Let’s solve each problem step by step. We’re adding mixed fractions with unlike denominators. That means we need to:
1. Add the whole numbers together.
2. Add the fractions — but first, find a common denominator so we can add them.
3. If the fraction part adds up to more than 1, turn it into a mixed number and add the whole number part to the total.
4. Simplify if needed.
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Problem 1: 1¼ + 1⅓
Whole numbers: 1 + 1 = 2
Fractions: ¼ + ⅓
Common denominator of 4 and 3 is 12.
¼ = 3/12
⅓ = 4/12
3/12 + 4/12 = 7/12
Total: 2 + 7/12 =
2⁷₁₂
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Problem 2: 2⅜ + 1½
Whole numbers: 2 + 1 = 3
Fractions: ⅜ + ½
Common denominator of 8 and 2 is 8.
½ = 4/8
⅜ + 4/8 = 7/8
Total: 3 + 7/8 =
3⁷⁄₈
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Problem 3: 2⅜ + 2¾
Whole numbers: 2 + 2 = 4
Fractions: ⅜ + ¾
Common denominator of 8 and 4 is 8.
¾ = 6/8
⅜ + 6/8 = 9/8 → that’s more than 1!
9/8 = 1¹⁄₈
Add that 1 to the whole number: 4 + 1 = 5
So total:
5¹⁄₈
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Problem 4: 2⅗ + 1⅔
Whole numbers: 2 + 1 = 3
Fractions: ⅗ + ⅔
Common denominator of 5 and 3 is 15.
⅗ = 9/15
⅔ = 10/15
9/15 + 10/15 = 19/15 → more than 1!
19/15 = 1⁴⁄₁₅
Add that 1 to the whole number: 3 + 1 = 4
So total:
4⁴⁄₁₅
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Problem 5: 2⅔ + 1¾
Whole numbers: 2 + 1 = 3
Fractions: ⅔ + ¾
Common denominator of 3 and 4 is 12.
⅔ = 8/12
¾ = 9/12
8/12 + 9/12 = 17/12 → more than 1!
17/12 = 1⁵₁₂
Add that 1 to the whole number: 3 + 1 = 4
So total:
4⁵⁄₁₂
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Problem 6: 1³⁄₇ + ½
Whole numbers: 1 + 0 = 1 (since ½ has no whole number)
Fractions: ³⁄₇ + ½
Common denominator of 7 and 2 is 14.
³⁄₇ = 6/14
½ = 7/14
6/14 + 7/14 = 13/14
Total: 1 + 13/14 =
1¹³⁄₁₄
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Final Answer:
1¼ + 1⅓ = 2⁷⁄₁₂
2⅜ + 1½ = 3⁷⁄₈
2⅜ + 2¾ = 5¹⁄₈
2⅗ + 1⅔ = 4⁴⁄₁₅
2⅔ + 1¾ = 4⁵⁄₁₂
1³⁄₇ + ½ = 1¹³⁄₁₄
Parent Tip: Review the logic above to help your child master the concept of adding mixed fractions with unlike denominators worksheet.
