Solve: Combining (6/7)x + (8/7)x + 3⅔x with Like Terms

Because they have the same denominator (7) and the same variable (x)! When fractions have like denominators, you simply add the numerators: $\frac{6+8}{7} = \frac{14}{7}$.

Think of 2x as $2\frac{0}{3}x$! Now you can add: $2\frac{0}{3} + 3\frac{2}{3} = 5\frac{2}{3}$. The whole numbers add (2+3=5) and the fractions add separately.

Mixed numbers like 3⅔ show whole parts + fractional parts clearly. The improper fraction $\frac{11}{3}$ is the same value but harder to visualize. Both are correct!

Absolutely! Converting $3\frac{2}{3} = \frac{11}{3}$ first can make the addition clearer. Just remember to find a common denominator for all fractions before adding.

Convert back and verify: $\frac{6}{7} + \frac{8}{7} + \frac{11}{3} = \frac{18+24+77}{21} = \frac{119}{21} = 5\frac{14}{21} = 5\frac{2}{3}$ ✓