Math worksheet teaching students to represent ratios using tape diagrams, including problems for dividing amounts according to given ratios.

Let's solve this worksheet step by step.

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## Section A: Recognizing Tape Diagrams

Goal: Match each ratio to the tape diagram that visually represents it.

We have 4 ratios and 4 diagrams. We need to count the number of equal-sized boxes in each part of the diagram to match the ratio.

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Ratio: 3:1

- This means 3 parts to 1 part.
- Look for a diagram with one row of 3 boxes and another row of 1 box (or vice versa).
- Diagram 1 (top left): Has 3 boxes on top, 1 box below → Matches 3:1

✔ 3:1 → First diagram

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Ratio: 1:2

- 1 part to 2 parts.
- Look for a diagram with 1 box and 2 boxes.
- Diagram 3 (bottom left): Has 1 box on top, 2 boxes below → Matches 1:2

✔ 1:2 → Third diagram

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Ratio: 2:1:3

- Three-part ratio: 2, then 1, then 3.
- Look for a diagram with 3 rows or sections: 2 boxes, 1 box, 3 boxes.
- Diagram 4 (bottom right): Has 2 boxes (top), 1 box (middle), 3 boxes (bottom) — but arranged vertically? Actually, looking at the shape: it’s an L-shape with 2 on top, 1 on side, 3 on bottom? Wait — let’s count total boxes per “section”.

Actually, let’s re-express:

Looking at Diagram 2 (top right): It has 2 boxes on top row, 1 box on bottom left, 3 boxes total? No.

Wait — Diagram 4 (bottom right) is a 3x3 grid missing some? Let’s count the boxes:

Actually, Diagram 2 (second from left): Top row: 3 boxes, bottom row: 2 boxes → that’s 3:2.

Diagram 4 (last one): Looks like:
- Top row: 2 boxes
- Middle: 1 box (offset)
- Bottom: 3 boxes

That’s 2 + 1 + 3 = 6 boxes total, split as 2, 1, 3 → perfect for 2:1:3

✔ 2:1:3 → Fourth diagram

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Ratio: 3:2

- 3 parts to 2 parts.
- Diagram 2 (second from left): Top row: 3 boxes, bottom row: 2 boxes → matches 3:2

✔ 3:2 → Second diagram

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✔ Final Matching for Section A:

- 3:1 → First diagram
- 1:2 → Third diagram
- 2:1:3 → Fourth diagram
- 3:2 → Second diagram

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## Section B: Dividing an amount into a given ratio

Use tape diagrams to divide amounts. The key idea: add up the parts, divide total amount by total parts → value per part → multiply by each person’s parts.

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1) Hayley and Tom share $160 in the ratio 5:3

Tape diagram shows:
- Hayley: 5 boxes
- Tom: 3 boxes
→ Total parts = 5 + 3 = 8 parts

Each part = $160 ÷ 8 = $20

- Hayley: 5 × $20 = $100
- Tom: 3 × $20 = $60

✔ Hayley: $100, Tom: $60

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2) Lewis and Ruby share $95 in the ratio 2:3

Tape diagram:
- Lewis: 2 boxes
- Ruby: 3 boxes
→ Total parts = 2 + 3 = 5 parts

Each part = $95 ÷ 5 = $19

- Lewis: 2 × $19 = $38
- Ruby: 3 × $19 = $57

✔ Lewis: $38, Ruby: $57

*(Also, fill in the blank under the bracket: $95)*

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3) Kyle and Keisha share $66 in the ratio 5:6

Tape diagram:
- One person: 5 boxes → Kyle
- Other: 6 boxes → Keisha
→ Total parts = 5 + 6 = 11 parts

Each part = $66 ÷ 11 = $6

- Kyle: 5 × $6 = $30
- Keisha: 6 × $6 = $36

✔ Kyle: $30, Keisha: $36

*(Fill in labels: top row = Kyle, bottom = Keisha; total = $66)*

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4) Ayah and Saira share $120 in the ratio 3:2

You must construct your own bar model.

#### Step-by-step:

- Draw two bars:
- Ayah’s bar: 3 equal boxes
- Saira’s bar: 2 equal boxes
- Total parts = 3 + 2 = 5 parts
- Each part = $120 ÷ 5 = $24
- Ayah: 3 × $24 = $72
- Saira: 2 × $24 = $48

✔ Ayah: $72, Saira: $48

*(Label your drawing: Ayah with 3 boxes, Saira with 2 boxes, total $120)*

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## ✔ FINAL ANSWERS:

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Section A Matching:

- 3:1 → First diagram (3 boxes over 1)
- 1:2 → Third diagram (1 box over 2)
- 2:1:3 → Fourth diagram (2, 1, 3 boxes in L-shape)
- 3:2 → Second diagram (3 over 2)

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Section B:

1)
Hayley: $100
Tom: $60

2)
Lewis: $38
Ruby: $57
*(Total label: $95)*

3)
Kyle: $30
Keisha: $36
*(Label bars: Kyle (top, 5 boxes), Keisha (bottom, 6 boxes); Total: $66)*

4) *(Your own model)*
Ayah: $72
Saira: $48

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Let me know if you’d like a visual sketch of the bar models!