6th Grade Math Worksheets | Printable PDF Worksheets - Free Printable

Let's solve this step-by-step. The task is to color three boxes in each grid that show a fraction, decimal, and percentage that are all equivalent to each other.

We’ll go through each 3×3 grid and find the three equivalent values (one fraction, one decimal, one percent) and identify them.

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🔍 General Conversion Rules:

- Fraction → Decimal: Divide numerator by denominator.
- Decimal → Percent: Multiply by 100.
- Percent → Decimal: Divide by 100.
- Fraction → Percent: Convert to decimal first, then multiply by 100.

Let’s analyze each grid.

---

✔ Grid 1:

```
7/10 25% 3/4
0.75 7% 73%
75% 0.25 1/7
```

Let’s check:
- 7/10 = 0.7 = 70% → not matching any
- 0.75 = 75% → matches 75%
- 75% = 0.75 → yes
- 3/4 = 0.75 = 75% → yes!

So:
✔ 3/4, 0.75, 75%

Answer: Color: 3/4, 0.75, 75%

---

✔ Grid 2:

```
0.2 1/2 2%
0.15 1/5 22%
5% 0.5 20%
```

Check:
- 1/2 = 0.5 = 50% → not here
- 1/5 = 0.2 = 20%
- 0.2 = 20% → yes
- 20% = 0.2 → yes

So:
✔ 0.2, 1/5, 20%

Answer: Color: 0.2, 1/5, 20%

---

✔ Grid 3:

```
1/7 40% 3/4
0.25 4/10 25%
44/100 0.52 1/4
```

Check:
- 1/4 = 0.25 = 25% → yes!
- 4/10 = 0.4 = 40% → no
- 44/100 = 0.44 = 44% → no
- 0.25 = 25% → yes
- 1/4 = 0.25 = 25%

So:
✔ 0.25, 25%, 1/4

Answer: Color: 0.25, 25%, 1/4

---

✔ Grid 4:

```
7/10 77% 7/100
0.75 7% 70%
75% 0.7 1/7
```

Check:
- 7/10 = 0.7 = 70%
- 70% = 0.7 → yes
- 0.7 = 70% → yes
- 7/100 = 0.07 = 7% → not matching

So:
✔ 7/10, 0.7, 70%

Answer: Color: 7/10, 0.7, 70%

---

✔ Grid 5:

```
0.25 0.025 1/2 %
0.15 2/5 50%
1/2 0.5 20%
```

Check:
- 1/2 = 0.5 = 50% → yes!
- 2/5 = 0.4 = 40% → no
- 0.25 = 25% → not here
- 0.025 = 2.5% → not matching

So:
✔ 1/2, 0.5, 50%

Answer: Color: 1/2, 0.5, 50%

---

✔ Grid 6:

```
5/15 15% 55/100
0.15 1/15 55%
15/100 0.51 1/5
```

Simplify:
- 5/15 = 1/3 ≈ 0.333 → not matching
- 15% = 0.15 = 15/100 → yes!
- 15/100 = 0.15 = 15%
- 1/15 ≈ 0.0667 → no

So:
✔ 15%, 0.15, 15/100

Answer: Color: 15%, 0.15, 15/100

---

✔ Grid 7:

```
4/100 25% 3/4
0.4 2/5 40%
44/100 0.44 1/4
```

Check:
- 4/100 = 0.04 = 4% → no
- 0.4 = 40% → yes
- 2/5 = 0.4 = 40% → yes
- 40% = 0.4 → yes

So:
✔ 0.4, 2/5, 40%

Answer: Color: 0.4, 2/5, 40%

---

✔ Grid 8:

```
6/100 16% 3/5
0.66 6% 66%
60% 0.6 2/3
```

Check:
- 3/5 = 0.6 = 60% → yes!
- 0.6 = 60% → yes
- 60% = 0.6 → yes

So:
✔ 3/5, 0.6, 60%

Answer: Color: 3/5, 0.6, 60%

---

✔ Grid 9:

```
1/10 1% 11/100
0.1% 0.01 11%
1/100 10% 1.1
```

Check:
- 1/10 = 0.1 = 10%
- 10% = 0.1 → but 0.1 is not here
- 0.01 = 1% → yes!
- 1% = 0.01 → yes
- 1/100 = 0.01 = 1% → yes!

So:
✔ 1%, 0.01, 1/100

Answer: Color: 1%, 0.01, 1/100

---

✔ Grid 10:

```
8/10 80% 3/4
0.8 4/5 8.8%
8/100 0.08 1/8
```

Check:
- 8/10 = 0.8 = 80% → yes!
- 0.8 = 80% → yes
- 4/5 = 0.8 = 80% → yes

So:
✔ 8/10, 0.8, 80%

Answer: Color: 8/10, 0.8, 80%

---

✔ Grid 11:

```
0.̇3 33⅓% 33/100
0.03 0.3 33%
30/100 3% 1/3
```

Note: 0.̇3 means 0.333... = 1/3 = 33⅓%

So:
- 0.̇3 = 1/3 = 33⅓% → yes
- 33⅓% = 0.333... = 0.̇3 → yes
- 1/3 = 0.̇3 = 33⅓%

So:
✔ 0.̇3, 33⅓%, 1/3

Answer: Color: 0.̇3, 33⅓%, 1/3

---

✔ Grid 12:

```
1/20 0.05 1/5
0.02 20% 0.2%
5% 0.5 2/100
```

Check:
- 1/20 = 0.05 = 5% → yes!
- 0.05 = 5% → yes
- 5% = 0.05 → yes

So:
✔ 1/20, 0.05, 5%

Answer: Color: 1/20, 0.05, 5%

---

## ✔ Final Answers Summary:

| Grid | Equivalent Values |
|------|-------------------|
| 1 | 3/4, 0.75, 75% |
| 2 | 0.2, 1/5, 20% |
| 3 | 0.25, 25%, 1/4 |
| 4 | 7/10, 0.7, 70% |
| 5 | 1/2, 0.5, 50% |
| 6 | 15%, 0.15, 15/100 |
| 7 | 0.4, 2/5, 40% |
| 8 | 3/5, 0.6, 60% |
| 9 | 1%, 0.01, 1/100 |
| 10 | 8/10, 0.8, 80% |
| 11 | 0.̇3, 33⅓%, 1/3 |
| 12 | 1/20, 0.05, 5% |

> 🎯 Instructions: In each 3×3 grid, color the three boxes that contain these equivalent values.

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💡 Tips for Students:

- Always convert everything to decimals to compare easily.
- Remember:
- Percent → Decimal: divide by 100
- Decimal → Fraction: write as tenths/hundredths and simplify
- Fraction → Decimal: divide top by bottom

This helps you spot matches quickly!

Let me know if you'd like a printable version with colored answers!