Solve -13*2/3-0.34*2/7+1/3*1.33-5/7*0.34

$$- 13 \times \frac { 2 } { 3 } - 0.34 \times \frac { 2 } { 7 } + \frac { 1 } { 3 } \times 1.33 - \frac { 5 } { 7 } \times 0.34$$

Evaluate

$$-\frac{2569}{300}\approx -8.563333333$$

Solution Steps

Express -13\times \frac{2}{3} as a single fraction.

$$\frac{-13\times 2}{3}-0.34\times \frac{2}{7}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Multiply -13 and 2 to get -26.

$$\frac{-26}{3}-0.34\times \frac{2}{7}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Fraction \frac{-26}{3} can be rewritten as -\frac{26}{3} by extracting the negative sign.

$$-\frac{26}{3}-0.34\times \frac{2}{7}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Convert decimal number 0.34 to fraction \frac{34}{100}. Reduce the fraction \frac{34}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{26}{3}-\frac{17}{50}\times \frac{2}{7}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Multiply \frac{17}{50} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{26}{3}-\frac{17\times 2}{50\times 7}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Do the multiplications in the fraction \frac{17\times 2}{50\times 7}.

$$-\frac{26}{3}-\frac{34}{350}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Reduce the fraction \frac{34}{350} to lowest terms by extracting and canceling out 2.

$$-\frac{26}{3}-\frac{17}{175}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Least common multiple of 3 and 175 is 525. Convert -\frac{26}{3} and \frac{17}{175} to fractions with denominator 525.

$$-\frac{4550}{525}-\frac{51}{525}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Since -\frac{4550}{525} and \frac{51}{525} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4550-51}{525}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Subtract 51 from -4550 to get -4601.

$$-\frac{4601}{525}+\frac{1}{3}\times 1.33-\frac{5}{7}\times 0.34$$

Convert decimal number 1.33 to fraction \frac{133}{100}.

$$-\frac{4601}{525}+\frac{1}{3}\times \frac{133}{100}-\frac{5}{7}\times 0.34$$

Multiply \frac{1}{3} times \frac{133}{100} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4601}{525}+\frac{1\times 133}{3\times 100}-\frac{5}{7}\times 0.34$$

Do the multiplications in the fraction \frac{1\times 133}{3\times 100}.

$$-\frac{4601}{525}+\frac{133}{300}-\frac{5}{7}\times 0.34$$

Least common multiple of 525 and 300 is 2100. Convert -\frac{4601}{525} and \frac{133}{300} to fractions with denominator 2100.

$$-\frac{18404}{2100}+\frac{931}{2100}-\frac{5}{7}\times 0.34$$

Since -\frac{18404}{2100} and \frac{931}{2100} have the same denominator, add them by adding their numerators.

$$\frac{-18404+931}{2100}-\frac{5}{7}\times 0.34$$

Add -18404 and 931 to get -17473.

$$-\frac{17473}{2100}-\frac{5}{7}\times 0.34$$

Convert decimal number 0.34 to fraction \frac{34}{100}. Reduce the fraction \frac{34}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{17473}{2100}-\frac{5}{7}\times \frac{17}{50}$$

Multiply \frac{5}{7} times \frac{17}{50} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{17473}{2100}-\frac{5\times 17}{7\times 50}$$

Do the multiplications in the fraction \frac{5\times 17}{7\times 50}.

$$-\frac{17473}{2100}-\frac{85}{350}$$

Reduce the fraction \frac{85}{350} to lowest terms by extracting and canceling out 5.

$$-\frac{17473}{2100}-\frac{17}{70}$$

Least common multiple of 2100 and 70 is 2100. Convert -\frac{17473}{2100} and \frac{17}{70} to fractions with denominator 2100.

$$-\frac{17473}{2100}-\frac{510}{2100}$$

Since -\frac{17473}{2100} and \frac{510}{2100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17473-510}{2100}$$

Subtract 510 from -17473 to get -17983.

$$\frac{-17983}{2100}$$

Reduce the fraction \frac{-17983}{2100} to lowest terms by extracting and canceling out 7.

$$-\frac{2569}{300}$$

Factor

$$-\frac{2569}{300} = -8\frac{169}{300} = -8.563333333333333$$