Adding Mixed Numbers: Fifth Grade Mathematics
Adding mixed numbers combines whole-number addition with unlike-fraction addition, requiring common denominators and regrouping improper fractions into whole numbers.
The Standard Method: Separating Wholes and Fractions
The most intuitive method for adding mixed numbers is to add the whole numbers together and add the fractions together separately.
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| ADDING MIXED NUMBERS STEP-BY-STEP |
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| Problem: 3 2/5 + 4 1/2 |
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| Step 1: Find LCD of 5 and 2: LCD = 10 |
| Step 2: Rename fractions: |
| 3 2/5 = 3 4/10 |
| 4 1/2 = 4 5/10 |
| Step 3: Add whole numbers: 3 + 4 = 7 |
| Step 4: Add fractions: 4/10 + 5/10 = 9/10 |
| Step 5: Combine parts: 7 + 9/10 = 7 9/10 |
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Regrouping Improper Fraction Sums
When the sum of the fractions produces an improper fraction (greater than or equal to 1), you must rename the improper fraction as a mixed number and carry the whole number into the whole-number sum.
Adding with Regrouping: 2 5/8 + 3 7/8
Step 1: Add whole numbers: 2 + 3 = 5.
Step 2: Add fractions: 5/8 + 7/8 = 12/8.
Step 3: Notice 12/8 is improper:
12/8 = 1 4/8 = 1 1/2.
Step 4: Regroup the 1 whole into the whole-number total:
5 + 1 1/2 = 6 1/2.
Vertical Setup for Neat Alignment
Writing mixed number addition vertically keeps whole numbers, fractions, and renamed fractions clearly organized.
Vertical Layout:
4 5/6 ---> 4 10/12
+ 2 3/4 --->+ 2 9/12
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6 19/12 ---> 6 + 1 7/12 = 7 7/12
Exercises and Solutions
Exercise 1: Addition Requiring Regrouping. Solve 3 5/6 + 2 2/3. Show the common denominator, the addition of wholes and fractions, the regrouping of the improper fraction, and the final simplified answer.
Solution 1: Find the LCD of 6 and 3: 6 is a multiple of 3, so LCD = 6. Rename 2 2/3: 2/3 = (2 * 2) / (3 * 2) = 4/6, so 2 2/3 = 2 4/6. Keep 3 5/6 as 3 5/6. Add whole numbers: 3 + 2 = 5. Add fractions: 5/6 + 4/6 = 9/6. The fraction 9/6 is improper: 9 / 6 = 1 with remainder 3, so 9/6 = 1 3/6. Regroup 1 into the whole numbers: 5 + 1 3/6 = 6 3/6. Simplify 3/6 by dividing numerator and denominator by 3: 3/6 = 1/2. The final answer is 6 1/2.
Exercise 2: Recipe Measurement Application. A chef mixes 2 1/4 cups of chicken broth with 1 7/8 cups of beef broth to prepare a soup base. What is the total volume of broth in the soup?
Solution 2: Add 2 1/4 + 1 7/8. Find the LCD of 4 and 8: 8 is a multiple of 4, so LCD = 8. Rename 2 1/4: (1 * 2) / (4 * 2) = 2/8, so 2 1/4 = 2 2/8. Add whole numbers: 2 + 1 = 3. Add fractions: 2/8 + 7/8 = 9/8. Convert 9/8 to a mixed number: 9/8 = 1 1/8. Add the whole number 1 to 3: 3 + 1 1/8 = 4 1/8 cups. The total volume of broth is 4 1/8 cups.