Solve -47/14+7/4+11/4/frac{4{3}}

$$\frac{ \frac{ -47 }{ 14 } + \frac{ 7 }{ 4 } + \frac{ 11 }{ 4 } }{ \frac{ 4 }{ 3 } }$$

Evaluate

$$\frac{6}{7}\approx 0.857142857$$

Solution Steps

Fraction \frac{-47}{14} can be rewritten as -\frac{47}{14} by extracting the negative sign.

$$\frac{-\frac{47}{14}+\frac{7}{4}+\frac{11}{4}}{\frac{4}{3}}$$

Least common multiple of 14 and 4 is 28. Convert -\frac{47}{14} and \frac{7}{4} to fractions with denominator 28.

$$\frac{-\frac{94}{28}+\frac{49}{28}+\frac{11}{4}}{\frac{4}{3}}$$

Since -\frac{94}{28} and \frac{49}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-94+49}{28}+\frac{11}{4}}{\frac{4}{3}}$$

Add -94 and 49 to get -45.

$$\frac{-\frac{45}{28}+\frac{11}{4}}{\frac{4}{3}}$$

Least common multiple of 28 and 4 is 28. Convert -\frac{45}{28} and \frac{11}{4} to fractions with denominator 28.

$$\frac{-\frac{45}{28}+\frac{77}{28}}{\frac{4}{3}}$$

Since -\frac{45}{28} and \frac{77}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-45+77}{28}}{\frac{4}{3}}$$

Add -45 and 77 to get 32.

$$\frac{\frac{32}{28}}{\frac{4}{3}}$$

Reduce the fraction \frac{32}{28} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{8}{7}}{\frac{4}{3}}$$

Divide \frac{8}{7} by \frac{4}{3} by multiplying \frac{8}{7} by the reciprocal of \frac{4}{3}.

$$\frac{8}{7}\times \frac{3}{4}$$

Multiply \frac{8}{7} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 3}{7\times 4}$$

Do the multiplications in the fraction \frac{8\times 3}{7\times 4}.

$$\frac{24}{28}$$

Reduce the fraction \frac{24}{28} to lowest terms by extracting and canceling out 4.

$$\frac{6}{7}$$

Factor

$$\frac{2 \cdot 3}{7} = 0.8571428571428571$$