\( 2\frac{5}{2}+6\frac{12}{8} \) is equals to? solve it step by step.

To solve the expression 2⁵⁄₂ + 6¹²⁄₈, we will proceed step by step.

Step 1: Convert Mixed Numbers to Improper Fractions

• For 2⁵⁄₂:
  • Multiply the whole number by the denominator: 2 × 2 = 4
  • Add the numerator: 4 + 5 = 9
  • Thus, 2⁵⁄₂ = 9⁵⁄₂
• For 6¹²⁄₈:
  • Multiply the whole number by the denominator: 6 × 8 = 48
  • Add the numerator: 48 + 12 = 60
  • Thus, 6¹²⁄₈ = 60¹²⁄₈

Step 2: Add the Improper Fractions

Now, we need to add the two fractions:

We have:

• 9⁵⁄₂ + 60¹²⁄₈

To add these fractions, we need a common denominator. The least common multiple of 2 and 8 is 8.

• Convert 9⁵⁄₂ to a fraction with denominator 8: 9⁵⁄₂ = (9 × 4)⁵⁄₈ = 36²⁰⁄₈
• Now we add: 36²⁰⁄₈ + 60¹²⁄₈ = (36 + 60)²⁰⁄₈ = 96²⁰⁄₈

Step 3: Simplify the Result

The result is:

• 96²⁰⁄₈ = 12⁰⁄₁ = 12

Thus, the final answer is 12.

Quick Takeaway: When adding mixed numbers, always convert them to improper fractions first to simplify the process.