fractions
Adding Mixed Numbers
The 4-Step Method
1
Convert
to improper fractions
2
Find
common denominator
3
Add
the numerators
4
Simplify
the result
Detailed Example: 2½ + 1¾
1
Convert to improper fractions
2½ = 5/2 and 1¾ = 7/4(2×2+1)/2 = 5/2, (1×4+3)/4 = 7/4
2
Find common denominator
LCD of 2 and 4 is 45/2 = 10/4 (multiply by 2/2)
3
Add the numerators
10/4 + 7/4 = 17/4Keep denominator, add numerators
4
Convert to mixed number
17/4 = 4¼17 ÷ 4 = 4 remainder 1
2½ + 1¾ = 4¼✓
💡Alternative Method: Add Wholes and Fractions Separately
(1) Add whole numbers: 2 + 1 = 3, (2) Add fractions: ½ + ¾ = 5/4 = 1¼, (3) Combine: 3 + 1¼ = 4¼. Same answer!
More Examples
3⅓ + 2½= 5⁵⁄₆10/3 + 5/2 = 20/6 + 15/6 = 35/6
1¼ + 2¼= 3½5/4 + 9/4 = 14/4 = 7/2
4⅔ + 1⅙= 5⁵⁄₆14/3 + 7/6 = 28/6 + 7/6 = 35/6
⚠️ Common Mistakes to Avoid
- Don't just add whole numbers and fractions separately without proper handling
- Don't forget to find a common denominator before adding
- Remember to simplify your final answer