Solve -3,2*211/18+3,2*313/18-3,2*7/18=

$$- 3,2 \cdot 2 \frac { 11 } { 18 } + 3,2 \cdot 3 \frac { 13 } { 18 } - 3,2 \cdot \frac { 7 } { 18 } =$$

Evaluate

$$\frac{104}{45}\approx 2,311111111$$

Solution Steps

Multiply 2 and 18 to get 36.

$$-3,2\times \frac{36+11}{18}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Add 36 and 11 to get 47.

$$-3,2\times \frac{47}{18}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Convert decimal number -3,2 to fraction -\frac{32}{10}. Reduce the fraction -\frac{32}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{16}{5}\times \frac{47}{18}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Multiply -\frac{16}{5} times \frac{47}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16\times 47}{5\times 18}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Do the multiplications in the fraction \frac{-16\times 47}{5\times 18}.

$$\frac{-752}{90}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Reduce the fraction \frac{-752}{90} to lowest terms by extracting and canceling out 2.

$$-\frac{376}{45}+3,2\times \frac{3\times 18+13}{18}-3,2\times \frac{7}{18}$$

Multiply 3 and 18 to get 54.

$$-\frac{376}{45}+3,2\times \frac{54+13}{18}-3,2\times \frac{7}{18}$$

Add 54 and 13 to get 67.

$$-\frac{376}{45}+3,2\times \frac{67}{18}-3,2\times \frac{7}{18}$$

Convert decimal number 3,2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{376}{45}+\frac{16}{5}\times \frac{67}{18}-3,2\times \frac{7}{18}$$

Multiply \frac{16}{5} times \frac{67}{18} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{376}{45}+\frac{16\times 67}{5\times 18}-3,2\times \frac{7}{18}$$

Do the multiplications in the fraction \frac{16\times 67}{5\times 18}.

$$-\frac{376}{45}+\frac{1072}{90}-3,2\times \frac{7}{18}$$

Reduce the fraction \frac{1072}{90} to lowest terms by extracting and canceling out 2.

$$-\frac{376}{45}+\frac{536}{45}-3,2\times \frac{7}{18}$$

Since -\frac{376}{45} and \frac{536}{45} have the same denominator, add them by adding their numerators.

$$\frac{-376+536}{45}-3,2\times \frac{7}{18}$$

Add -376 and 536 to get 160.

$$\frac{160}{45}-3,2\times \frac{7}{18}$$

Reduce the fraction \frac{160}{45} to lowest terms by extracting and canceling out 5.

$$\frac{32}{9}-3,2\times \frac{7}{18}$$

Convert decimal number 3,2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{32}{9}-\frac{16}{5}\times \frac{7}{18}$$

Multiply \frac{16}{5} times \frac{7}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32}{9}-\frac{16\times 7}{5\times 18}$$

Do the multiplications in the fraction \frac{16\times 7}{5\times 18}.

$$\frac{32}{9}-\frac{112}{90}$$

Reduce the fraction \frac{112}{90} to lowest terms by extracting and canceling out 2.

$$\frac{32}{9}-\frac{56}{45}$$

Least common multiple of 9 and 45 is 45. Convert \frac{32}{9} and \frac{56}{45} to fractions with denominator 45.

$$\frac{160}{45}-\frac{56}{45}$$

Since \frac{160}{45} and \frac{56}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{160-56}{45}$$

Subtract 56 from 160 to get 104.

$$\frac{104}{45}$$

Factor

$$\frac{13 \cdot 2 ^ {3}}{5 \cdot 3 ^ {2}} = 2\frac{14}{45} = 2.311111111111111$$