Adding Fractions with Unlike Denominators: 4/10 + 5/12

Because fractions represent parts of different wholes! Adding $\frac{4}{10}$ (4 out of 10) and $\frac{5}{12}$ (5 out of 12) directly would be like adding 4 apples from a group of 10 to 5 oranges from a group of 12 - it doesn't make mathematical sense!

Use prime factorization: 10 = 2×5 and 12 = 2²×3. Take the highest power of each prime factor: 2²×3×5 = 60. This gives you the smallest number both denominators divide into evenly.

Always check if you can simplify! In this problem, $\frac{49}{60}$ is already in lowest terms because 49 and 60 share no common factors other than 1.

Any common multiple will work, but using the LCD (60) keeps your numbers smaller and easier to work with. Using 120 or 180 would still give the right answer, just with bigger fractions to simplify later.

Convert both original fractions to decimals: $\frac{4}{10} = 0.4$ and $\frac{5}{12} ≈ 0.417$, so 0.4 + 0.417 = 0.817. Then check: $\frac{49}{60} ≈ 0.817$ ✓

We need both fractions to have denominator 60. Since 10×6=60, we multiply $\frac{4}{10}$ by $\frac{6}{6}$. Since 12×5=60, we multiply $\frac{5}{12}$ by $\frac{5}{5}$. Remember: multiplying by these forms of 1 doesn't change the value!