Solve 3/5:2/3-4/5*4/3+frac{1}{3}-frac{3}{4}:frac{3}{7}=-frac{19}{12}

$$\frac { 3 } { 5 } : \frac { 2 } { 3 } - \frac { 4 } { 5 } \cdot \frac { 4 } { 3 } + \frac { 1 } { 3 } - \frac { 3 } { 4 } : \frac { 3 } { 7 } = - \frac { 19 } { 12 }$$

Verify

Solution Steps

Divide \frac{3}{5} by \frac{2}{3} by multiplying \frac{3}{5} by the reciprocal of \frac{2}{3}.

$$\frac{3}{5}\times \frac{3}{2}-\frac{4}{5}\times \frac{4}{3}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Multiply \frac{3}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{5\times 2}-\frac{4}{5}\times \frac{4}{3}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Do the multiplications in the fraction \frac{3\times 3}{5\times 2}.

$$\frac{9}{10}-\frac{4}{5}\times \frac{4}{3}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Multiply \frac{4}{5} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{10}-\frac{4\times 4}{5\times 3}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Do the multiplications in the fraction \frac{4\times 4}{5\times 3}.

$$\frac{9}{10}-\frac{16}{15}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Least common multiple of 10 and 15 is 30. Convert \frac{9}{10} and \frac{16}{15} to fractions with denominator 30.

$$\frac{27}{30}-\frac{32}{30}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Since \frac{27}{30} and \frac{32}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-32}{30}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Subtract 32 from 27 to get -5.

$$\frac{-5}{30}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Reduce the fraction \frac{-5}{30} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{6}+\frac{1}{3}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Least common multiple of 6 and 3 is 6. Convert -\frac{1}{6} and \frac{1}{3} to fractions with denominator 6.

$$-\frac{1}{6}+\frac{2}{6}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Since -\frac{1}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{-1+2}{6}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Add -1 and 2 to get 1.

$$\frac{1}{6}-\frac{\frac{3}{4}}{\frac{3}{7}}=-\frac{19}{12}$$

Divide \frac{3}{4} by \frac{3}{7} by multiplying \frac{3}{4} by the reciprocal of \frac{3}{7}.

$$\frac{1}{6}-\frac{3}{4}\times \frac{7}{3}=-\frac{19}{12}$$

Multiply \frac{3}{4} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}-\frac{3\times 7}{4\times 3}=-\frac{19}{12}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{6}-\frac{7}{4}=-\frac{19}{12}$$

Least common multiple of 6 and 4 is 12. Convert \frac{1}{6} and \frac{7}{4} to fractions with denominator 12.

$$\frac{2}{12}-\frac{21}{12}=-\frac{19}{12}$$

Since \frac{2}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-21}{12}=-\frac{19}{12}$$

Subtract 21 from 2 to get -19.

$$-\frac{19}{12}=-\frac{19}{12}$$

Compare -\frac{19}{12} and -\frac{19}{12}.

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