Solve (4/5+5/8-3/4)div21/50=frac{4}{9}

$$( \frac { 4 } { 5 } + \frac { 5 } { 8 } - \frac { 3 } { 4 } ) \div \frac { 21 } { 50 } = \frac { 4 } { 9 }$$

Verify

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{4}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{\frac{32}{40}+\frac{25}{40}-\frac{3}{4}}{\frac{21}{50}}=\frac{4}{9}$$

Since \frac{32}{40} and \frac{25}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{32+25}{40}-\frac{3}{4}}{\frac{21}{50}}=\frac{4}{9}$$

Add 32 and 25 to get 57.

$$\frac{\frac{57}{40}-\frac{3}{4}}{\frac{21}{50}}=\frac{4}{9}$$

Least common multiple of 40 and 4 is 40. Convert \frac{57}{40} and \frac{3}{4} to fractions with denominator 40.

$$\frac{\frac{57}{40}-\frac{30}{40}}{\frac{21}{50}}=\frac{4}{9}$$

Since \frac{57}{40} and \frac{30}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{57-30}{40}}{\frac{21}{50}}=\frac{4}{9}$$

Subtract 30 from 57 to get 27.

$$\frac{\frac{27}{40}}{\frac{21}{50}}=\frac{4}{9}$$

Divide \frac{27}{40} by \frac{21}{50} by multiplying \frac{27}{40} by the reciprocal of \frac{21}{50}.

$$\frac{27}{40}\times \frac{50}{21}=\frac{4}{9}$$

Multiply \frac{27}{40} times \frac{50}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 50}{40\times 21}=\frac{4}{9}$$

Do the multiplications in the fraction \frac{27\times 50}{40\times 21}.

$$\frac{1350}{840}=\frac{4}{9}$$

Reduce the fraction \frac{1350}{840} to lowest terms by extracting and canceling out 30.

$$\frac{45}{28}=\frac{4}{9}$$

Least common multiple of 28 and 9 is 252. Convert \frac{45}{28} and \frac{4}{9} to fractions with denominator 252.

$$\frac{405}{252}=\frac{112}{252}$$

Compare \frac{405}{252} and \frac{112}{252}.

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