Equivalent Fractions worksheet (B) with exercises for creating equivalent fractions, divided into three sections for practice.

Explanation:
We need to fill in the blanks so that each pair (or chain) of fractions is equivalent. That means they represent the same value — just written differently.

To find an equivalent fraction, we multiply or divide both the numerator and denominator by the same number.

Let’s go section by section.

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Section A: All are of the form
  1 / ? = ? / ?
So we’re scaling 1/x to get a new fraction with numerator given (like 6, 7, 9, etc.) or denominator given.

General rule:
If 1/a = b/c, then cross-multiplying gives:
1 × c = a × b → c = a × b
So denominator = original denominator × new numerator.

Let’s do each:

1. 1/2 = 6/□
→ denominator = 2 × 6 = 12
✔ 1/2 = 6/12

2. 1/3 = 7/□
→ denominator = 3 × 7 = 21
✔ 1/3 = 7/21

3. 1/6 = 9/□
→ denominator = 6 × 9 = 54
✔ 1/6 = 9/54

4. 1/7 = □/14
Now numerator is missing.
Since denominator doubled (7 → 14), numerator must also double: 1 → 2
✔ 1/7 = 2/14

5. 1/9 = 5/□
→ denominator = 9 × 5 = 45
✔ 1/9 = 5/45

6. 1/8 = 4/□
→ denominator = 8 × 4 = 32
✔ 1/8 = 4/32

7. 1/12 = 3/□
→ denominator = 12 × 3 = 36
✔ 1/12 = 3/36

8. 1/8 = □/32
Denominator went from 8 → 32 → multiplied by 4 ⇒ numerator 1 × 4 = 4
✔ 1/8 = 4/32

9. 1/5 = 9/□
→ denominator = 5 × 9 = 45
✔ 1/5 = 9/45

10. 1/11 = 4/□
→ denominator = 11 × 4 = 44
✔ 1/11 = 4/44

11. 1/6 = 12/□
→ denominator = 6 × 12 = 72
✔ 1/6 = 12/72

12. 1/7 = □/49
7 → 49 = ×7 ⇒ numerator 1 × 7 = 7
✔ 1/7 = 7/49

13. 1/8 = 3/□
→ denominator = 8 × 3 = 24
✔ 1/8 = 3/24

14. 1/6 = 7/□
→ denominator = 6 × 7 = 42
✔ 1/6 = 7/42

15. 1/12 = 10/□
→ denominator = 12 × 10 = 120
✔ 1/12 = 10/120

16. 1/9 = □/63
9 → 63 = ×7 ⇒ numerator = 1 × 7 = 7
✔ 1/9 = 7/63

✔ Section A done.

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Section B: Now numerators/denominators are not always 1.

Use same idea: multiply numerator and denominator by same number.

1. 2/3 = 4/□
2 → 4 = ×2 ⇒ denominator 3 × 2 = 6
✔ 2/3 = 4/6

2. 4/5 = 12/□
4 → 12 = ×3 ⇒ 5 × 3 = 15
✔ 4/5 = 12/15

3. 3/4 = 21/□
3 → 21 = ×7 ⇒ 4 × 7 = 28
✔ 3/4 = 21/28

4. 2/5 = 10/□
2 → 10 = ×5 ⇒ 5 × 5 = 25
✔ 2/5 = 10/25

5. 2/9 = 16/□
2 → 16 = ×8 ⇒ 9 × 8 = 72
✔ 2/9 = 16/72

6. 9/10 = 18/□
9 → 18 = ×2 ⇒ 10 × 2 = 20
✔ 9/10 = 18/20

7. 4/7 = 16/□
4 → 16 = ×4 ⇒ 7 × 4 = 28
✔ 4/7 = 16/28

8. 3/11 = 27/□
3 → 27 = ×9 ⇒ 11 × 9 = 99
✔ 3/11 = 27/99

9. 7/8 = □/56
8 → 56 = ×7 ⇒ numerator 7 × 7 = 49
✔ 7/8 = 49/56

10. 2/3 = □/36
3 → 36 = ×12 ⇒ numerator 2 × 12 = 24
✔ 2/3 = 24/36

11. 5/6 = □/48
6 → 48 = ×8 ⇒ numerator 5 × 8 = 40
✔ 5/6 = 40/48

12. 3/7 = □/84
7 → 84 = ×12 ⇒ numerator 3 × 12 = 36
✔ 3/7 = 36/84

13. 1/20 = □/160
20 → 160 = ×8 ⇒ numerator 1 × 8 = 8
✔ 1/20 = 8/160

14. 3/50 = □/150
50 → 150 = ×3 ⇒ numerator 3 × 3 = 9
✔ 3/50 = 9/150

15. 11/30 = □/120
30 → 120 = ×4 ⇒ numerator 11 × 4 = 44
✔ 11/30 = 44/120

16. 9/25 = □/100
25 → 100 = ×4 ⇒ numerator 9 × 4 = 36
✔ 9/25 = 36/100

✔ Section B done.

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Section C: Chains of 3 or 4 equivalent fractions.

We’ll find the common multiplier step by step.

1. 2/3 = □/9 = 12/□ = □/21
Start: 2/3 → to get denominator 9: 3 × 3 = 9 ⇒ numerator 2 × 3 = 6
So first blank = 6 → 2/3 = 6/9
Next: 6/9 = 12/□ → 6 → 12 = ×2 ⇒ denominator 9 × 2 = 18
So second blank = 18
Then: 12/18 = □/21
Simplify 12/18 = 2/3, so we want 2/3 = x/21 ⇒ x = 2 × 7 = 14
(since 3 × 7 = 21)
So third blank = 14
✔ Chain: 2/3 = 6/9 = 12/18 = 14/21

2. 3/5 = □/25 = 36/□ = 24/□
3/5 → denominator 25: 5 × 5 = 25 ⇒ numerator 3 × 5 = 15
First blank = 15
15/25 = 36/□
Simplify 15/25 = 3/5, so 3/5 = 36/x ⇒ x = 36 × 5 ÷ 3 = 60
(Because 3x = 5×36 = 180 → x = 60)
Second blank = 60
Now 36/60 = 24/x
Simplify 36/60 = 3/5 again
So 3/5 = 24/x ⇒ x = 24 × 5 ÷ 3 = 40
Third blank = 40
✔ Chain: 3/5 = 15/25 = 36/60 = 24/40

3. 6/7 = □/14 = 36/□ = □/56
6/7 → denominator 14: 7 × 2 = 14 ⇒ numerator 6 × 2 = 12
First blank = 12
12/14 = 36/□
12 → 36 = ×3 ⇒ denominator 14 × 3 = 42
Second blank = 42
Now 36/42 = x/56
Simplify 36/42 = 6/7
So 6/7 = x/56 ⇒ x = 6 × 8 = 48 (since 7 × 8 = 56)
Third blank = 48
✔ Chain: 6/7 = 12/14 = 36/42 = 48/56

4. 11/20 = □/40 = 66/□ = 132/□
11/20 → denominator 40: ×2 ⇒ numerator 11 × 2 = 22
First blank = 22
22/40 = 66/□
22 → 66 = ×3 ⇒ denominator 40 × 3 = 120
Second blank = 120
Now 66/120 = 132/x
66 → 132 = ×2 ⇒ denominator 120 × 2 = 240
Third blank = 240
✔ Chain: 11/20 = 22/40 = 66/120 = 132/240

Let me double-check a few tricky ones:

- 1/6 = 9/54? 9÷54 = 1/6 ✔️
- 3/7 = 36/84? 36÷84 = 3/7 ✔️ (divide both by 12)
- 2/3 = 14/21? 14÷21 = 2/3 ✔️
- 11/20 = 132/240? 132÷240 = 11/20 ✔️ (divide by 12)

All correct.

Final Answer:
Section A:
12, 21, 54, 2, 45, 32, 36, 4, 45, 44, 72, 7, 24, 42, 120, 7

Section B:
6, 15, 28, 25, 72, 20, 28, 99, 49, 24, 40, 36, 8, 9, 44, 36

Section C:
6, 18, 14;
15, 60, 40;
12, 42, 48;
22, 120, 240