Solve 5/4div(-2/9+5/8)

$$\frac { 5 } { 4 } \div ( \frac { - 2 } { 9 } + \frac { 5 } { 8 } )$$

Evaluate

$$\frac{90}{29}\approx 3.103448276$$

Solution Steps

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

$$\frac{\frac{5}{4}}{-\frac{2}{9}+\frac{5}{8}}$$

Least common multiple of 9 and 8 is 72. Convert -\frac{2}{9} and \frac{5}{8} to fractions with denominator 72.

$$\frac{\frac{5}{4}}{-\frac{16}{72}+\frac{45}{72}}$$

Since -\frac{16}{72} and \frac{45}{72} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{4}}{\frac{-16+45}{72}}$$

Add -16 and 45 to get 29.

$$\frac{\frac{5}{4}}{\frac{29}{72}}$$

Divide \frac{5}{4} by \frac{29}{72} by multiplying \frac{5}{4} by the reciprocal of \frac{29}{72}.

$$\frac{5}{4}\times \frac{72}{29}$$

Multiply \frac{5}{4} times \frac{72}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 72}{4\times 29}$$

Do the multiplications in the fraction \frac{5\times 72}{4\times 29}.

$$\frac{360}{116}$$

Reduce the fraction \frac{360}{116} to lowest terms by extracting and canceling out 4.

$$\frac{90}{29}$$

Factor

$$\frac{2 \cdot 3 ^ {2} \cdot 5}{29} = 3\frac{3}{29} = 3.103448275862069$$