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

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

Evaluate

$$\frac{52}{15}\approx 3.466666667$$

Solution Steps

Since \frac{2}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}+\frac{\frac{1}{5}\times \frac{2-1}{3}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Subtract 1 from 2 to get 1.

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

Multiply \frac{1}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{5\times 3}.

$$\frac{4}{3}+\frac{\frac{1}{15}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Least common multiple of 15 and 5 is 15. Convert \frac{1}{15} and \frac{4}{5} to fractions with denominator 15.

$$\frac{4}{3}+\frac{\frac{1}{15}+\frac{12}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Since \frac{1}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{4}{3}+\frac{\frac{1+12}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Add 1 and 12 to get 13.

$$\frac{4}{3}+\frac{\frac{13}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Divide \frac{13}{15} by \frac{3}{7} by multiplying \frac{13}{15} by the reciprocal of \frac{3}{7}.

$$\frac{4}{3}+\frac{13}{15}\times \frac{7}{3}+\frac{1}{9}$$

Multiply \frac{13}{15} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{3}+\frac{13\times 7}{15\times 3}+\frac{1}{9}$$

Do the multiplications in the fraction \frac{13\times 7}{15\times 3}.

$$\frac{4}{3}+\frac{91}{45}+\frac{1}{9}$$

Least common multiple of 3 and 45 is 45. Convert \frac{4}{3} and \frac{91}{45} to fractions with denominator 45.

$$\frac{60}{45}+\frac{91}{45}+\frac{1}{9}$$

Since \frac{60}{45} and \frac{91}{45} have the same denominator, add them by adding their numerators.

$$\frac{60+91}{45}+\frac{1}{9}$$

Add 60 and 91 to get 151.

$$\frac{151}{45}+\frac{1}{9}$$

Least common multiple of 45 and 9 is 45. Convert \frac{151}{45} and \frac{1}{9} to fractions with denominator 45.

$$\frac{151}{45}+\frac{5}{45}$$

Since \frac{151}{45} and \frac{5}{45} have the same denominator, add them by adding their numerators.

$$\frac{151+5}{45}$$

Add 151 and 5 to get 156.

$$\frac{156}{45}$$

Reduce the fraction \frac{156}{45} to lowest terms by extracting and canceling out 3.

$$\frac{52}{15}$$

Factor

$$\frac{2 ^ {2} \cdot 13}{3 \cdot 5} = 3\frac{7}{15} = 3.466666666666667$$