Operations with Fractions (A) Worksheet | 5th Grade PDF Worksheets - Free Printable

Let’s solve each section step by step, carefully checking all calculations.

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Section A: Find the sum or difference. Write your answers in simplest form.

1) 1/7 + 3/7
Same denominator → add numerators: (1+3)/7 = 4/7
✔ Already simplified.

2) 2/5 + 8/15
Find common denominator: LCM of 5 and 15 is 15.
Convert 2/5 → (2×3)/(5×3) = 6/15
Now: 6/15 + 8/15 = 14/15
✔ Already simplified.

3) 2/3 + 1/4
LCM of 3 and 4 is 12.
2/3 → 8/12; 1/4 → 3/12
8/12 + 3/12 = 11/12
✔ Already simplified.

4) 3/10 - 1/10
Same denominator → subtract numerators: (3-1)/10 = 2/10
Simplify: divide numerator and denominator by 2 → 1/5
✔ Final answer: 1/5

5) 11/24 - 3/8
LCM of 24 and 8 is 24.
3/8 → (3×3)/(8×3) = 9/24
11/24 - 9/24 = 2/24
Simplify: divide by 2 → 1/12
✔ Final answer: 1/12

6) 5/6 - 1/16
LCM of 6 and 16 is 48.
5/6 → (5×8)/(6×8) = 40/48
1/16 → (1×3)/(16×3) = 3/48
40/48 - 3/48 = 37/48
✔ Already simplified.

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Section B: Find the product or quotient. Write your answers in simplest form.

1) 2/7 × 3/5
Multiply straight across: (2×3)/(7×5) = 6/35
✔ Already simplified.

2) 5/8 × 2/3
(5×2)/(8×3) = 10/24
Simplify: divide by 2 → 5/12
✔ Final answer: 5/12

3) 8/9 × 3/10
(8×3)/(9×10) = 24/90
Simplify: divide by 6 → 4/15
✔ Final answer: 4/15

4) 9/11 ÷ 5/6
Dividing fractions: multiply by reciprocal → 9/11 × 6/5 = (9×6)/(11×5) = 54/55
✔ Already simplified.

5) 3/8 ÷ 5/12
→ 3/8 × 12/5 = (3×12)/(8×5) = 36/40
Simplify: divide by 4 → 9/10
✔ Final answer: 9/10

6) 8/12 ÷ 4
First simplify 8/12 → 2/3
Then: 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6
✔ Final answer: 1/6

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Section C: Simplify and leave your answers as mixed numbers.

1) 12 + 8/11
This is already a whole number plus a fraction → 12 8/11
✔ Done.

2) 7/15 × 9
Write 9 as 9/1 → (7×9)/(15×1) = 63/15
Simplify: divide numerator and denominator by 3 → 21/5
Convert to mixed number: 21 ÷ 5 = 4 with remainder 1 → 4 1/5
✔ Final answer: 4 1/5

3) 12 - 8/3
Convert 12 to thirds: 12 = 36/3
36/3 - 8/3 = 28/3
Convert to mixed number: 28 ÷ 3 = 9 with remainder 1 → 9 1/3
✔ Final answer: 9 1/3

4) 1 2/3 - 2/9
Convert 1 2/3 to improper fraction: (1×3 + 2)/3 = 5/3
Now: 5/3 - 2/9
Common denominator 9: 5/3 = 15/9
15/9 - 2/9 = 13/9
Convert to mixed number: 13 ÷ 9 = 1 with remainder 4 → 1 4/9
✔ Final answer: 1 4/9

5) 12/5 + 4/6
First simplify 4/6 → 2/3
Now: 12/5 + 2/3
LCM of 5 and 3 is 15
12/5 = 36/15; 2/3 = 10/15
36/15 + 10/15 = 46/15
Convert to mixed number: 46 ÷ 15 = 3 with remainder 1 → 3 1/15
✔ Final answer: 3 1/15

6) 10 ÷ 4/7
→ 10 × 7/4 = 70/4
Simplify: divide by 2 → 35/2
Convert to mixed number: 35 ÷ 2 = 17 with remainder 1 → 17 1/2
✔ Final answer: 17 1/2

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Extension: Solve the following:

2/10 [ ((1/12 + 3/4) ÷ 4/7) ]

Step 1: Inside innermost parentheses: 1/12 + 3/4
LCM of 12 and 4 is 12
3/4 = 9/12
So: 1/12 + 9/12 = 10/12 = 5/6

Step 2: Divide by 4/7 → 5/6 ÷ 4/7 = 5/6 × 7/4 = 35/24

Step 3: Multiply by 2/10 → 2/10 × 35/24
Simplify 2/10 → 1/5
So: 1/5 × 35/24 = 35/120
Simplify: divide numerator and denominator by 5 → 7/24

✔ Final answer for extension: 7/24

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Final Answer:
Section A:
1) 4/7
2) 14/15
3) 11/12
4) 1/5
5) 1/12
6) 37/48

Section B:
1) 6/35
2) 5/12
3) 4/15
4) 54/55
5) 9/10
6) 1/6

Section C:
1) 12 8/11
2) 4 1/5
3) 9 1/3
4) 1 4/9
5) 3 1/15
6) 17 1/2

Extension: 7/24