Solve 4/3*7/4(-45/14+7/16*8)

$$\frac{ 4 }{ 3 } \times \frac{ 7 }{ 4 } (- \frac{ 45 }{ 14 } + \frac{ 7 }{ 16 } \times 8)$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Multiply \frac{4}{3} times \frac{7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 7}{3\times 4}\left(-\frac{45}{14}+\frac{7}{16}\times 8\right)$$

Cancel out 4 in both numerator and denominator.

$$\frac{7}{3}\left(-\frac{45}{14}+\frac{7}{16}\times 8\right)$$

Express \frac{7}{16}\times 8 as a single fraction.

$$\frac{7}{3}\left(-\frac{45}{14}+\frac{7\times 8}{16}\right)$$

Multiply 7 and 8 to get 56.

$$\frac{7}{3}\left(-\frac{45}{14}+\frac{56}{16}\right)$$

Reduce the fraction \frac{56}{16} to lowest terms by extracting and canceling out 8.

$$\frac{7}{3}\left(-\frac{45}{14}+\frac{7}{2}\right)$$

Least common multiple of 14 and 2 is 14. Convert -\frac{45}{14} and \frac{7}{2} to fractions with denominator 14.

$$\frac{7}{3}\left(-\frac{45}{14}+\frac{49}{14}\right)$$

Since -\frac{45}{14} and \frac{49}{14} have the same denominator, add them by adding their numerators.

$$\frac{7}{3}\times \frac{-45+49}{14}$$

Add -45 and 49 to get 4.

$$\frac{7}{3}\times \frac{4}{14}$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{7}{3}\times \frac{2}{7}$$

Multiply \frac{7}{3} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 2}{3\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$