Solve 23/5--4-2/3-2.75+-7-2/3-21/3--3frac{1}{2}

$$\frac{ 23 }{ 5 } --4- \frac{ 2 }{ 3 } -2.75+-7- \frac{ 2 }{ 3 } -2 \frac{ 1 }{ 3 } --3 \frac{ 1 }{ 2 }$$

Evaluate

$$-\frac{79}{60}\approx -1.316666667$$

Solution Steps

The opposite of -4 is 4.

$$\frac{23}{5}+4-\frac{2}{3}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{23}{5}+\frac{20}{5}-\frac{2}{3}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Since \frac{23}{5} and \frac{20}{5} have the same denominator, add them by adding their numerators.

$$\frac{23+20}{5}-\frac{2}{3}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Add 23 and 20 to get 43.

$$\frac{43}{5}-\frac{2}{3}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Least common multiple of 5 and 3 is 15. Convert \frac{43}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{129}{15}-\frac{10}{15}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Since \frac{129}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{129-10}{15}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Subtract 10 from 129 to get 119.

$$\frac{119}{15}-2.75-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Convert decimal number 2.75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\frac{119}{15}-\frac{11}{4}-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Least common multiple of 15 and 4 is 60. Convert \frac{119}{15} and \frac{11}{4} to fractions with denominator 60.

$$\frac{476}{60}-\frac{165}{60}-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Since \frac{476}{60} and \frac{165}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{476-165}{60}-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Subtract 165 from 476 to get 311.

$$\frac{311}{60}-7-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Convert 7 to fraction \frac{420}{60}.

$$\frac{311}{60}-\frac{420}{60}-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Since \frac{311}{60} and \frac{420}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{311-420}{60}-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Subtract 420 from 311 to get -109.

$$-\frac{109}{60}-\frac{2}{3}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Least common multiple of 60 and 3 is 60. Convert -\frac{109}{60} and \frac{2}{3} to fractions with denominator 60.

$$-\frac{109}{60}-\frac{40}{60}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Since -\frac{109}{60} and \frac{40}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-109-40}{60}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Subtract 40 from -109 to get -149.

$$-\frac{149}{60}-\frac{2\times 3+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Multiply 2 and 3 to get 6.

$$-\frac{149}{60}-\frac{6+1}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Add 6 and 1 to get 7.

$$-\frac{149}{60}-\frac{7}{3}-\left(-\frac{3\times 2+1}{2}\right)$$

Least common multiple of 60 and 3 is 60. Convert -\frac{149}{60} and \frac{7}{3} to fractions with denominator 60.

$$-\frac{149}{60}-\frac{140}{60}-\left(-\frac{3\times 2+1}{2}\right)$$

Since -\frac{149}{60} and \frac{140}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-149-140}{60}-\left(-\frac{3\times 2+1}{2}\right)$$

Subtract 140 from -149 to get -289.

$$-\frac{289}{60}-\left(-\frac{3\times 2+1}{2}\right)$$

Multiply 3 and 2 to get 6.

$$-\frac{289}{60}-\left(-\frac{6+1}{2}\right)$$

Add 6 and 1 to get 7.

$$-\frac{289}{60}-\left(-\frac{7}{2}\right)$$

The opposite of -\frac{7}{2} is \frac{7}{2}.

$$-\frac{289}{60}+\frac{7}{2}$$

Least common multiple of 60 and 2 is 60. Convert -\frac{289}{60} and \frac{7}{2} to fractions with denominator 60.

$$-\frac{289}{60}+\frac{210}{60}$$

Since -\frac{289}{60} and \frac{210}{60} have the same denominator, add them by adding their numerators.

$$\frac{-289+210}{60}$$

Add -289 and 210 to get -79.

$$-\frac{79}{60}$$

Factor

$$-\frac{79}{60} = -1\frac{19}{60} = -1.3166666666666667$$