Solve 1-(5/94/83/7+5/9frac{4}{8}frac{4}{7}+frac{5}{9}frac{4}{8}frac{4}{7})

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

Evaluate

$$\frac{71}{126}\approx 0.563492063$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$1-\left(\frac{5}{9}\times \frac{1}{2}\times \frac{3}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Multiply \frac{5}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$1-\left(\frac{5\times 1}{9\times 2}\times \frac{3}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Do the multiplications in the fraction \frac{5\times 1}{9\times 2}.

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

Multiply \frac{5}{18} times \frac{3}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 3}{18\times 7}.

$$1-\left(\frac{15}{126}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Reduce the fraction \frac{15}{126} to lowest terms by extracting and canceling out 3.

$$1-\left(\frac{5}{42}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$1-\left(\frac{5}{42}+\frac{5}{9}\times \frac{1}{2}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Multiply \frac{5}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$1-\left(\frac{5}{42}+\frac{5\times 1}{9\times 2}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Do the multiplications in the fraction \frac{5\times 1}{9\times 2}.

$$1-\left(\frac{5}{42}+\frac{5}{18}\times \frac{4}{7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Multiply \frac{5}{18} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$1-\left(\frac{5}{42}+\frac{5\times 4}{18\times 7}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Do the multiplications in the fraction \frac{5\times 4}{18\times 7}.

$$1-\left(\frac{5}{42}+\frac{20}{126}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Reduce the fraction \frac{20}{126} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{5}{42}+\frac{10}{63}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Least common multiple of 42 and 63 is 126. Convert \frac{5}{42} and \frac{10}{63} to fractions with denominator 126.

$$1-\left(\frac{15}{126}+\frac{20}{126}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Since \frac{15}{126} and \frac{20}{126} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{15+20}{126}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Add 15 and 20 to get 35.

$$1-\left(\frac{35}{126}+\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}\right)$$

Reduce the fraction \frac{35}{126} to lowest terms by extracting and canceling out 7.

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

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$1-\left(\frac{5}{18}+\frac{5}{9}\times \frac{1}{2}\times \frac{4}{7}\right)$$

Multiply \frac{5}{9} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$1-\left(\frac{5}{18}+\frac{5\times 1}{9\times 2}\times \frac{4}{7}\right)$$

Do the multiplications in the fraction \frac{5\times 1}{9\times 2}.

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

Multiply \frac{5}{18} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 4}{18\times 7}.

$$1-\left(\frac{5}{18}+\frac{20}{126}\right)$$

Reduce the fraction \frac{20}{126} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{5}{18}+\frac{10}{63}\right)$$

Least common multiple of 18 and 63 is 126. Convert \frac{5}{18} and \frac{10}{63} to fractions with denominator 126.

$$1-\left(\frac{35}{126}+\frac{20}{126}\right)$$

Since \frac{35}{126} and \frac{20}{126} have the same denominator, add them by adding their numerators.

$$1-\frac{35+20}{126}$$

Add 35 and 20 to get 55.

$$1-\frac{55}{126}$$

Convert 1 to fraction \frac{126}{126}.

$$\frac{126}{126}-\frac{55}{126}$$

Since \frac{126}{126} and \frac{55}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{126-55}{126}$$

Subtract 55 from 126 to get 71.

$$\frac{71}{126}$$

Factor

$$\frac{71}{2 \cdot 3 ^ {2} \cdot 7} = 0.5634920634920635$$