Math worksheet focusing on equivalent ratios using tables, tape diagrams, and double number lines.

Let’s solve each part of the worksheet step by step.

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## Part 1: Equivalent Ratios — Tables

We need to find missing values in tables so that each column represents an equivalent ratio (i.e., the top number divided by the bottom number is constant in each table).

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Table 1:

```
? ? 20 10
90 48 60 ?
```

Find the ratio: Look at column 3 → 20 / 60 = 1/3

So, every top number is 1/3 of the bottom number.

- Column 1: top = 90 × (1/3) = 30
- Column 2: top = 48 × (1/3) = 16
- Column 4: top = 10 → bottom = 10 ÷ (1/3) = 30

✔ Completed Table 1:
```
30 16 20 10
90 48 60 30
```

---

Table 2:

```
4 ? ? 5
24 18 60 ?
```

Ratio: 4 / 24 = 1/6

Check: 18 × (1/6) = 3 → so top should be 3
60 × (1/6) = 10
5 → bottom = 5 ÷ (1/6) = 30

✔ Completed Table 2:
```
4 3 10 5
24 18 60 30
```

---

Table 3:

```
? 40 9 ?
50 ? 90 300
```

Use column 3: 9 / 90 = 1/10

So top = 1/10 × bottom

- Column 1: top = 50 × (1/10) = 5
- Column 2: bottom = 40 ÷ (1/10) = 400
- Column 4: top = 300 × (1/10) = 30

✔ Completed Table 3:
```
5 40 9 30
50 400 90 300
```

---

Table 4:

```
6 20 ? 10
? 60 42 ?
```

Use column 2: 20 / 60 = 1/3

So top = 1/3 × bottom

- Column 1: bottom = 6 ÷ (1/3) = 18
- Column 3: top = 42 × (1/3) = 14
- Column 4: bottom = 10 ÷ (1/3) = 30

✔ Completed Table 4:
```
6 20 14 10
18 60 42 30
```

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## Part 2: Tape Diagrams — Word Problems

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Problem 1: Debby’s Clothing Store

> Sold 312 shirts. Ratio short sleeve : long sleeve = 2:6. How many short sleeve shirts?

Simplify ratio: 2:6 = 1:3

Total parts = 1 + 3 = 4 parts

Each part = 312 ÷ 4 = 78

Short sleeve = 1 part = 78 shirts

✔ Answer: 78 short sleeve shirts

*(Tape diagram: Short = 1 box, Long = 3 boxes, total 4 boxes = 312 → each box = 78)*

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Problem 2: Adam’s Ice Cream Hut

> Sold 830 shakes. Chocolate : Vanilla = 6:4 → simplify to 3:2

Total parts = 3 + 2 = 5 parts

Each part = 830 ÷ 5 = 166

Chocolate = 3 parts = 3 × 166 = 498

✔ Answer: 498 chocolate shakes

*(Tape diagram: Chocolate = 3 boxes, Vanilla = 2 boxes, total 5 boxes = 830 → each box = 166)*

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## Part 3: Double Number Lines — Word Problems

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Problem 1: Boys to Girls at Park

> Ratio boys : girls = 4:5. There are 8 boys. How many girls?

Set up proportion:

4 boys → 5 girls
8 boys → ? girls

Since 8 is 2×4, multiply girls by 2 → 5 × 2 = 10 girls

✔ Answer: 10 girls

*(Double number line: Boys: 4 → 8; Girls: 5 → 10)*

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Problem 2: School Fundraiser — Boxes and Points

> For every 9 boxes sold, earn 4 points. If you sell 72 boxes, how many points?

72 ÷ 9 = 8 groups

Each group gives 4 points → 8 × 4 = 32 points

✔ Answer: 32 points

*(Double number line: Boxes: 9 → 18 → 27 → ... → 72; Points: 4 → 8 → 12 → ... → 32)*

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Problem 3: Cashews Sale

> 10 bags cost $9. Want 50 bags. How much?

50 ÷ 10 = 5 groups

Each group costs $9 → 5 × 9 = $45

✔ Answer: $45

*(Double number line: Bags: 10 → 20 → 30 → 40 → 50; Price: $9 → $18 → $27 → $36 → $45)*

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## ✔ FINAL ANSWERS SUMMARY:

Tables:

Table 1:
```
30 16 20 10
90 48 60 30
```

Table 2:
```
4 3 10 5
24 18 60 30
```

Table 3:
```
5 40 9 30
50 400 90 300
```

Table 4:
```
6 20 14 10
18 60 42 30
```

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Tape Diagrams:

- Short sleeve shirts: 78
- Chocolate shakes: 498

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Double Number Lines:

- Girls at park: 10
- Points earned: 32
- Cost for 50 bags: $45

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Let me know if you’d like a visual sketch of the tape diagrams or number lines!