Ratios with Tape Diagrams worksheet from Khan Academy.

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Let me walk you through how to solve common types of ratio problems using tape diagrams, and if you provide the specific details or numbers from the worksheet, I can give you a tailored solution.

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🔍 What is a Tape Diagram?

A tape diagram is a visual tool that represents ratios using rectangular bars (or "tapes") divided into equal parts. It helps compare quantities and solve ratio problems by showing proportional relationships.

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📌 Common Types of Ratio Problems

Let’s assume the worksheet includes problems like:

#### Example Problem 1:
> The ratio of blue crayons to green crayons is 3:2. If there are 15 blue crayons, how many green crayons are there?

Step-by-step Solution Using a Tape Diagram:

1. Draw two tapes: One for blue, one for green.
- Blue: 3 equal parts
- Green: 2 equal parts

2. Since blue = 15 and it's 3 parts:
- Each part = 15 ÷ 3 = 5

3. Green has 2 parts → 2 × 5 = 10 green crayons

✔ Answer: 10 green crayons

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#### Example Problem 2:
> There are 12 red pencils and 8 blue pencils. Draw a tape diagram and find the ratio.

Solution:

1. Draw two tapes:
- Red: 12 units
- Blue: 8 units

2. Find the GCF of 12 and 8 → GCF = 4

3. Divide each by 4:
- Red: 12 ÷ 4 = 3 parts
- Blue: 8 ÷ 4 = 2 parts

4. So, the simplified ratio is 3:2

✔ Answer: 3:2

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#### Example Problem 3:
> A mixture of paint has a ratio of white to blue of 5:3. If you have 20 liters of white paint, how much blue paint do you need?

Tape Diagram Steps:

- White: 5 parts = 20 liters → 1 part = 20 ÷ 5 = 4 liters
- Blue: 3 parts = 3 × 4 = 12 liters

✔ Answer: 12 liters of blue paint

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✔ Tips for Solving Tape Diagram Problems:

1. Identify the ratio given (e.g., 3:2).
2. Draw bars with equal segments representing each part.
3. Use known values to find the value of one part.
4. Multiply to find unknown quantities.
5. Simplify ratios when possible.

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If you can describe the exact problem(s) on the worksheet (e.g., “The ratio of boys to girls is 4:5, and there are 20 boys…”), I can give you the exact solution with steps and even draw the tape diagram in text.

Please share the details of the questions, and I’ll solve them step by step!