Solve 8/9-[2/9+1/5-(4/15*frac{45}{16}-frac{1}{4})*frac{3}{5}+frac{2}{3}]=

$$\frac { 8 } { 9 } - [ \frac { 2 } { 9 } + \frac { 1 } { 5 } - ( \frac { 4 } { 15 } \cdot \frac { 45 } { 16 } - \frac { 1 } { 4 } ) \cdot \frac { 3 } { 5 } + \frac { 2 } { 3 } ] =$$

Evaluate

$$\frac{1}{10}=0.1$$

Solution Steps

Least common multiple of 9 and 5 is 45. Convert \frac{2}{9} and \frac{1}{5} to fractions with denominator 45.

$$\frac{8}{9}-\left(\frac{10}{45}+\frac{9}{45}-\left(\frac{4}{15}\times \frac{45}{16}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Since \frac{10}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{8}{9}-\left(\frac{10+9}{45}-\left(\frac{4}{15}\times \frac{45}{16}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Add 10 and 9 to get 19.

$$\frac{8}{9}-\left(\frac{19}{45}-\left(\frac{4}{15}\times \frac{45}{16}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Multiply \frac{4}{15} times \frac{45}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{9}-\left(\frac{19}{45}-\left(\frac{4\times 45}{15\times 16}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{4\times 45}{15\times 16}.

$$\frac{8}{9}-\left(\frac{19}{45}-\left(\frac{180}{240}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Reduce the fraction \frac{180}{240} to lowest terms by extracting and canceling out 60.

$$\frac{8}{9}-\left(\frac{19}{45}-\left(\frac{3}{4}-\frac{1}{4}\right)\times \frac{3}{5}+\frac{2}{3}\right)$$

Since \frac{3}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{9}-\left(\frac{19}{45}-\frac{3-1}{4}\times \frac{3}{5}+\frac{2}{3}\right)$$

Subtract 1 from 3 to get 2.

$$\frac{8}{9}-\left(\frac{19}{45}-\frac{2}{4}\times \frac{3}{5}+\frac{2}{3}\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{8}{9}-\left(\frac{19}{45}-\frac{1}{2}\times \frac{3}{5}+\frac{2}{3}\right)$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{9}-\left(\frac{19}{45}-\frac{1\times 3}{2\times 5}+\frac{2}{3}\right)$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$\frac{8}{9}-\left(\frac{19}{45}-\frac{3}{10}+\frac{2}{3}\right)$$

Least common multiple of 45 and 10 is 90. Convert \frac{19}{45} and \frac{3}{10} to fractions with denominator 90.

$$\frac{8}{9}-\left(\frac{38}{90}-\frac{27}{90}+\frac{2}{3}\right)$$

Since \frac{38}{90} and \frac{27}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{9}-\left(\frac{38-27}{90}+\frac{2}{3}\right)$$

Subtract 27 from 38 to get 11.

$$\frac{8}{9}-\left(\frac{11}{90}+\frac{2}{3}\right)$$

Least common multiple of 90 and 3 is 90. Convert \frac{11}{90} and \frac{2}{3} to fractions with denominator 90.

$$\frac{8}{9}-\left(\frac{11}{90}+\frac{60}{90}\right)$$

Since \frac{11}{90} and \frac{60}{90} have the same denominator, add them by adding their numerators.

$$\frac{8}{9}-\frac{11+60}{90}$$

Add 11 and 60 to get 71.

$$\frac{8}{9}-\frac{71}{90}$$

Least common multiple of 9 and 90 is 90. Convert \frac{8}{9} and \frac{71}{90} to fractions with denominator 90.

$$\frac{80}{90}-\frac{71}{90}$$

Since \frac{80}{90} and \frac{71}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{80-71}{90}$$

Subtract 71 from 80 to get 9.

$$\frac{9}{90}$$

Reduce the fraction \frac{9}{90} to lowest terms by extracting and canceling out 9.

$$\frac{1}{10}$$

Factor

$$\frac{1}{2 \cdot 5} = 0.1$$