Solve 1786/2947*384^2/14857+864/3874*88216/73485

$$\frac { 1786 } { 2947 } \times \frac { 384 ^ { 2 } } { 14857 } + \frac { 864 } { 3874 } \times \frac { 88216 } { 73485 }$$

Evaluate

$$\frac{4350536835514752}{692463790950295}\approx 6.282692167$$

Solution Steps

Calculate 384 to the power of 2 and get 147456.

$$\frac{1786}{2947}\times \frac{147456}{14857}+\frac{864}{3874}\times \frac{88216}{73485}$$

Multiply \frac{1786}{2947} times \frac{147456}{14857} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1786\times 147456}{2947\times 14857}+\frac{864}{3874}\times \frac{88216}{73485}$$

Do the multiplications in the fraction \frac{1786\times 147456}{2947\times 14857}.

$$\frac{263356416}{43783579}+\frac{864}{3874}\times \frac{88216}{73485}$$

Reduce the fraction \frac{864}{3874} to lowest terms by extracting and canceling out 2.

$$\frac{263356416}{43783579}+\frac{432}{1937}\times \frac{88216}{73485}$$

Multiply \frac{432}{1937} times \frac{88216}{73485} by multiplying numerator times numerator and denominator times denominator.

$$\frac{263356416}{43783579}+\frac{432\times 88216}{1937\times 73485}$$

Do the multiplications in the fraction \frac{432\times 88216}{1937\times 73485}.

$$\frac{263356416}{43783579}+\frac{38109312}{142340445}$$

Reduce the fraction \frac{38109312}{142340445} to lowest terms by extracting and canceling out 9.

$$\frac{263356416}{43783579}+\frac{4234368}{15815605}$$

Least common multiple of 43783579 and 15815605 is 692463790950295. Convert \frac{263356416}{43783579} and \frac{4234368}{15815605} to fractions with denominator 692463790950295.

$$\frac{4165141049671680}{692463790950295}+\frac{185395785843072}{692463790950295}$$

Since \frac{4165141049671680}{692463790950295} and \frac{185395785843072}{692463790950295} have the same denominator, add them by adding their numerators.

$$\frac{4165141049671680+185395785843072}{692463790950295}$$

Add 4165141049671680 and 185395785843072 to get 4350536835514752.

$$\frac{4350536835514752}{692463790950295}$$

Factor

$$\frac{2 ^ {7} \cdot 3 \cdot 151 \cdot 2083 \cdot 36020141}{5 \cdot 7 \cdot 13 \cdot 23 \cdot 71 \cdot 83 \cdot 149 \cdot 179 \cdot 421} = 6\frac{195754089812982}{692463790950295} = 6.282692167260242$$