Solve 1/5-(-7/9)-(-1/2)=

$$\frac { 1 } { 5 } - ( - \frac { 7 } { 9 } ) - ( - \frac { 1 } { 2 } ) =$$

Evaluate

$$\frac{133}{90}\approx 1.477777778$$

Solution Steps

The opposite of -\frac{7}{9} is \frac{7}{9}.

$$\frac{1}{5}+\frac{7}{9}-\left(-\frac{1}{2}\right)$$

Least common multiple of 5 and 9 is 45. Convert \frac{1}{5} and \frac{7}{9} to fractions with denominator 45.

$$\frac{9}{45}+\frac{35}{45}-\left(-\frac{1}{2}\right)$$

Since \frac{9}{45} and \frac{35}{45} have the same denominator, add them by adding their numerators.

$$\frac{9+35}{45}-\left(-\frac{1}{2}\right)$$

Add 9 and 35 to get 44.

$$\frac{44}{45}-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{44}{45}+\frac{1}{2}$$

Least common multiple of 45 and 2 is 90. Convert \frac{44}{45} and \frac{1}{2} to fractions with denominator 90.

$$\frac{88}{90}+\frac{45}{90}$$

Since \frac{88}{90} and \frac{45}{90} have the same denominator, add them by adding their numerators.

$$\frac{88+45}{90}$$

Add 88 and 45 to get 133.

$$\frac{133}{90}$$

Factor

$$\frac{7 \cdot 19}{2 \cdot 3 ^ {2} \cdot 5} = 1\frac{43}{90} = 1.4777777777777779$$