}{7} times \frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{75}{49}+\frac{5\times 14}{7\times 15}$$

Do the multiplications in the fraction \frac{5\times 14}{7\times 15}.

$$\frac{75}{49}+\frac{70}{105}$$

Reduce the fraction \frac{70}{105} to lowest terms by extracting and canceling out 35.

$$\frac{75}{49}+\frac{2}{3}$$

Least common multiple of 49 and 3 is 147. Convert \frac{75}{49} and \frac{2}{3} to fractions with denominator 147.

$$\frac{225}{147}+\frac{98}{147}$$

Since \frac{225}{147} and \frac{98}{147} have the same denominator, add them by adding their numerators.

$$\frac{225+98}{147}$$

Add 225 and 98 to get 323.

$$\frac{323}{147}$$

Factor

$$\frac{17 \cdot 19}{3 \cdot 7 ^ {2}} = 2\frac{29}{147} = 2.197278911564626$$