Solve 7/9-3/4div9/10+5/9

$$\frac { 7 } { 9 } - \frac { 3 } { 4 } \div \frac { 9 } { 10 } + \frac { 5 } { 9 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Divide \frac{3}{4} by \frac{9}{10} by multiplying \frac{3}{4} by the reciprocal of \frac{9}{10}.

$$\frac{7}{9}-\frac{3}{4}\times \frac{10}{9}+\frac{5}{9}$$

Multiply \frac{3}{4} times \frac{10}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{9}-\frac{3\times 10}{4\times 9}+\frac{5}{9}$$

Do the multiplications in the fraction \frac{3\times 10}{4\times 9}.

$$\frac{7}{9}-\frac{30}{36}+\frac{5}{9}$$

Reduce the fraction \frac{30}{36} to lowest terms by extracting and canceling out 6.

$$\frac{7}{9}-\frac{5}{6}+\frac{5}{9}$$

Least common multiple of 9 and 6 is 18. Convert \frac{7}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{14}{18}-\frac{15}{18}+\frac{5}{9}$$

Since \frac{14}{18} and \frac{15}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-15}{18}+\frac{5}{9}$$

Subtract 15 from 14 to get -1.

$$-\frac{1}{18}+\frac{5}{9}$$

Least common multiple of 18 and 9 is 18. Convert -\frac{1}{18} and \frac{5}{9} to fractions with denominator 18.

$$-\frac{1}{18}+\frac{10}{18}$$

Since -\frac{1}{18} and \frac{10}{18} have the same denominator, add them by adding their numerators.

$$\frac{-1+10}{18}$$

Add -1 and 10 to get 9.

$$\frac{9}{18}$$

Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$