Solve 7/15*1/21+(7/3+frac{35/11)}{1}

$$\frac { \frac { 7 } { 15 } \cdot \frac { 1 } { 21 } + ( \frac { 7 } { 3 } + \frac { 35 } { 11 } ) } { 1 }$$

Evaluate

$$\frac{2741}{495}\approx 5.537373737$$

Solution Steps

Multiply \frac{7}{15} times \frac{1}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 1}{15\times 21}+\frac{7}{3}+\frac{35}{11}}{1}$$

Do the multiplications in the fraction \frac{7\times 1}{15\times 21}.

$$\frac{\frac{7}{315}+\frac{7}{3}+\frac{35}{11}}{1}$$

Reduce the fraction \frac{7}{315} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{1}{45}+\frac{7}{3}+\frac{35}{11}}{1}$$

Least common multiple of 45 and 3 is 45. Convert \frac{1}{45} and \frac{7}{3} to fractions with denominator 45.

$$\frac{\frac{1}{45}+\frac{105}{45}+\frac{35}{11}}{1}$$

Since \frac{1}{45} and \frac{105}{45} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+105}{45}+\frac{35}{11}}{1}$$

Add 1 and 105 to get 106.

$$\frac{\frac{106}{45}+\frac{35}{11}}{1}$$

Least common multiple of 45 and 11 is 495. Convert \frac{106}{45} and \frac{35}{11} to fractions with denominator 495.

$$\frac{\frac{1166}{495}+\frac{1575}{495}}{1}$$

Since \frac{1166}{495} and \frac{1575}{495} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1166+1575}{495}}{1}$$

Add 1166 and 1575 to get 2741.

$$\frac{\frac{2741}{495}}{1}$$

Anything divided by one gives itself.

$$\frac{2741}{495}$$

Factor

$$\frac{2741}{3 ^ {2} \cdot 5 \cdot 11} = 5\frac{266}{495} = 5.537373737373738$$