Solve 8/9-(3/7-1/9)

$$\frac { 8 } { 9 } - ( \frac { 3 } { 7 } - \frac { 1 } { 9 } )$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{3}{7} and \frac{1}{9} to fractions with denominator 63.

$$\frac{8}{9}-\left(\frac{27}{63}-\frac{7}{63}\right)$$

Since \frac{27}{63} and \frac{7}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{9}-\frac{27-7}{63}$$

Subtract 7 from 27 to get 20.

$$\frac{8}{9}-\frac{20}{63}$$

Least common multiple of 9 and 63 is 63. Convert \frac{8}{9} and \frac{20}{63} to fractions with denominator 63.

$$\frac{56}{63}-\frac{20}{63}$$

Since \frac{56}{63} and \frac{20}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-20}{63}$$

Subtract 20 from 56 to get 36.

$$\frac{36}{63}$$

Reduce the fraction \frac{36}{63} to lowest terms by extracting and canceling out 9.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$