➕ Fraction Add & Subtract: Different Denominators 🍕

Adding and subtracting fractions is like adding slices of pizza — but only when the slices are the same size! If denominators are different, you must convert them to a common denominator first.

✅ Same Denominator (Easy!)
25 + 15 = 35   Just add the numerators!
🔄 Different Denominators — Find the LCM
13 + 14 → LCM of 3 & 4 = 12 → 412 + 312 = 712
🔢 Mixed Numbers
Add whole parts first, then fraction parts.
213 + 116 = 312

The 4-Step Method for Different Denominators:

Step 1 — Find the LCM of both denominators (the smallest number both divide into).
Step 2 — Convert each fraction so it has the LCM as its new denominator. Multiply top AND bottom by the same number.
Step 3 — Add or subtract the numerators. Keep the denominator the same.
Step 4 — Simplify the answer if possible (divide top and bottom by their HCF).

The Golden Rules:

📝 Worked Examples

Study these step by step before trying the exercises!

Example 1: Same Denominator

Question: 37 + 27

Denominators are the same (both 7) ✓
Add the numerators: 3 + 2 = 5
Keep the denominator: 7

Answer: 57

Example 2: Different Denominators

Question: 13 + 14

Step 1: LCM of 3 and 4 = 12
Step 2: Convert → 13 = 412   (×4)   and   14 = 312   (×3)
Step 3: 412 + 312 = 712
Step 4: Can 7/12 be simplified? HCF of 7 and 12 = 1 → already in simplest form.

Answer: 712

Example 3: Subtraction with Different Denominators

Question: 56 − 14

Step 1: LCM of 6 and 4 = 12
Step 2: 56 = 1012   (×2)   and   14 = 312   (×3)
Step 3: 1012 − 312 = 712

Answer: 712

Example 4: Adding Mixed Numbers

Question: 123 + 216

Step 1: Add whole numbers → 1 + 2 = 3
Step 2: LCM of 3 and 6 = 6
Step 3: 23 = 46, so 46 + 16 = 56
Step 4: Combine → 3 + 56

Answer: 356

🔬 Fraction Bar Visualizer

Enter two fractions to add or subtract and see the fraction bars!

+

Click + to switch to subtraction

🧩 Drag 1: Same Denominator — Add the Numerators

Drag the correct numerator to complete:   38 + 28 = ___ /  8

5
6
1
38 + 28 =
8

🧩 Drag 2: Find the Common Denominator

To add 14 + 16, we need a common denominator.
Drag the correct LCM and the converted numerators.

12
3
2
8
24
LCM of 4 and 6 =
14 =
12    16 =
12

🧩 Drag 3: Complete the Addition

Complete all steps for: 25 + 13

15
6
5
11
10
3
LCM =
25 =
15   13 =
15
615 + 515 =
15

🧩 Drag 4: Subtraction with Different Denominators

Complete all steps for: 34 − 16

12
9
2
7
6
5
LCM of 4 and 6 =
34 =
12   16 =
12
912 − 212 =
12

🧩 Drag 5: Adding Mixed Numbers

Complete:   112 + 213

3
5
6
5/6
4
12
Whole numbers: 1 + 2 =
LCM of 2 and 3 =
36 + 26 =
6
Answer =
3

🧩 Drag 6: Subtracting Mixed Numbers

Complete:   334 − 113

2
5
12
5/12
9
4
Whole numbers: 3 − 1 =
LCM of 4 and 3 =
912 − 412 =
12
Answer =
2

📝 Practice Questions

Simplify all answers where possible. Convert improper fractions to mixed numbers.

  1. 29 + 49
  2. 710 − 310
  3. 12 + 14
  4. 13 + 16
  5. 34 − 18
  6. 23 + 15
  7. 56 − 29
  8. 38 + 512
  9. 78 − 13
  10. 25 + 34
  11. 113 + 213
  12. 312 − 114
  13. 213 + 114
  14. 423 − 216
  15. 134 + 216
  16. 12 + 13 + 16
  17. 56 + 23 (simplify your answer)
  18. What is 34 + 12? Write as a mixed number.
  19. What must be added to 38 to make 1?
  20. What is 710 − 25? Simplify your answer.
  1. 6/9 = 2/3
  2. 4/10 = 2/5
  3. 2/4 + 1/4 = 3/4
  4. 2/6 + 1/6 = 3/6 = 1/2
  5. 6/8 − 1/8 = 5/8
  6. 10/15 + 3/15 = 13/15
  7. 15/18 − 4/18 = 11/18
  8. 9/24 + 10/24 = 19/24
  9. 21/24 − 8/24 = 13/24
  10. 8/20 + 15/20 = 23/20 = 1 3/20
  11. 1 + 2 = 3, 1/3 + 1/3 = 2/3 → 3 2/3
  12. 3 − 1 = 2, 2/4 − 1/4 = 1/4 → 2 1/4
  13. 2 + 1 = 3, 4/12 + 3/12 = 7/12 → 3 7/12
  14. 4 − 2 = 2, 4/6 − 1/6 = 3/6 = 1/2 → 2 1/2
  15. 1 + 2 = 3, 9/12 + 2/12 = 11/12 → 3 11/12
  16. 3/6 + 2/6 + 1/6 = 6/6 = 1
  17. 5/6 + 4/6 = 9/6 = 1 1/2
  18. 3/4 + 2/4 = 5/4 = 1 1/4
  19. 1 − 3/8 = 5/8
  20. 7/10 − 4/10 = 3/10

🔥 Challenge: Fraction Word Problems

Show all working. Simplify all answers!

  1. A recipe needs 23 cup of sugar and 34 cup of flour. How much dry ingredient is needed altogether?
  2. Sarah ran 35 km in the morning and 710 km in the afternoon. How far did she run in total?
  3. A plank of wood is 234 m long. A carpenter cuts off 58 m. How much is left?
  4. In a class, 13 of pupils walk to school and 25 cycle. What fraction walk or cycle? What fraction travel by another method?
  5. A tank is 38 full. More water is added to make it 712 full. What fraction of the tank was added?
  6. Three friends share a pizza. Ali eats 13, Beth eats 14, and Carl eats 16. How much pizza is left?
  7. A shelf holds 123 m of books. A second shelf holds 256 m. How many metres of books are there in total?
  8. A jug holds 1 litre. It already contains 38 litre. How much more can be poured in?
  9. Josh cycled 312 km on Monday and 223 km on Tuesday. How much further did he cycle on Monday?
  10. A rope is cut into three pieces: 14 m, 38 m, and 512 m. What is the total length of the rope?
  1. 8/12 + 9/12 = 17/12 = 1 5/12 cups
  2. 6/10 + 7/10 = 13/10 = 1 3/10 km
  3. 2 3/4 − 5/8 = 2 6/8 − 5/8 = 2 1/8 m
  4. 5/15 + 6/15 = 11/15 walk or cycle. Remaining: 1 − 11/15 = 4/15
  5. 7/12 − 3/8 = 7/12 − 4.5/12… LCM=24: 14/24 − 9/24 = 5/24
  6. 4/12 + 3/12 + 2/12 = 9/12 = 3/4 eaten. Left: 1 − 3/4 = 1/4
  7. 1 + 2 = 3. 4/6 + 5/6 = 9/6 = 1 3/6 = 1 1/2. Total: 4 1/2 m
  8. 1 − 3/8 = 5/8 litre
  9. 3 1/2 − 2 2/3 = 3 3/6 − 2 4/6 = 2 9/6 − 2 4/6 = 5/6 km further
  10. 3/12 + 4.5/12… LCM=24: 6/24 + 9/24 + 10/24 = 25/24 = 1 1/24 m
Created by Mr Josh ✨ FractionRush