Equivalent Ratios with Ratio Tables, Double Number Lines, and Tape ... - Free Printable

Let’s solve each problem step by step, using the concept of equivalent ratios and proportional reasoning.

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## 🔢 PART 1: FILL IN THE TABLES (Equivalent Ratios)

We need to find missing values so that each column forms an equivalent ratio — meaning the top number divided by the bottom number is the same in every column.

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🟦 Table 1:

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

Let’s find the ratio for the third column:
20 / 60 = 1/3

So every top number should be 1/3 of the bottom number.

- First column: top = 90 × (1/3) = 30
- Second column: top = 48 × (1/3) = 16
- Fourth column: bottom = 10 ÷ (1/3) = 10 × 3 = 30

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

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🟦 Table 2:

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

Find ratio from first column: 4 / 24 = 1/6

So top = 1/6 × bottom

- Second column: top = 18 × (1/6) = 3
- Third column: top = 60 × (1/6) = 10
- Fourth column: bottom = 5 ÷ (1/6) = 5 × 6 = 30

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

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🟦 Table 3:

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

Use third column: 9 / 90 = 1/10

Top = 1/10 × bottom

- First column: top = 50 × (1/10) = 5
- Second column: bottom = 40 ÷ (1/10) = 40 × 10 = 400
- Fourth column: top = 300 × (1/10) = 30

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

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🟦 Table 4:

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

Use second column: 20 / 60 = 1/3

Top = 1/3 × bottom

- First column: bottom = 6 ÷ (1/3) = 6 × 3 = 18
- Third column: top = 42 × (1/3) = 14
- Fourth column: bottom = 10 ÷ (1/3) = 10 × 3 = 30

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

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## 📊 PART 2: TAPE DIAGRAM PROBLEMS

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🧵 Problem 1: Debby’s Clothing Store

> Sold 312 shirts. Ratio of short sleeve to long sleeve = 2:6 → which simplifies to 1:3

Total parts = 1 + 3 = 4 parts

Each part = 312 ÷ 4 = 78

Short sleeve = 1 part = 78 shirts

Long sleeve = 3 parts = 3 × 78 = 234

✔ Answer: 78 short sleeve shirts

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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

Vanilla = 2 parts = 2 × 166 = 332

✔ Answer: 498 chocolate shakes

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## 📈 PART 3: DOUBLE NUMBER LINE PROBLEMS

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👦👧 Problem 1: Boys to Girls Ratio

> 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

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🍫📊 Problem 2: Fundraiser 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

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💰🥜 Problem 3: Cashew Sale

> 10 bags cost $9
> Want 50 bags → how much?

50 ÷ 10 = 5 groups

Each group costs $9 → 5 × 9 = $45

✔ Answer: $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 of cashews: $45

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Let me know if you’d like visuals or step-by-step diagrams for any part!