Solve (-2.39)+(-1.57)+(+35/6)+(-51/7)+(+21/6)+(-7.61)+(-326/7)+(+1.57)

$$(-2.39)+(-1.57)+(+ 3 \frac { 5 } { 6 } )+(- 5 \frac { 1 } { 7 } )+(+ 2 \frac { 1 } { 6 } )+(-7.61)+(- 32 \frac { 6 } { 7 } )+(+1.57)$$

Evaluate

$$-42$$

Solution Steps

Subtract 1.57 from -2.39 to get -3.96.

$$-3.96+\frac{3\times 6+5}{6}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Multiply 3 and 6 to get 18.

$$-3.96+\frac{18+5}{6}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Add 18 and 5 to get 23.

$$-3.96+\frac{23}{6}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Convert decimal number -3.96 to fraction -\frac{396}{100}. Reduce the fraction -\frac{396}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{99}{25}+\frac{23}{6}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Least common multiple of 25 and 6 is 150. Convert -\frac{99}{25} and \frac{23}{6} to fractions with denominator 150.

$$-\frac{594}{150}+\frac{575}{150}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Since -\frac{594}{150} and \frac{575}{150} have the same denominator, add them by adding their numerators.

$$\frac{-594+575}{150}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Add -594 and 575 to get -19.

$$-\frac{19}{150}-\frac{5\times 7+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Multiply 5 and 7 to get 35.

$$-\frac{19}{150}-\frac{35+1}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Add 35 and 1 to get 36.

$$-\frac{19}{150}-\frac{36}{7}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Least common multiple of 150 and 7 is 1050. Convert -\frac{19}{150} and \frac{36}{7} to fractions with denominator 1050.

$$-\frac{133}{1050}-\frac{5400}{1050}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Since -\frac{133}{1050} and \frac{5400}{1050} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-133-5400}{1050}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Subtract 5400 from -133 to get -5533.

$$-\frac{5533}{1050}+\frac{2\times 6+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Multiply 2 and 6 to get 12.

$$-\frac{5533}{1050}+\frac{12+1}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Add 12 and 1 to get 13.

$$-\frac{5533}{1050}+\frac{13}{6}-7.61-\frac{32\times 7+6}{7}+1.57$$

Least common multiple of 1050 and 6 is 1050. Convert -\frac{5533}{1050} and \frac{13}{6} to fractions with denominator 1050.

$$-\frac{5533}{1050}+\frac{2275}{1050}-7.61-\frac{32\times 7+6}{7}+1.57$$

Since -\frac{5533}{1050} and \frac{2275}{1050} have the same denominator, add them by adding their numerators.

$$\frac{-5533+2275}{1050}-7.61-\frac{32\times 7+6}{7}+1.57$$

Add -5533 and 2275 to get -3258.

$$\frac{-3258}{1050}-7.61-\frac{32\times 7+6}{7}+1.57$$

Reduce the fraction \frac{-3258}{1050} to lowest terms by extracting and canceling out 6.

$$-\frac{543}{175}-7.61-\frac{32\times 7+6}{7}+1.57$$

Convert decimal number 7.61 to fraction \frac{761}{100}.

$$-\frac{543}{175}-\frac{761}{100}-\frac{32\times 7+6}{7}+1.57$$

Least common multiple of 175 and 100 is 700. Convert -\frac{543}{175} and \frac{761}{100} to fractions with denominator 700.

$$-\frac{2172}{700}-\frac{5327}{700}-\frac{32\times 7+6}{7}+1.57$$

Since -\frac{2172}{700} and \frac{5327}{700} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2172-5327}{700}-\frac{32\times 7+6}{7}+1.57$$

Subtract 5327 from -2172 to get -7499.

$$-\frac{7499}{700}-\frac{32\times 7+6}{7}+1.57$$

Multiply 32 and 7 to get 224.

$$-\frac{7499}{700}-\frac{224+6}{7}+1.57$$

Add 224 and 6 to get 230.

$$-\frac{7499}{700}-\frac{230}{7}+1.57$$

Least common multiple of 700 and 7 is 700. Convert -\frac{7499}{700} and \frac{230}{7} to fractions with denominator 700.

$$-\frac{7499}{700}-\frac{23000}{700}+1.57$$

Since -\frac{7499}{700} and \frac{23000}{700} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7499-23000}{700}+1.57$$

Subtract 23000 from -7499 to get -30499.

$$\frac{-30499}{700}+1.57$$

Reduce the fraction \frac{-30499}{700} to lowest terms by extracting and canceling out 7.

$$-\frac{4357}{100}+1.57$$

Convert decimal number 1.57 to fraction \frac{157}{100}.

$$-\frac{4357}{100}+\frac{157}{100}$$

Since -\frac{4357}{100} and \frac{157}{100} have the same denominator, add them by adding their numerators.

$$\frac{-4357+157}{100}$$

Add -4357 and 157 to get -4200.

$$\frac{-4200}{100}$$

Divide -4200 by 100 to get -42.

$$-42$$

Factor

$$-42$$