Solve 2-4,59:1,5*(53/5-65/18-14/15)

$$2 - 4,59 : 1,5 \cdot ( 5 \frac { 3 } { 5 } - 6 \frac { 5 } { 18 } - 1 \frac { 4 } { 15 } )$$

Evaluate

$$7,95$$

Solution Steps

Expand \frac{4,59}{1,5} by multiplying both numerator and the denominator by 100.

$$2-\frac{459}{150}\left(\frac{5\times 5+3}{5}-\frac{6\times 18+5}{18}-\frac{1\times 15+4}{15}\right)$$

Reduce the fraction \frac{459}{150} to lowest terms by extracting and canceling out 3.

$$2-\frac{153}{50}\left(\frac{5\times 5+3}{5}-\frac{6\times 18+5}{18}-\frac{1\times 15+4}{15}\right)$$

Multiply 5 and 5 to get 25.

$$2-\frac{153}{50}\left(\frac{25+3}{5}-\frac{6\times 18+5}{18}-\frac{1\times 15+4}{15}\right)$$

Add 25 and 3 to get 28.

$$2-\frac{153}{50}\left(\frac{28}{5}-\frac{6\times 18+5}{18}-\frac{1\times 15+4}{15}\right)$$

Multiply 6 and 18 to get 108.

$$2-\frac{153}{50}\left(\frac{28}{5}-\frac{108+5}{18}-\frac{1\times 15+4}{15}\right)$$

Add 108 and 5 to get 113.

$$2-\frac{153}{50}\left(\frac{28}{5}-\frac{113}{18}-\frac{1\times 15+4}{15}\right)$$

Least common multiple of 5 and 18 is 90. Convert \frac{28}{5} and \frac{113}{18} to fractions with denominator 90.

$$2-\frac{153}{50}\left(\frac{504}{90}-\frac{565}{90}-\frac{1\times 15+4}{15}\right)$$

Since \frac{504}{90} and \frac{565}{90} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{153}{50}\left(\frac{504-565}{90}-\frac{1\times 15+4}{15}\right)$$

Subtract 565 from 504 to get -61.

$$2-\frac{153}{50}\left(-\frac{61}{90}-\frac{1\times 15+4}{15}\right)$$

Multiply 1 and 15 to get 15.

$$2-\frac{153}{50}\left(-\frac{61}{90}-\frac{15+4}{15}\right)$$

Add 15 and 4 to get 19.

$$2-\frac{153}{50}\left(-\frac{61}{90}-\frac{19}{15}\right)$$

Least common multiple of 90 and 15 is 90. Convert -\frac{61}{90} and \frac{19}{15} to fractions with denominator 90.

$$2-\frac{153}{50}\left(-\frac{61}{90}-\frac{114}{90}\right)$$

Since -\frac{61}{90} and \frac{114}{90} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{153}{50}\times \frac{-61-114}{90}$$

Subtract 114 from -61 to get -175.

$$2-\frac{153}{50}\times \frac{-175}{90}$$

Reduce the fraction \frac{-175}{90} to lowest terms by extracting and canceling out 5.

$$2-\frac{153}{50}\left(-\frac{35}{18}\right)$$

Multiply \frac{153}{50} times -\frac{35}{18} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{153\left(-35\right)}{50\times 18}$$

Do the multiplications in the fraction \frac{153\left(-35\right)}{50\times 18}.

$$2-\frac{-5355}{900}$$

Reduce the fraction \frac{-5355}{900} to lowest terms by extracting and canceling out 45.

$$2-\left(-\frac{119}{20}\right)$$

The opposite of -\frac{119}{20} is \frac{119}{20}.

$$2+\frac{119}{20}$$

Convert 2 to fraction \frac{40}{20}.

$$\frac{40}{20}+\frac{119}{20}$$

Since \frac{40}{20} and \frac{119}{20} have the same denominator, add them by adding their numerators.

$$\frac{40+119}{20}$$

Add 40 and 119 to get 159.

$$\frac{159}{20}$$

Factor

$$\frac{3 \cdot 53}{5 \cdot 2 ^ {2}} = 7\frac{19}{20} = 7.95$$