Fractions worksheet for adding and comparing fractions.

Let’s solve each problem step by step.

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Part 1: Add the fractions and reduce to lowest terms

We need to add two fractions. To do that, we find a common denominator (the least common multiple of the two denominators), convert both fractions to have that denominator, add the numerators, then simplify if needed.

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Problem 1:
5/7 + 3/4

- Denominators: 7 and 4 → LCM = 28
- Convert:
5/7 = (5×4)/(7×4) = 20/28
3/4 = (3×7)/(4×7) = 21/28
- Add: 20/28 + 21/28 = 41/28
- Simplify? 41 is prime, doesn’t divide by 28 → already reduced.
But 41/28 is an improper fraction — we can write as mixed number: 1 13/28
*(Note: The worksheet says “reduce to lowest terms” — it doesn’t say convert to mixed number, so either form is acceptable unless specified. But since 41 and 28 share no common factors, 41/28 is reduced.)*

Wait — let me double-check: GCF(41,28)=1 → yes, reduced.

✔ Final for #1: 41/28 or 1 13/28

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Problem 2:
4/3 + 7/9

- Denominators: 3 and 9 → LCM = 9
- Convert:
4/3 = (4×3)/(3×3) = 12/9
7/9 stays same
- Add: 12/9 + 7/9 = 19/9
- Simplify? GCF(19,9)=1 → reduced. Mixed number: 2 1/9

✔ Final for #2: 19/9 or 2 1/9

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Problem 3:
4/6 + 1/3

First, simplify 4/6 → 2/3 (divide numerator and denominator by 2)

Now: 2/3 + 1/3 = 3/3 = 1

✔ Final for #3: 1

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Problem 4:
8/9 + 3/8

- Denominators: 9 and 8 → LCM = 72
- Convert:
8/9 = (8×8)/(9×8) = 64/72
3/8 = (3×9)/(8×9) = 27/72
- Add: 64 + 27 = 91 → 91/72
- Simplify? GCF(91,72): 91=7×13, 72=8×9 → no common factors → reduced. Mixed: 1 19/72

✔ Final for #4: 91/72 or 1 19/72

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Problem 5:
3/5 + 2/3

- Denominators: 5 and 3 → LCM = 15
- Convert:
3/5 = 9/15
2/3 = 10/15
- Add: 9+10=19 → 19/15
- Reduced? GCF(19,15)=1 → yes. Mixed: 1 4/15

✔ Final for #5: 19/15 or 1 4/15

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Problem 6:
3/6 + 2/9

Simplify 3/6 → 1/2

Now: 1/2 + 2/9

- LCM of 2 and 9 = 18
- Convert:
1/2 = 9/18
2/9 = 4/18
- Add: 9+4=13 → 13/18
- Reduced? GCF(13,18)=1 → yes

✔ Final for #6: 13/18

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Part 2: Compare using <, >, or =

To compare fractions, we can either get common denominators or cross-multiply.

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Problem 1:
2/3 ○ 2/4

Same numerator → smaller denominator means larger fraction.
3 < 4 → so 2/3 > 2/4

Or cross multiply:
2×4 = 8, 2×3 = 6 → 8 > 6 → so 2/3 > 2/4

✔ Answer: >

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Problem 2:
3/5 ○ 1/2

Cross multiply:
3×2 = 6, 1×5 = 5 → 6 > 5 → so 3/5 > 1/2

✔ Answer: >

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Problem 3:
5/6 ○ 5/9

Same numerator → smaller denominator = bigger fraction
6 < 9 → so 5/6 > 5/9

✔ Answer: >

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Problem 4:
4/9 ○ 4/5

Same numerator → 9 > 5 → so 4/9 < 4/5

✔ Answer: <

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Problem 5:
4/9 ○ 8/18

Notice: 8/18 simplifies to 4/9 (divide top and bottom by 2)

So they are equal!

✔ Answer: =

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Problem 6:
3/7 ○ 5/14

Get common denominator: LCM of 7 and 14 = 14

Convert 3/7 → (3×2)/(7×2) = 6/14

Compare 6/14 and 5/14 → 6 > 5 → so 3/7 > 5/14

✔ Answer: >

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Final Answers:

Addition Problems:

1. 41/28 (or 1 13/28)
2. 19/9 (or 2 1/9)
3. 1
4. 91/72 (or 1 19/72)
5. 19/15 (or 1 4/15)
6. 13/18

Comparison Problems:

1. >
2. >
3. >
4. <
5. =
6. >

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Final Answer:
Addition:
1. 41/28
2. 19/9
3. 1
4. 91/72
5. 19/15
6. 13/18

Comparison:
1. >
2. >
3. >
4. <
5. =
6. >