Solve (5/6-1/9):13/9+5/9=frac{13}{36}

$$( \frac { 5 } { 6 } - \frac { 1 } { 9 } ) : \frac { 13 } { 9 } + \frac { 5 } { 9 } = \frac { 13 } { 36 }$$

Verify

Solution Steps

Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{1}{9} to fractions with denominator 18.

$$\frac{\frac{15}{18}-\frac{2}{18}}{\frac{13}{9}}+\frac{5}{9}=\frac{13}{36}$$

Since \frac{15}{18} and \frac{2}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-2}{18}}{\frac{13}{9}}+\frac{5}{9}=\frac{13}{36}$$

Subtract 2 from 15 to get 13.

$$\frac{\frac{13}{18}}{\frac{13}{9}}+\frac{5}{9}=\frac{13}{36}$$

Divide \frac{13}{18} by \frac{13}{9} by multiplying \frac{13}{18} by the reciprocal of \frac{13}{9}.

$$\frac{13}{18}\times \frac{9}{13}+\frac{5}{9}=\frac{13}{36}$$

Multiply \frac{13}{18} times \frac{9}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 9}{18\times 13}+\frac{5}{9}=\frac{13}{36}$$

Cancel out 13 in both numerator and denominator.

$$\frac{9}{18}+\frac{5}{9}=\frac{13}{36}$$

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

$$\frac{1}{2}+\frac{5}{9}=\frac{13}{36}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{5}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{10}{18}=\frac{13}{36}$$

Since \frac{9}{18} and \frac{10}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+10}{18}=\frac{13}{36}$$

Add 9 and 10 to get 19.

$$\frac{19}{18}=\frac{13}{36}$$

Least common multiple of 18 and 36 is 36. Convert \frac{19}{18} and \frac{13}{36} to fractions with denominator 36.

$$\frac{38}{36}=\frac{13}{36}$$

Compare \frac{38}{36} and \frac{13}{36}.

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