Solve left(1/3+1/4right)left(8/2+4/3right)frac{-8}{3}6

$$\left( \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } \right) \left( \frac{ 8 }{ 2 } + \frac{ 4 }{ 3 } \right) \frac{ -8 }{ 3 } 6$$

Evaluate

$$-\frac{448}{9}\approx -49.777777778$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\left(\frac{4}{12}+\frac{3}{12}\right)\left(\frac{8}{2}+\frac{4}{3}\right)\times \frac{-8}{3}\times 6$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{12}\left(\frac{8}{2}+\frac{4}{3}\right)\times \frac{-8}{3}\times 6$$

Add 4 and 3 to get 7.

$$\frac{7}{12}\left(\frac{8}{2}+\frac{4}{3}\right)\times \frac{-8}{3}\times 6$$

Divide 8 by 2 to get 4.

$$\frac{7}{12}\left(4+\frac{4}{3}\right)\times \frac{-8}{3}\times 6$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{7}{12}\left(\frac{12}{3}+\frac{4}{3}\right)\times \frac{-8}{3}\times 6$$

Since \frac{12}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}\times \frac{12+4}{3}\times \frac{-8}{3}\times 6$$

Add 12 and 4 to get 16.

$$\frac{7}{12}\times \frac{16}{3}\times \frac{-8}{3}\times 6$$

Multiply \frac{7}{12} times \frac{16}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 16}{12\times 3}\times \frac{-8}{3}\times 6$$

Do the multiplications in the fraction \frac{7\times 16}{12\times 3}.

$$\frac{112}{36}\times \frac{-8}{3}\times 6$$

Reduce the fraction \frac{112}{36} to lowest terms by extracting and canceling out 4.

$$\frac{28}{9}\times \frac{-8}{3}\times 6$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$\frac{28}{9}\left(-\frac{8}{3}\right)\times 6$$

Multiply \frac{28}{9} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28\left(-8\right)}{9\times 3}\times 6$$

Do the multiplications in the fraction \frac{28\left(-8\right)}{9\times 3}.

$$\frac{-224}{27}\times 6$$

Fraction \frac{-224}{27} can be rewritten as -\frac{224}{27} by extracting the negative sign.

$$-\frac{224}{27}\times 6$$

Express -\frac{224}{27}\times 6 as a single fraction.

$$\frac{-224\times 6}{27}$$

Multiply -224 and 6 to get -1344.

$$\frac{-1344}{27}$$

Reduce the fraction \frac{-1344}{27} to lowest terms by extracting and canceling out 3.

$$-\frac{448}{9}$$

Factor

$$-\frac{448}{9} = -49\frac{7}{9} = -49.77777777777778$$