Solve 3.587-(-5)+(-51/2)+(+7)-(+31/4)-(+1.587)

$$3.587 - ( - 5 ) + ( - 5 \frac { 1 } { 2 } ) + ( + 7 ) - ( + 3 \frac { 1 } { 4 } ) - ( + 1.587 )$$

Evaluate

$$5.25$$

Solution Steps

The opposite of -5 is 5.

$$3.587+5-\frac{5\times 2+1}{2}+7-\frac{3\times 4+1}{4}-1.587$$

Add 3.587 and 5 to get 8.587.

$$8.587-\frac{5\times 2+1}{2}+7-\frac{3\times 4+1}{4}-1.587$$

Multiply 5 and 2 to get 10.

$$8.587-\frac{10+1}{2}+7-\frac{3\times 4+1}{4}-1.587$$

Add 10 and 1 to get 11.

$$8.587-\frac{11}{2}+7-\frac{3\times 4+1}{4}-1.587$$

Convert decimal number 8.587 to fraction \frac{8587}{1000}.

$$\frac{8587}{1000}-\frac{11}{2}+7-\frac{3\times 4+1}{4}-1.587$$

Least common multiple of 1000 and 2 is 1000. Convert \frac{8587}{1000} and \frac{11}{2} to fractions with denominator 1000.

$$\frac{8587}{1000}-\frac{5500}{1000}+7-\frac{3\times 4+1}{4}-1.587$$

Since \frac{8587}{1000} and \frac{5500}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8587-5500}{1000}+7-\frac{3\times 4+1}{4}-1.587$$

Subtract 5500 from 8587 to get 3087.

$$\frac{3087}{1000}+7-\frac{3\times 4+1}{4}-1.587$$

Convert 7 to fraction \frac{7000}{1000}.

$$\frac{3087}{1000}+\frac{7000}{1000}-\frac{3\times 4+1}{4}-1.587$$

Since \frac{3087}{1000} and \frac{7000}{1000} have the same denominator, add them by adding their numerators.

$$\frac{3087+7000}{1000}-\frac{3\times 4+1}{4}-1.587$$

Add 3087 and 7000 to get 10087.

$$\frac{10087}{1000}-\frac{3\times 4+1}{4}-1.587$$

Multiply 3 and 4 to get 12.

$$\frac{10087}{1000}-\frac{12+1}{4}-1.587$$

Add 12 and 1 to get 13.

$$\frac{10087}{1000}-\frac{13}{4}-1.587$$

Least common multiple of 1000 and 4 is 1000. Convert \frac{10087}{1000} and \frac{13}{4} to fractions with denominator 1000.

$$\frac{10087}{1000}-\frac{3250}{1000}-1.587$$

Since \frac{10087}{1000} and \frac{3250}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10087-3250}{1000}-1.587$$

Subtract 3250 from 10087 to get 6837.

$$\frac{6837}{1000}-1.587$$

Convert decimal number 1.587 to fraction \frac{1587}{1000}.

$$\frac{6837}{1000}-\frac{1587}{1000}$$

Since \frac{6837}{1000} and \frac{1587}{1000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6837-1587}{1000}$$

Subtract 1587 from 6837 to get 5250.

$$\frac{5250}{1000}$$

Reduce the fraction \frac{5250}{1000} to lowest terms by extracting and canceling out 250.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$