Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let’s solve each problem step by step.

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Problem 1: 2/4 + 3/8

First, simplify 2/4 → that’s the same as 1/2.
Now we have 1/2 + 3/8.
Find a common denominator — 8 works.
Convert 1/2 to 4/8.
Now add: 4/8 + 3/8 = 7/8.
✔ Already in simplest form.

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Problem 2: 5/6 + 1/9

Common denominator of 6 and 9 is 18.
Convert:
5/6 = 15/18
1/9 = 2/18
Add: 15/18 + 2/18 = 17/18
✔ Simplest form.

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Problem 3: 9/2 - 5/2

Same denominator! Subtract numerators:
9 - 5 = 4 → so 4/2 = 2
✔ Answer is 2 (whole number).

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Problem 4: 7/8 - 1/4

Convert 1/4 to eighths → 2/8
Now subtract: 7/8 - 2/8 = 5/8
✔ Simplest form.

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Problem 5: 9/20 + 2/15

Find LCD of 20 and 15 → it’s 60.
Convert:
9/20 = 27/60
2/15 = 8/60
Add: 27 + 8 = 35 → 35/60
Simplify: divide numerator and denominator by 5 → 7/12
✔ Final answer: 7/12

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Problem 6: 8/3 - 1/2

LCD of 3 and 2 is 6.
Convert:
8/3 = 16/6
1/2 = 3/6
Subtract: 16/6 - 3/6 = 13/6
That’s an improper fraction → can write as mixed number: 2 1/6
But since question says “simplest form”, either is fine — but usually improper is acceptable unless specified. Let’s keep as 13/6 for now. Actually, let’s check if they want mixed — no instruction, so 13/6 is correct. But maybe simplify? It’s already simplified. ✔ 13/6 or 2 1/6 — I’ll go with 13/6 unless told otherwise. Wait — looking at other problems, some results are whole numbers or proper fractions. Maybe convert to mixed? The problem doesn’t specify, so both are valid. But to be safe, let’s use improper unless it’s clearly expected. Hmm — actually, in elementary math, often mixed numbers are preferred for answers >1. Let me check problem 3 — they got 2, which is whole. So perhaps here too? 13/6 = 2 1/6. I think 2 1/6 is better. But let’s see what’s standard. Since the instruction says “simplest form”, and 13/6 is simpler than writing mixed? No — actually, simplest form usually means reduced fraction, not necessarily mixed. But many curricula prefer mixed numbers for final answers when greater than 1. To avoid confusion, I’ll provide both? No — must pick one. Looking at problem 10: 2/3 + 7/9 — will likely give improper or mixed. Let’s proceed with improper unless it simplifies to whole. For consistency, I’ll use improper fractions unless it’s a whole number. So 13/6 is fine. But wait — let’s look ahead. Problem 7: 7/6 + 2/9 — will also be >1. I think for this level, mixed numbers are acceptable. Actually, let’s do this: if the result is an improper fraction, leave it unless instructed to convert. The problem says “simplest form” — which typically means lowest terms, not necessarily mixed. So 13/6 is okay. But to match typical worksheet expectations, I’ll convert to mixed where appropriate. Let me recheck problem 3: they did 9/2 - 5/2 = 4/2 = 2 — they converted to whole number. So probably expect conversion. So for 13/6, write as 2 1/6. Similarly later ones. Okay, changing mind: for any improper fraction, convert to mixed number if possible. So:

13/6 = 2 1/6 ✔

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Problem 7: 7/6 + 2/9

LCD of 6 and 9 is 18.
Convert:
7/6 = 21/18
2/9 = 4/18
Add: 21 + 4 = 25 → 25/18
Convert to mixed: 1 7/18
✔ Final answer: 1 7/18

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Problem 8: 3/7 - 1/7

Same denominator: 3 - 1 = 2 → 2/7
✔ Simplest form.

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Problem 9: 4/12 - 2/24

First, simplify 4/12 → 1/3
Now: 1/3 - 2/24
Convert 1/3 to 8/24
Subtract: 8/24 - 2/24 = 6/24
Simplify: divide by 6 → 1/4
✔ Final answer: 1/4

Alternatively, without simplifying first:
4/12 = 8/24, then 8/24 - 2/24 = 6/24 = 1/4 — same.

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Problem 10: 2/3 + 7/9

LCD is 9.
2/3 = 6/9
6/9 + 7/9 = 13/9
Convert to mixed: 1 4/9
✔ Final answer: 1 4/9

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Problem 11: 2/6 + 7/18

Simplify 2/6 → 1/3
Now: 1/3 + 7/18
LCD is 18.
1/3 = 6/18
6/18 + 7/18 = 13/18
✔ Already simplest form.

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Problem 12: 3/6 - 2/12

Simplify 3/6 → 1/2
Now: 1/2 - 2/12
Convert 1/2 to 6/12
6/12 - 2/12 = 4/12
Simplify: 1/3
✔ Final answer: 1/3

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Problem 13: 5/8 + 4/8

Same denominator: 5 + 4 = 9 → 9/8
Convert to mixed: 1 1/8
✔ Final answer: 1 1/8

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Problem 14: 3/18 - 1/9

Simplify 3/18 → 1/6
Now: 1/6 - 1/9
LCD of 6 and 9 is 18.
1/6 = 3/18
1/9 = 2/18
Subtract: 3/18 - 2/18 = 1/18
✔ Final answer: 1/18

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Now, compiling all answers:

1. 7/8
2. 17/18
3. 2
4. 5/8
5. 7/12
6. 2 1/6
7. 1 7/18
8. 2/7
9. 1/4
10. 1 4/9
11. 13/18
12. 1/3
13. 1 1/8
14. 1/18

All checked and verified.

Final Answer:
1. \frac{7}{8}
2. \frac{17}{18}
3. 2
4. \frac{5}{8}
5. \frac{7}{12}
6. 2\frac{1}{6}
7. 1\frac{7}{18}
8. \frac{2}{7}
9. \frac{1}{4}
10. 1\frac{4}{9}
11. \frac{13}{18}
12. \frac{1}{3}
13. 1\frac{1}{8}
14. \frac{1}{18}