Adding Fractions Problems with Different Denominator - Free Printable

Let’s solve each fraction addition problem step by step.

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Problem 1: 6/3 + 8/4

First, simplify each fraction if possible.

- 6 ÷ 3 = 2 → so 6/3 = 2
- 8 ÷ 4 = 2 → so 8/4 = 2

Now add: 2 + 2 = 4

✔ Answer: 4

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Problem 2: 10/4 + 4/6

These fractions have different denominators. We need a common denominator.

Find the least common multiple (LCM) of 4 and 6 → LCM is 12.

Convert both fractions to twelfths:

- 10/4 = (10 × 3)/(4 × 3) = 30/12
- 4/6 = (4 × 2)/(6 × 2) = 8/12

Add: 30/12 + 8/12 = 38/12

Simplify 38/12:

Divide numerator and denominator by 2 → 19/6

We can also write as mixed number: 19 ÷ 6 = 3 with remainder 1 → 3 1/6

But since the worksheet doesn’t specify format, we’ll leave as improper fraction unless told otherwise. However, looking at other problems, some are whole numbers or simple fractions — let’s check if simplifying further helps.

Actually, 38/12 reduces to 19/6 — that’s simplest form.

✔ Answer: 19/6 (or 3 1/6)

Wait — let me double-check calculation:

10/4 = 2.5
4/6 ≈ 0.666...
Sum ≈ 3.166..., which is 19/6 = 3.166... ✔️

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Problem 3: 6/7 + 2/9

Different denominators: 7 and 9 → LCM = 63

Convert:

- 6/7 = (6×9)/(7×9) = 54/63
- 2/9 = (2×7)/(9×7) = 14/63

Add: 54 + 14 = 68 → 68/63

This is an improper fraction. Can it be simplified? 68 and 63 share no common factors (63=7×9, 68=4×17) → already simplified.

As mixed number: 68 ÷ 63 = 1 R5 → 1 5/63

Again, depending on expected format — but since others may expect simplified fractions, we'll go with 68/63 or 1 5/63. Let’s see what fits best.

Looking ahead, Problem 5 gives same denominator — maybe they want exact fractions.

I’ll keep as 68/63 for now.

✔ Answer: 68/63 (or 1 5/63)

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Problem 4: 3/5 + 9/6

First, simplify 9/6 → divide top and bottom by 3 → 3/2

So now: 3/5 + 3/2

Denominators 5 and 2 → LCM = 10

Convert:

- 3/5 = 6/10
- 3/2 = 15/10

Add: 6 + 15 = 21 → 21/10

That’s 2 1/10 as mixed number.

Check: 3/5 = 0.6, 9/6 = 1.5 → sum = 2.1 = 21/10 ✔️

✔ Answer: 21/10 (or 2 1/10)

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Problem 5: 7/5 + 3/5

Same denominator! Just add numerators:

7 + 3 = 10 → 10/5 = 2

✔ Answer: 2

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Problem 6: 5/4 + 1/2

Different denominators: 4 and 2 → LCM = 4

Convert 1/2 to fourths: 1/2 = 2/4

Now: 5/4 + 2/4 = 7/4

7/4 = 1 3/4 as mixed number.

Check: 5/4 = 1.25, 1/2 = 0.5 → sum = 1.75 = 7/4 ✔️

✔ Answer: 7/4 (or 1 3/4)

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Now, compiling all answers in order as they appear on the sheet:

Top row left to right:
1. 6/3 + 8/4 = 4
2. 10/4 + 4/6 = 19/6

Middle row:
3. 6/7 + 2/9 = 68/63
4. 3/5 + 9/6 = 21/10

Bottom row:
5. 7/5 + 3/5 = 2
6. 5/4 + 1/2 = 7/4

Some teachers prefer mixed numbers over improper fractions. Since the worksheet doesn't specify, and given that some results are whole numbers, perhaps mixed numbers are acceptable. But again, without instruction, either is mathematically correct.

However, looking at the layout — boxes are blank, likely expecting simplified fractions or whole numbers.

Let me re-express any improper fractions as mixed numbers where appropriate, just in case:

- 19/6 = 3 1/6
- 68/63 = 1 5/63
- 21/10 = 2 1/10
- 7/4 = 1 3/4

But wait — in Problem 1 and 5, we got whole numbers. Maybe the worksheet expects simplest form, whether improper or mixed.

Actually, let's look back: In many elementary worksheets, if the result is greater than 1, they often accept either, but sometimes prefer mixed numbers.

To be safe, I’ll provide both forms in reasoning, but for Final Answer, since the box is empty and no format specified, I’ll give the most reduced fractional form — including mixed numbers if cleaner.

Alternatively, perhaps the worksheet expects decimal? Unlikely — title says “Fraction Addition”.

Another thought: Maybe reduce before adding when possible.

For example, in Problem 2: 10/4 + 4/6 → could reduce first: 5/2 + 2/3 → then common denominator 6: 15/6 + 4/6 = 19/6 → same as before.

All checks out.

Final decision: Provide answers in simplest form — use mixed numbers if the fraction is improper and greater than 1, because that’s commonly taught at this level.

So:

1. 4 → stays 4
2. 19/6 → 3 1/6
3. 68/63 → 1 5/63
4. 21/10 → 2 1/10
5. 2 → stays 2
6. 7/4 → 1 3/4

Yes, that seems student-friendly.

Double-checking one more time:

Problem 3: 6/7 + 2/9 = 54/63 + 14/63 = 68/63 = 1 5/63 ✔️
Problem 4: 3/5 + 9/6 = 3/5 + 3/2 = 6/10 + 15/10 = 21/10 = 2 1/10 ✔️
Problem 6: 5/4 + 1/2 = 5/4 + 2/4 = 7/4 = 1 3/4 ✔️

Perfect.

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Final Answer:
4, 3 1/6, 1 5/63, 2 1/10, 2, 1 3/4