Solve +57:(-6.5)-(-41/4)+83/4-(+31/2)+5

$$+ 57 : ( - 6.5 ) - ( - 4 \frac { 1 } { 4 } ) + 8 \frac { 3 } { 4 } - ( + 3 \frac { 1 } { 2 } ) + 5$$

Evaluate

$$\frac{149}{26}\approx 5.730769231$$

Solution Steps

Expand \frac{57}{-6.5} by multiplying both numerator and the denominator by 10.

$$\frac{570}{-65}-\left(-\frac{4\times 4+1}{4}\right)+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Reduce the fraction \frac{570}{-65} to lowest terms by extracting and canceling out 5.

$$-\frac{114}{13}-\left(-\frac{4\times 4+1}{4}\right)+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Multiply 4 and 4 to get 16.

$$-\frac{114}{13}-\left(-\frac{16+1}{4}\right)+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Add 16 and 1 to get 17.

$$-\frac{114}{13}-\left(-\frac{17}{4}\right)+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

The opposite of -\frac{17}{4} is \frac{17}{4}.

$$-\frac{114}{13}+\frac{17}{4}+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Least common multiple of 13 and 4 is 52. Convert -\frac{114}{13} and \frac{17}{4} to fractions with denominator 52.

$$-\frac{456}{52}+\frac{221}{52}+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Since -\frac{456}{52} and \frac{221}{52} have the same denominator, add them by adding their numerators.

$$\frac{-456+221}{52}+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Add -456 and 221 to get -235.

$$-\frac{235}{52}+\frac{8\times 4+3}{4}-\frac{3\times 2+1}{2}+5$$

Multiply 8 and 4 to get 32.

$$-\frac{235}{52}+\frac{32+3}{4}-\frac{3\times 2+1}{2}+5$$

Add 32 and 3 to get 35.

$$-\frac{235}{52}+\frac{35}{4}-\frac{3\times 2+1}{2}+5$$

Least common multiple of 52 and 4 is 52. Convert -\frac{235}{52} and \frac{35}{4} to fractions with denominator 52.

$$-\frac{235}{52}+\frac{455}{52}-\frac{3\times 2+1}{2}+5$$

Since -\frac{235}{52} and \frac{455}{52} have the same denominator, add them by adding their numerators.

$$\frac{-235+455}{52}-\frac{3\times 2+1}{2}+5$$

Add -235 and 455 to get 220.

$$\frac{220}{52}-\frac{3\times 2+1}{2}+5$$

Reduce the fraction \frac{220}{52} to lowest terms by extracting and canceling out 4.

$$\frac{55}{13}-\frac{3\times 2+1}{2}+5$$

Multiply 3 and 2 to get 6.

$$\frac{55}{13}-\frac{6+1}{2}+5$$

Add 6 and 1 to get 7.

$$\frac{55}{13}-\frac{7}{2}+5$$

Least common multiple of 13 and 2 is 26. Convert \frac{55}{13} and \frac{7}{2} to fractions with denominator 26.

$$\frac{110}{26}-\frac{91}{26}+5$$

Since \frac{110}{26} and \frac{91}{26} have the same denominator, subtract them by subtracting their numerators.

$$\frac{110-91}{26}+5$$

Subtract 91 from 110 to get 19.

$$\frac{19}{26}+5$$

Convert 5 to fraction \frac{130}{26}.

$$\frac{19}{26}+\frac{130}{26}$$

Since \frac{19}{26} and \frac{130}{26} have the same denominator, add them by adding their numerators.

$$\frac{19+130}{26}$$

Add 19 and 130 to get 149.

$$\frac{149}{26}$$

Factor

$$\frac{149}{2 \cdot 13} = 5\frac{19}{26} = 5.730769230769231$$