Solve 2/3+1/5-2/3div4/9=frac{2}{3}+frac{1}{5}-frac{3}{2}

$$\frac { 2 } { 3 } + \frac { 1 } { 5 } - \frac { 2 } { 3 } \div \frac { 4 } { 9 } = \frac { 2 } { 3 } + \frac { 1 } { 5 } - \frac { 3 } { 2 }$$

Verify

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{3}{15}-\frac{\frac{2}{3}}{\frac{4}{9}}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{15}-\frac{\frac{2}{3}}{\frac{4}{9}}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Add 10 and 3 to get 13.

$$\frac{13}{15}-\frac{\frac{2}{3}}{\frac{4}{9}}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Divide \frac{2}{3} by \frac{4}{9} by multiplying \frac{2}{3} by the reciprocal of \frac{4}{9}.

$$\frac{13}{15}-\frac{2}{3}\times \frac{9}{4}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Multiply \frac{2}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{15}-\frac{2\times 9}{3\times 4}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Do the multiplications in the fraction \frac{2\times 9}{3\times 4}.

$$\frac{13}{15}-\frac{18}{12}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{13}{15}-\frac{3}{2}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Least common multiple of 15 and 2 is 30. Convert \frac{13}{15} and \frac{3}{2} to fractions with denominator 30.

$$\frac{26}{30}-\frac{45}{30}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Since \frac{26}{30} and \frac{45}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{26-45}{30}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Subtract 45 from 26 to get -19.

$$-\frac{19}{30}=\frac{2}{3}+\frac{1}{5}-\frac{3}{2}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$-\frac{19}{30}=\frac{10}{15}+\frac{3}{15}-\frac{3}{2}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$-\frac{19}{30}=\frac{10+3}{15}-\frac{3}{2}$$

Add 10 and 3 to get 13.

$$-\frac{19}{30}=\frac{13}{15}-\frac{3}{2}$$

Least common multiple of 15 and 2 is 30. Convert \frac{13}{15} and \frac{3}{2} to fractions with denominator 30.

$$-\frac{19}{30}=\frac{26}{30}-\frac{45}{30}$$

Since \frac{26}{30} and \frac{45}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{30}=\frac{26-45}{30}$$

Subtract 45 from 26 to get -19.

$$-\frac{19}{30}=-\frac{19}{30}$$

Compare -\frac{19}{30} and -\frac{19}{30}.

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