Solve 5/21*15/7+2/21*5/7

$$\frac{ 5 }{ 21 } \times 1 \frac{ 5 }{ 7 } + \frac{ 2 }{ 21 } \times \frac{ 5 }{ 7 }$$

Evaluate

$$\frac{10}{21}\approx 0.476190476$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{5}{21}\times \frac{7+5}{7}+\frac{2}{21}\times \frac{5}{7}$$

Add 7 and 5 to get 12.

$$\frac{5}{21}\times \frac{12}{7}+\frac{2}{21}\times \frac{5}{7}$$

Multiply \frac{5}{21} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 12}{21\times 7}+\frac{2}{21}\times \frac{5}{7}$$

Do the multiplications in the fraction \frac{5\times 12}{21\times 7}.

$$\frac{60}{147}+\frac{2}{21}\times \frac{5}{7}$$

Reduce the fraction \frac{60}{147} to lowest terms by extracting and canceling out 3.

$$\frac{20}{49}+\frac{2}{21}\times \frac{5}{7}$$

Multiply \frac{2}{21} times \frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20}{49}+\frac{2\times 5}{21\times 7}$$

Do the multiplications in the fraction \frac{2\times 5}{21\times 7}.

$$\frac{20}{49}+\frac{10}{147}$$

Least common multiple of 49 and 147 is 147. Convert \frac{20}{49} and \frac{10}{147} to fractions with denominator 147.

$$\frac{60}{147}+\frac{10}{147}$$

Since \frac{60}{147} and \frac{10}{147} have the same denominator, add them by adding their numerators.

$$\frac{60+10}{147}$$

Add 60 and 10 to get 70.

$$\frac{70}{147}$$

Reduce the fraction \frac{70}{147} to lowest terms by extracting and canceling out 7.

$$\frac{10}{21}$$

Factor

$$\frac{2 \cdot 5}{3 \cdot 7} = 0.47619047619047616$$