Solve (0.666+7/2)+(0.1+1/2)

$$(0.666+ \frac{ 7 }{ 2 } )+(0.1+ \frac{ 1 }{ 2 } )$$

Evaluate

$$4.766$$

Solution Steps

Convert decimal number 0.666 to fraction \frac{666}{1000}. Reduce the fraction \frac{666}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{333}{500}+\frac{7}{2}+0.1+\frac{1}{2}$$

Least common multiple of 500 and 2 is 500. Convert \frac{333}{500} and \frac{7}{2} to fractions with denominator 500.

$$\frac{333}{500}+\frac{1750}{500}+0.1+\frac{1}{2}$$

Since \frac{333}{500} and \frac{1750}{500} have the same denominator, add them by adding their numerators.

$$\frac{333+1750}{500}+0.1+\frac{1}{2}$$

Add 333 and 1750 to get 2083.

$$\frac{2083}{500}+0.1+\frac{1}{2}$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{2083}{500}+\frac{1}{10}+\frac{1}{2}$$

Least common multiple of 500 and 10 is 500. Convert \frac{2083}{500} and \frac{1}{10} to fractions with denominator 500.

$$\frac{2083}{500}+\frac{50}{500}+\frac{1}{2}$$

Since \frac{2083}{500} and \frac{50}{500} have the same denominator, add them by adding their numerators.

$$\frac{2083+50}{500}+\frac{1}{2}$$

Add 2083 and 50 to get 2133.

$$\frac{2133}{500}+\frac{1}{2}$$

Least common multiple of 500 and 2 is 500. Convert \frac{2133}{500} and \frac{1}{2} to fractions with denominator 500.

$$\frac{2133}{500}+\frac{250}{500}$$

Since \frac{2133}{500} and \frac{250}{500} have the same denominator, add them by adding their numerators.

$$\frac{2133+250}{500}$$

Add 2133 and 250 to get 2383.

$$\frac{2383}{500}$$

Factor

$$\frac{2383}{2 ^ {2} \cdot 5 ^ {3}} = 4\frac{383}{500} = 4.766$$