Equivalent Fractions worksheet for practicing fraction equivalence across three difficulty levels.

Absolutely! Let's solve this worksheet step by step. The goal is to fill in the blanks to create equivalent fractions — that means fractions that have the same value, even though they look different.

We do this by multiplying or dividing both the numerator and denominator by the same number (called a “scale factor”).

---

## ✔ Section A: Fill in the blanks to create equivalent fractions.

Each problem starts with `1/n = ?/m`, so we’re scaling up the unit fraction.

Strategy:

If you have `1/a = x/b`, then `x = b ÷ a`.

Let’s go row by row:

---

Row 1:

- `1/2 = 6/?` → 6 ÷ 1 = 6, so multiply denominator by 6 → 2 × 6 = 12
- `1/3 = 7/?` → 7 ÷ 1 = 7 → 3 × 7 = 21
- `1/6 = 9/?` → 9 ÷ 1 = 9 → 6 × 9 = 54
- `1/7 = ?/14` → 14 ÷ 7 = 2 → numerator = 1 × 2 = 2

✔ Answers: 12, 21, 54, 2

---

Row 2:

- `1/9 = 5/?` → 5 ÷ 1 = 5 → 9 × 5 = 45
- `1/8 = 4/?` → 4 ÷ 1 = 4 → 8 × 4 = 32
- `1/12 = 3/?` → 3 ÷ 1 = 3 → 12 × 3 = 36
- `1/8 = ?/32` → 32 ÷ 8 = 4 → numerator = 1 × 4 = 4

✔ Answers: 45, 32, 36, 4

---

Row 3:

- `1/5 = 9/?` → 9 ÷ 1 = 9 → 5 × 9 = 45
- `1/11 = 4/?` → 4 ÷ 1 = 4 → 11 × 4 = 44
- `1/6 = 12/?` → 12 ÷ 1 = 12 → 6 × 12 = 72
- `1/7 = ?/49` → 49 ÷ 7 = 7 → numerator = 1 × 7 = 7

✔ Answers: 45, 44, 72, 7

---

Row 4:

- `1/8 = 3/?` → 3 ÷ 1 = 3 → 8 × 3 = 24
- `1/6 = 7/?` → 7 ÷ 1 = 7 → 6 × 7 = 42
- `1/12 = 10/?` → 10 ÷ 1 = 10 → 12 × 10 = 120
- `1/9 = ?/63` → 63 ÷ 9 = 7 → numerator = 1 × 7 = 7

✔ Answers: 24, 42, 120, 7

---

## ✔ Section B: Fill in the blanks to create equivalent fractions.

Now we have non-unit fractions. We use the same rule: multiply numerator and denominator by the same number.

Strategy:

If `a/b = c/?`, then find the multiplier: `c ÷ a = multiplier`, then multiply denominator by it.

---

Row 1:

- `2/3 = 4/?` → 4 ÷ 2 = 2 → 3 × 2 = 6
- `4/5 = 12/?` → 12 ÷ 4 = 3 → 5 × 3 = 15
- `3/4 = 21/?` → 21 ÷ 3 = 7 → 4 × 7 = 28
- `2/5 = 10/?` → 10 ÷ 2 = 5 → 5 × 5 = 25

✔ Answers: 6, 15, 28, 25

---

Row 2:

- `2/9 = 16/?` → 16 ÷ 2 = 8 → 9 × 8 = 72
- `9/10 = 18/?` → 18 ÷ 9 = 2 → 10 × 2 = 20
- `4/7 = 16/?` → 16 ÷ 4 = 4 → 7 × 4 = 28
- `3/11 = 27/?` → 27 ÷ 3 = 9 → 11 × 9 = 99

✔ Answers: 72, 20, 28, 99

---

Row 3:

- `7/8 = ?/56` → 56 ÷ 8 = 7 → 7 × 7 = 49
- `2/3 = ?/36` → 36 ÷ 3 = 12 → 2 × 12 = 24
- `5/6 = ?/48` → 48 ÷ 6 = 8 → 5 × 8 = 40
- `3/7 = ?/84` → 84 ÷ 7 = 12 → 3 × 12 = 36

✔ Answers: 49, 24, 40, 36

---

Row 4:

- `1/20 = ?/160` → 160 ÷ 20 = 8 → 1 × 8 = 8
- `3/50 = ?/150` → 150 ÷ 50 = 3 → 3 × 3 = 9
- `11/30 = ?/120` → 120 ÷ 30 = 4 → 11 × 4 = 44
- `9/25 = ?/100` → 100 ÷ 25 = 4 → 9 × 4 = 36

✔ Answers: 8, 9, 44, 36

---

## ✔ Section C: Fill in the blanks to create equivalent fractions (chain of equivalents)

Here, we have one fraction equal to several others. We need to find missing numerators or denominators so all are equivalent.

Strategy:

Pick the original fraction and scale it up/down to match each blank.

---

First Chain: `2/3 = ?/9 = 12/? = ?/21`

Start with `2/3`

- `?/9`: 9 ÷ 3 = 3 → 2 × 3 = 6
- `12/?`: 12 ÷ 2 = 6 → 3 × 6 = 18
- `?/21`: 21 ÷ 3 = 7 → 2 × 7 = 14

✔ Answers: 6, 18, 14

---

Second Chain: `3/5 = ?/25 = 36/? = 24/?`

Start with `3/5`

- `?/25`: 25 ÷ 5 = 5 → 3 × 5 = 15
- `36/?`: 36 ÷ 3 = 12 → 5 × 12 = 60
- `24/?`: 24 ÷ 3 = 8 → 5 × 8 = 40

✔ Answers: 15, 60, 40

---

Third Chain: `6/7 = ?/14 = 36/? = ?/56`

Start with `6/7`

- `?/14`: 14 ÷ 7 = 2 → 6 × 2 = 12
- `36/?`: 36 ÷ 6 = 6 → 7 × 6 = 42
- `?/56`: 56 ÷ 7 = 8 → 6 × 8 = 48

✔ Answers: 12, 42, 48

---

Fourth Chain: `11/20 = ?/40 = 66/? = 132/?`

Start with `11/20`

- `?/40`: 40 ÷ 20 = 2 → 11 × 2 = 22
- `66/?`: 66 ÷ 11 = 6 → 20 × 6 = 120
- `132/?`: 132 ÷ 11 = 12 → 20 × 12 = 240

✔ Answers: 22, 120, 240

---

## 🎯 Final Answer Key:

---

Section A:

Row 1: 12, 21, 54, 2
Row 2: 45, 32, 36, 4
Row 3: 45, 44, 72, 7
Row 4: 24, 42, 120, 7

---

Section B:

Row 1: 6, 15, 28, 25
Row 2: 72, 20, 28, 99
Row 3: 49, 24, 40, 36
Row 4: 8, 9, 44, 36

---

Section C:

First chain: 6, 18, 14
Second chain: 15, 60, 40
Third chain: 12, 42, 48
Fourth chain: 22, 120, 240

---

✔ You’ve now filled in all blanks correctly using the concept of equivalent fractions — multiplying or dividing numerator and denominator by the same number to keep the value unchanged.

Let me know if you’d like a printable version or explanation for a specific problem! 😊