Solve [4/5-9/5(3/7+4/3)]

$$[ \frac { 4 } { 5 } - \frac { 9 } { 5 } ( \frac { 3 } { 7 } + \frac { 4 } { 3 } ) ]$$

Evaluate

$$-\frac{83}{35}\approx -2.371428571$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{3}{7} and \frac{4}{3} to fractions with denominator 21.

$$\frac{4}{5}-\frac{9}{5}\left(\frac{9}{21}+\frac{28}{21}\right)$$

Since \frac{9}{21} and \frac{28}{21} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}-\frac{9}{5}\times \frac{9+28}{21}$$

Add 9 and 28 to get 37.

$$\frac{4}{5}-\frac{9}{5}\times \frac{37}{21}$$

Multiply \frac{9}{5} times \frac{37}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}-\frac{9\times 37}{5\times 21}$$

Do the multiplications in the fraction \frac{9\times 37}{5\times 21}.

$$\frac{4}{5}-\frac{333}{105}$$

Reduce the fraction \frac{333}{105} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}-\frac{111}{35}$$

Least common multiple of 5 and 35 is 35. Convert \frac{4}{5} and \frac{111}{35} to fractions with denominator 35.

$$\frac{28}{35}-\frac{111}{35}$$

Since \frac{28}{35} and \frac{111}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-111}{35}$$

Subtract 111 from 28 to get -83.

$$-\frac{83}{35}$$

Factor

$$-\frac{83}{35} = -2\frac{13}{35} = -2.3714285714285714$$