Math worksheet for finding and simplifying ratios using visual shapes.

Let's solve each ratio problem step by step based on the image provided. We'll count the number of each symbol and then compute the required ratios.

---

Problem 1: Hearts (♥) and Plus Signs (+)

Image:
- Rows of hearts (♥) and plus signs (+)
- Each row has 4 hearts and 8 plus signs
- There are 5 rows

So:
- Total ♥ = 5 × 4 = 20
- Total + = 5 × 8 = 40

#### (a) Ratio of ♥ to +
- Ratio = 20 : 40
- Simplified: divide both by 20 → 1 : 2

#### (b) Ratio of + to (♥ + +)
- Total symbols = 20 + 40 = 60
- Ratio of + to total = 40 : 60
- Simplified: divide by 20 → 2 : 3

✔ Answer 1:
- ♥ to + = 20 : 40 = 1 : 2
- + to (♥ + +) = 40 : 60 = 2 : 3

---

Problem 2: Black Circles (●) and Orange Crosses (✚)

Image:
- Grid of black circles (●) and orange crosses (✚)
- The grid is 7 rows high, 9 columns wide
- Count:
- ●: First 7 columns in all 7 rows → 7×7 = 49
- ✚: Last 2 columns → 7×2 = 14

Wait — actually, looking carefully:

The pattern:
- 7 columns of ● and 2 columns of ✚
- So:
- ● = 7 columns × 7 rows = 49
- ✚ = 2 columns × 7 rows = 14

#### (a) Ratio of ● to ✚
- 49 : 14
- Simplify: divide by 7 → 7 : 2

#### (b) Ratio of ✚ to (● + ✚)
- Total = 49 + 14 = 63
- ✚ : total = 14 : 63
- Simplify: divide by 7 → 2 : 9

✔ Answer 2:
- ● to ✚ = 49 : 14 = 7 : 2
- ✚ to (● + ✚) = 14 : 63 = 2 : 9

---

Problem 3: Black Diamonds (◆) and Blue Triangles (▲)

Image:
- Two rectangles side by side
- Left: 6 rows × 7 columns = 42 ◆
- Right: 6 rows × 8 columns = 48 ▲

Wait — let’s check:
- Both rectangles have 6 rows
- Left rectangle: 7 columns of ◆ → 6×7 = 42
- Right rectangle: 8 columns of ▲ → 6×8 = 48

#### (a) Ratio of ◆ to ▲
- 42 : 48
- Simplify: divide by 6 → 7 : 8

#### (b) Ratio of ▲ to (◆ + ▲)
- Total = 42 + 48 = 90
- ▲ : total = 48 : 90
- Simplify: divide by 6 → 8 : 15

✔ Answer 3:
- ◆ to ▲ = 42 : 48 = 7 : 8
- ▲ to (◆ + ▲) = 48 : 90 = 8 : 15

---

Problem 4: Orange Crosses (✚) and Red Circles (●)

Image:
- Two groups:
- Left: 5 rows × 8 columns = 40 ✚
- Right: 5 rows × 4 columns = 20 ●

So:
- ✚ = 40
- ● = 20

#### (a) Ratio of ✚ to ●
- 40 : 20 = 2 : 1

#### (b) Ratio of ● to (✚ + ●)
- Total = 40 + 20 = 60
- ● : total = 20 : 60 = 1 : 3

✔ Answer 4:
- ✚ to ● = 40 : 20 = 2 : 1
- ● to (✚ + ●) = 20 : 60 = 1 : 3

---

✔ Final Answers:

| Problem | Ratio | Answer (Unsimplified) | Simplified |
|--------|-------|------------------------|------------|
| 1a | ♥ to + | 20 : 40 | 1 : 2 |
| 1b | + to (♥ + +) | 40 : 60 | 2 : 3 |
| 2a | ● to ✚ | 49 : 14 | 7 : 2 |
| 2b | ✚ to (● + ✚) | 14 : 63 | 2 : 9 |
| 3a | ◆ to ▲ | 42 : 48 | 7 : 8 |
| 3b | ▲ to (◆ + ▲) | 48 : 90 | 8 : 15 |
| 4a | ✚ to ● | 40 : 20 | 2 : 1 |
| 4b | ● to (✚ + ●) | 20 : 60 | 1 : 3 |

---

You can now fill in the blanks on the worksheet accordingly.

Let me know if you'd like a printable version or explanation for any part!