Adding Mixed Numbers
Adding mixed numbers follows a two-step process in Grade 6 Saxon Math Course 1: first add the whole-number parts, then add the fractional parts using a common denominator. If the fractional sum is an improper fraction, convert it and add 1 to the whole number. For 3¾ + 1⅔: LCD of 4 and 3 is 12, giving 3⁹⁄₁₂ + 1⁸⁄₁₂ = 4¹⁷⁄₁₂ = 4 + 1⁵⁄₁₂ = 5⁵⁄₁₂. Always simplify the fractional part of the final answer.
Key Concepts
New Concept We rename the fraction parts of the mixed numbers so that the fractions have common denominators. Then we add. What’s next This is just the foundation. Next, you'll work through examples showing how to simplify sums, even when they create an improper fraction.
Common Questions
How do you add mixed numbers?
Add whole-number parts separately, add fraction parts using a common denominator, then combine. If the fraction sum is improper, convert and carry 1 to the whole number.
Add 3¾ + 1⅔.
LCD = 12. 3⁹⁄₁₂ + 1⁸⁄₁₂ = 4¹⁷⁄₁₂ = 4 + 1⁵⁄₁₂ = 5⁵⁄₁₂.
Add 2⅓ + 4⅓.
Whole parts: 2 + 4 = 6. Fractions: 1/3 + 1/3 = 2/3. Answer: 6⅔.
What do you do when the fractions add to more than 1?
Convert the improper fraction to a mixed number and add the whole-number part to the sum of whole numbers.
Do you need a common denominator when adding the whole-number parts?
No. Only the fractional parts need a common denominator. Whole-number parts add directly.