Year 5 Maths Worksheets - Printable Maths Worksheets Year 5 ... - Free Printable

Let's solve Section A of the worksheet titled *"Colourful Equivalences (A)"*, where we need to identify and colour three boxes in each grid that show a fraction, decimal, and percentage which are all equivalent.

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🔍 Step-by-step Guide:

We’ll go through each 3×2 grid (6 cells) and find the one set of three values (one fraction, one decimal, one percentage) that are equivalent.

We’ll convert everything to decimals for comparison:

- Fraction → Decimal: Divide numerator by denominator.
- Percentage → Decimal: Divide by 100.
- Then compare.

---

✔ Grid 1:

```
25/10 | 25% | 1/4
0.25 | 2% | 20%
```

- 25/10 = 2.5 ✘
- 25% = 0.25 ✔
- 1/4 = 0.25 ✔
- 0.25 = 0.25 ✔
- 2% = 0.02 ✘
- 20% = 0.20 ✘

✔ Equivalent group:
0.25, 25%, 1/4 → all equal to 0.25

> ✔️ Colour: 0.25, 25%, 1/4

---

✔ Grid 2:

```
0.5 | 1/2 | 2%
50% | 1/5 | 22%
```

- 0.5 = 0.5 ✔
- 1/2 = 0.5 ✔
- 50% = 0.5 ✔
- Others: 2% = 0.02, 1/5 = 0.2, 22% = 0.22 → not matching

✔ Equivalent group:
0.5, 1/2, 50%

> ✔️ Colour: 0.5, 1/2, 50%

---

✔ Grid 3:

```
1/4 | 75% | 3/4
0.75 | 5/7 | 0.57
```

- 1/4 = 0.25 ✘
- 75% = 0.75 ✔
- 3/4 = 0.75 ✔
- 0.75 = 0.75 ✔
- 5/7 ≈ 0.714 ✘
- 0.57 = 0.57 ✘

✔ Equivalent group:
0.75, 75%, 3/4

> ✔️ Colour: 0.75, 75%, 3/4

---

✔ Grid 4:

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

- 1/10 = 0.1 ✔
- 0.1 = 0.1 ✔
- 1/100 = 0.01 ✘
- 1.1 = 1.1 ✘
- 11% = 0.11 ✘
- 10% = 0.1 ✔

Wait:
- 1/10 = 0.1
- 0.1 = 0.1
- 10% = 0.1

✔ All three: 1/10, 0.1, 10% = 0.1

> ✔️ Colour: 1/10, 0.1, 10%

---

✔ Grid 5:

```
0.3 | 0.13 | 30%
1/30 | 3/10 | 33%
```

- 0.3 = 0.3 ✔
- 0.13 = 0.13 ✘
- 30% = 0.3 ✔
- 1/30 ≈ 0.033 ✘
- 3/10 = 0.3 ✔
- 33% = 0.33 ✘

So:
- 0.3, 30%, 3/10 → all = 0.3

✔ Equivalent group:
0.3, 30%, 3/10

> ✔️ Colour: 0.3, 30%, 3/10

---

✔ Grid 6:

```
7/10 | 70% | 0.07
0.7 | 7/15 | 57%
```

- 7/10 = 0.7 ✔
- 70% = 0.7 ✔
- 0.07 = 0.07 ✘
- 0.7 = 0.7 ✔
- 7/15 ≈ 0.466 ✘
- 57% = 0.57 ✘

✔ Equivalent group:
7/10, 70%, 0.7

> ✔️ Colour: 7/10, 70%, 0.7

---

✔ Grid 7:

```
9/10 | 90% | 9%
0.9 | 99/100 | 0.19
```

- 9/10 = 0.9 ✔
- 90% = 0.9 ✔
- 9% = 0.09 ✘
- 0.9 = 0.9 ✔
- 99/100 = 0.99 ✘
- 0.19 = 0.19 ✘

✔ Equivalent group:
9/10, 90%, 0.9

> ✔️ Colour: 9/10, 90%, 0.9

---

✔ Grid 8:

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

- 1/100 = 0.01 ✔
- 1% = 0.01 ✔
- 1/10 = 0.1 ✘
- 0.01 = 0.01 ✔
- 1.1 = 1.1 ✘
- 11% = 0.11 ✘

✔ Equivalent group:
1/100, 1%, 0.01

> ✔️ Colour: 1/100, 1%, 0.01

---

✔ Grid 9:

```
4/10 | 4% | 44/100
4/100 | 0.04 | 0.4
```

- 4/10 = 0.4 ✔
- 4% = 0.04 ✘
- 44/100 = 0.44 ✘
- 4/100 = 0.04 ✔
- 0.04 = 0.04 ✔
- 0.4 = 0.4 ✔

Now check:
- 4/10 = 0.4
- 0.4 = 0.4
- But is there a percentage? 40% = 0.4 → but 40% isn't here.
- 4% = 0.04 → matches 4/100 and 0.04

So:
- 4/100 = 0.04
- 4% = 0.04
- 0.04 = 0.04

✔ Equivalent group:
4/100, 4%, 0.04

> ✔️ Colour: 4/100, 4%, 0.04

Note: 4/10 = 0.4, but no 40% or 0.4 with matching percentage — so only one group.

---

✔ Grid 10:

```
1/5 | 20% | 2/100
0.02 | 2/5 | 0.2
```

- 1/5 = 0.2 ✔
- 20% = 0.2 ✔
- 2/100 = 0.02 ✘
- 0.02 = 0.02 ✘
- 2/5 = 0.4 ✘
- 0.2 = 0.2 ✔

So:
- 1/5 = 0.2
- 20% = 0.2
- 0.2 = 0.2

✔ Equivalent group:
1/5, 20%, 0.2

> ✔️ Colour: 1/5, 20%, 0.2

---

✔ Grid 11:

```
40% | 44% | 2/5
0.4 | 0.04 | 1/40
```

- 40% = 0.4 ✔
- 44% = 0.44 ✘
- 2/5 = 0.4 ✔
- 0.4 = 0.4 ✔
- 0.04 = 0.04 ✘
- 1/40 = 0.025 ✘

✔ Equivalent group:
40%, 2/5, 0.4

> ✔️ Colour: 40%, 2/5, 0.4

---

✔ Grid 12:

```
3/5 | 0.6 | 1/6
0.06 | 60% | 16%
```

- 3/5 = 0.6 ✔
- 0.6 = 0.6 ✔
- 1/6 ≈ 0.166 ✘
- 0.06 = 0.06 ✘
- 60% = 0.6 ✔
- 16% = 0.16 ✘

So:
- 3/5 = 0.6
- 0.6 = 0.6
- 60% = 0.6

✔ Equivalent group:
3/5, 0.6, 60%

> ✔️ Colour: 3/5, 0.6, 60%

---

## ✔ Final Answers – What to Colour in Each Grid:

| Grid | Equivalent Values |
|------|-------------------|
| 1 | 0.25, 25%, 1/4 |
| 2 | 0.5, 1/2, 50% |
| 3 | 0.75, 75%, 3/4 |
| 4 | 1/10, 0.1, 10% |
| 5 | 0.3, 30%, 3/10 |
| 6 | 7/10, 70%, 0.7 |
| 7 | 9/10, 90%, 0.9 |
| 8 | 1/100, 1%, 0.01 |
| 9 | 4/100, 4%, 0.04 |
| 10 | 1/5, 20%, 0.2 |
| 11 | 40%, 2/5, 0.4 |
| 12 | 3/5, 0.6, 60% |

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🎨 Section B: Make up your own!

You can create your own sets using known equivalences. For example:

#### Example 1:
- Fraction: 1/2
- Decimal: 0.5
- Percentage: 50%

#### Example 2:
- Fraction: 1/5
- Decimal: 0.2
- Percentage: 20%

#### Example 3:
- Fraction: 3/4
- Decimal: 0.75
- Percentage: 75%

Just ensure they’re all equivalent!

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✔ Summary

The task is to identify and colour the three equivalent values in each grid: one fraction, one decimal, and one percentage.

All correct answers have been identified above.

Let me know if you'd like a printable version or visual highlighting!