Grade 6 Fractions: Adding Mixed Numbers

Add mixed numbers with unlike denominators

What You'll Learn

Convert to improper
Add and simplify

📖Adding Mixed

Rename the fractions with a common denominator (2 1/2 + 1 2/3 = 2 3/6 + 1 4/6), add the wholes and the fractions, then regroup: 3 7/6 = 4 1/6. Or write both as improper fractions first.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
1 1/6 + 4 1/2 = ?
1. The fraction parts have different denominators, so rename them with a common denominator, 6: 1/6 = 1/6 and 1/2 = 3/6. Now it is 1 1/6 + 4 3/6.
2. Add the fraction parts: 1/6 + 3/6 = 4/6.
3. Add the whole numbers: 1 + 4 = 5.
4. Put them together: 5 4/6.
5. The greatest number that divides both 4 and 6 is 2.
6. Divide the top and bottom by 2: 4 ÷ 2 = 2 and 6 ÷ 2 = 3, so 4/6 = 2/3.
7. So 1 1/6 + 4 1/2 = 5 2/3.
Answer: 5 2/3
Example 2
1 1/3 + 4 5/6 = ?
1. The fraction parts have different denominators, so rename them with a common denominator, 6: 1/3 = 2/6 and 5/6 = 5/6. Now it is 1 2/6 + 4 5/6.
2. Add the fraction parts: 2/6 + 5/6 = 7/6.
3. Add the whole numbers: 1 + 4 = 5.
4. 7/6 is more than 1 whole: 7/6 = 1 and 1/6. Regroup the 1 whole: 5 + 1 = 6.
5. Put them together: 6 1/6.
6. So 1 1/3 + 4 5/6 = 6 1/6.
Answer: 6 1/6
Example 3
1 7/8 + 1 1/4 = ?
1. The fraction parts have different denominators, so rename them with a common denominator, 8: 7/8 = 7/8 and 1/4 = 2/8. Now it is 1 7/8 + 1 2/8.
2. Add the fraction parts: 7/8 + 2/8 = 9/8.
3. Add the whole numbers: 1 + 1 = 2.
4. 9/8 is more than 1 whole: 9/8 = 1 and 1/8. Regroup the 1 whole: 2 + 1 = 3.
5. Put them together: 3 1/8.
6. So 1 7/8 + 1 1/4 = 3 1/8.
Answer: 3 1/8