Solve 4/3+7/5*(1/2+4/9)-frac{1}{5}

$$\frac { 4 } { 3 } + \frac { 7 } { 5 } \cdot ( \frac { 1 } { 2 } + \frac { 4 } { 9 } ) - \frac { 1 } { 5 }$$

Evaluate

$$\frac{221}{90}\approx 2.455555556$$

Solution Steps

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{4}{3}+\frac{7}{5}\left(\frac{9}{18}+\frac{8}{18}\right)-\frac{1}{5}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{7}{5}\times \frac{9+8}{18}-\frac{1}{5}$$

Add 9 and 8 to get 17.

$$\frac{4}{3}+\frac{7}{5}\times \frac{17}{18}-\frac{1}{5}$$

Multiply \frac{7}{5} times \frac{17}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{7\times 17}{5\times 18}-\frac{1}{5}$$

Do the multiplications in the fraction \frac{7\times 17}{5\times 18}.

$$\frac{4}{3}+\frac{119}{90}-\frac{1}{5}$$

Least common multiple of 3 and 90 is 90. Convert \frac{4}{3} and \frac{119}{90} to fractions with denominator 90.

$$\frac{120}{90}+\frac{119}{90}-\frac{1}{5}$$

Since \frac{120}{90} and \frac{119}{90} have the same denominator, add them by adding their numerators.

$$\frac{120+119}{90}-\frac{1}{5}$$

Add 120 and 119 to get 239.

$$\frac{239}{90}-\frac{1}{5}$$

Least common multiple of 90 and 5 is 90. Convert \frac{239}{90} and \frac{1}{5} to fractions with denominator 90.

$$\frac{239}{90}-\frac{18}{90}$$

Since \frac{239}{90} and \frac{18}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{239-18}{90}$$

Subtract 18 from 239 to get 221.

$$\frac{221}{90}$$

Factor

$$\frac{13 \cdot 17}{2 \cdot 3 ^ {2} \cdot 5} = 2\frac{41}{90} = 2.4555555555555557$$