Solve 17*(-35/18)-35*11/36+(324/11-2.15)-[(-3.25)+(-207/11)]

$$17 \times ( - \frac { 35 } { 18 } ) - 35 \times \frac { 11 } { 36 } + ( 32 \frac { 4 } { 11 } - 2.15 ) - [ ( - 3.25 ) + ( - 20 \frac { 7 } { 11 } ) ]$$

Evaluate

$$10.35$$

Solution Steps

Express 17\left(-\frac{35}{18}\right) as a single fraction.

$$\frac{17\left(-35\right)}{18}-35\times \frac{11}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Multiply 17 and -35 to get -595.

$$\frac{-595}{18}-35\times \frac{11}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Fraction \frac{-595}{18} can be rewritten as -\frac{595}{18} by extracting the negative sign.

$$-\frac{595}{18}-35\times \frac{11}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Express 35\times \frac{11}{36} as a single fraction.

$$-\frac{595}{18}-\frac{35\times 11}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Multiply 35 and 11 to get 385.

$$-\frac{595}{18}-\frac{385}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Least common multiple of 18 and 36 is 36. Convert -\frac{595}{18} and \frac{385}{36} to fractions with denominator 36.

$$-\frac{1190}{36}-\frac{385}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Since -\frac{1190}{36} and \frac{385}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1190-385}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Subtract 385 from -1190 to get -1575.

$$\frac{-1575}{36}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Reduce the fraction \frac{-1575}{36} to lowest terms by extracting and canceling out 9.

$$-\frac{175}{4}+\frac{32\times 11+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Multiply 32 and 11 to get 352.

$$-\frac{175}{4}+\frac{352+4}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Add 352 and 4 to get 356.

$$-\frac{175}{4}+\frac{356}{11}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Least common multiple of 4 and 11 is 44. Convert -\frac{175}{4} and \frac{356}{11} to fractions with denominator 44.

$$-\frac{1925}{44}+\frac{1424}{44}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Since -\frac{1925}{44} and \frac{1424}{44} have the same denominator, add them by adding their numerators.

$$\frac{-1925+1424}{44}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Add -1925 and 1424 to get -501.

$$-\frac{501}{44}-2.15-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Convert decimal number 2.15 to fraction \frac{215}{100}. Reduce the fraction \frac{215}{100} to lowest terms by extracting and canceling out 5.

$$-\frac{501}{44}-\frac{43}{20}-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Least common multiple of 44 and 20 is 220. Convert -\frac{501}{44} and \frac{43}{20} to fractions with denominator 220.

$$-\frac{2505}{220}-\frac{473}{220}-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Since -\frac{2505}{220} and \frac{473}{220} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2505-473}{220}-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Subtract 473 from -2505 to get -2978.

$$\frac{-2978}{220}-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Reduce the fraction \frac{-2978}{220} to lowest terms by extracting and canceling out 2.

$$-\frac{1489}{110}-\left(-3.25-\frac{20\times 11+7}{11}\right)$$

Multiply 20 and 11 to get 220.

$$-\frac{1489}{110}-\left(-3.25-\frac{220+7}{11}\right)$$

Add 220 and 7 to get 227.

$$-\frac{1489}{110}-\left(-3.25-\frac{227}{11}\right)$$

Convert decimal number -3.25 to fraction -\frac{325}{100}. Reduce the fraction -\frac{325}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{1489}{110}-\left(-\frac{13}{4}-\frac{227}{11}\right)$$

Least common multiple of 4 and 11 is 44. Convert -\frac{13}{4} and \frac{227}{11} to fractions with denominator 44.

$$-\frac{1489}{110}-\left(-\frac{143}{44}-\frac{908}{44}\right)$$

Since -\frac{143}{44} and \frac{908}{44} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1489}{110}-\frac{-143-908}{44}$$

Subtract 908 from -143 to get -1051.

$$-\frac{1489}{110}-\left(-\frac{1051}{44}\right)$$

The opposite of -\frac{1051}{44} is \frac{1051}{44}.

$$-\frac{1489}{110}+\frac{1051}{44}$$

Least common multiple of 110 and 44 is 220. Convert -\frac{1489}{110} and \frac{1051}{44} to fractions with denominator 220.

$$-\frac{2978}{220}+\frac{5255}{220}$$

Since -\frac{2978}{220} and \frac{5255}{220} have the same denominator, add them by adding their numerators.

$$\frac{-2978+5255}{220}$$

Add -2978 and 5255 to get 2277.

$$\frac{2277}{220}$$

Reduce the fraction \frac{2277}{220} to lowest terms by extracting and canceling out 11.

$$\frac{207}{20}$$

Factor

$$\frac{23 \cdot 3 ^ {2}}{5 \cdot 2 ^ {2}} = 10\frac{7}{20} = 10.35$$