Solve 5.5+(755-678)/(755-635)+(755-678(3)

$$5.5+ \frac{ (755-678) }{ (755-635)+(755-678 } (3)$$

Evaluate

$$\frac{2629}{394}\approx 6.672588832$$

Solution Steps

Subtract 678 from 755 to get 77.

$$5.5+\frac{77}{755-635+755-678}\times 3$$

Subtract 635 from 755 to get 120.

$$5.5+\frac{77}{120+755-678}\times 3$$

Add 120 and 755 to get 875.

$$5.5+\frac{77}{875-678}\times 3$$

Subtract 678 from 875 to get 197.

$$5.5+\frac{77}{197}\times 3$$

Express \frac{77}{197}\times 3 as a single fraction.

$$5.5+\frac{77\times 3}{197}$$

Multiply 77 and 3 to get 231.

$$5.5+\frac{231}{197}$$

Convert decimal number 5.5 to fraction \frac{55}{10}. Reduce the fraction \frac{55}{10} to lowest terms by extracting and canceling out 5.

$$\frac{11}{2}+\frac{231}{197}$$

Least common multiple of 2 and 197 is 394. Convert \frac{11}{2} and \frac{231}{197} to fractions with denominator 394.

$$\frac{2167}{394}+\frac{462}{394}$$

Since \frac{2167}{394} and \frac{462}{394} have the same denominator, add them by adding their numerators.

$$\frac{2167+462}{394}$$

Add 2167 and 462 to get 2629.

$$\frac{2629}{394}$$

Factor

$$\frac{11 \cdot 239}{2 \cdot 197} = 6\frac{265}{394} = 6.6725888324873095$$