Solve 70/27+-7/3/7+frac{35{27}}

$$\frac{ \frac{ 70 }{ 27 } + \frac{ -7 }{ 3 } }{ 7+ \frac{ 35 }{ 27 } }$$

Evaluate

$$\frac{1}{32}=0.03125$$

Solution Steps

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$\frac{\frac{70}{27}-\frac{7}{3}}{7+\frac{35}{27}}$$

Least common multiple of 27 and 3 is 27. Convert \frac{70}{27} and \frac{7}{3} to fractions with denominator 27.

$$\frac{\frac{70}{27}-\frac{63}{27}}{7+\frac{35}{27}}$$

Since \frac{70}{27} and \frac{63}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{70-63}{27}}{7+\frac{35}{27}}$$

Subtract 63 from 70 to get 7.

$$\frac{\frac{7}{27}}{7+\frac{35}{27}}$$

Convert 7 to fraction \frac{189}{27}.

$$\frac{\frac{7}{27}}{\frac{189}{27}+\frac{35}{27}}$$

Since \frac{189}{27} and \frac{35}{27} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{27}}{\frac{189+35}{27}}$$

Add 189 and 35 to get 224.

$$\frac{\frac{7}{27}}{\frac{224}{27}}$$

Divide \frac{7}{27} by \frac{224}{27} by multiplying \frac{7}{27} by the reciprocal of \frac{224}{27}.

$$\frac{7}{27}\times \frac{27}{224}$$

Multiply \frac{7}{27} times \frac{27}{224} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 27}{27\times 224}$$

Cancel out 27 in both numerator and denominator.

$$\frac{7}{224}$$

Reduce the fraction \frac{7}{224} to lowest terms by extracting and canceling out 7.

$$\frac{1}{32}$$

Factor

$$\frac{1}{2 ^ {5}} = 0.03125$$