Solve 4/3+lfloor1/5(2/3-1/3)+frac{4}{5}rfloordivfrac{3}{7}+frac{1}{9}

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

Evaluate

$$\frac{13}{9}\approx 1.444444444$$

Solution Steps

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

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

Subtract 1 from 2 to get 1.

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

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

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

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

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

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

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

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

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

Add 1 and 12 to get 13.

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

Dividing 13 by 15 gives 0 and remainder 13. Rewrite \frac{13}{15} as 0+\frac{13}{15}.

$$\frac{4}{3}+\frac{\lfloor 0+\frac{13}{15}\rfloor }{\frac{3}{7}}+\frac{1}{9}$$

The floor of a real number a is the largest integer number less than or equal to a. The floor of 0+\frac{13}{15} is 0.

$$\frac{4}{3}+\frac{0}{\frac{3}{7}}+\frac{1}{9}$$

Zero divided by any non-zero number gives zero.

$$\frac{4}{3}+0+\frac{1}{9}$$

Add \frac{4}{3} and 0 to get \frac{4}{3}.

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

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{1}{9} to fractions with denominator 9.

$$\frac{12}{9}+\frac{1}{9}$$

Since \frac{12}{9} and \frac{1}{9} have the same denominator, add them by adding their numerators.

$$\frac{12+1}{9}$$

Add 12 and 1 to get 13.

$$\frac{13}{9}$$

Factor

$$\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444$$