Solve (-9/5div7/5)-(-25/7div5/7)

$$( \frac { - 9 } { 5 } \div \frac { 7 } { 5 } ) - ( \frac { - 25 } { 7 } \div \frac { 5 } { 7 } )$$

Evaluate

$$\frac{26}{7}\approx 3.714285714$$

Solution Steps

Divide \frac{-9}{5} by \frac{7}{5} by multiplying \frac{-9}{5} by the reciprocal of \frac{7}{5}.

$$\frac{-9\times 5}{5\times 7}-\frac{\frac{-25}{7}}{\frac{5}{7}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-9}{7}-\frac{\frac{-25}{7}}{\frac{5}{7}}$$

Fraction \frac{-9}{7} can be rewritten as -\frac{9}{7} by extracting the negative sign.

$$-\frac{9}{7}-\frac{\frac{-25}{7}}{\frac{5}{7}}$$

Divide \frac{-25}{7} by \frac{5}{7} by multiplying \frac{-25}{7} by the reciprocal of \frac{5}{7}.

$$-\frac{9}{7}-\frac{-25\times 7}{7\times 5}$$

Cancel out 5\times 7 in both numerator and denominator.

$$-\frac{9}{7}-\left(-5\right)$$

The opposite of -5 is 5.

$$-\frac{9}{7}+5$$

Convert 5 to fraction \frac{35}{7}.

$$-\frac{9}{7}+\frac{35}{7}$$

Since -\frac{9}{7} and \frac{35}{7} have the same denominator, add them by adding their numerators.

$$\frac{-9+35}{7}$$

Add -9 and 35 to get 26.

$$\frac{26}{7}$$

Factor

$$\frac{2 \cdot 13}{7} = 3\frac{5}{7} = 3.7142857142857144$$