Math worksheet titled "Length and Distance Conversion" that teaches students how to convert measurements like yards, feet, and inches into centimeters and meters using unit conversion with cross-cancellation.

The image you've uploaded is a math worksheet titled *"Length and Distance Conversion: Centimeters and Meters 1"*, designed to teach unit conversion using dimensional analysis (cross-canceling units). The goal is to convert various lengths from U.S. customary units (yards, feet, inches) into metric units (centimeters and meters), using a step-by-step method.

Let’s go through the solution process, explain how each conversion works, and verify the results.

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🔧 Key Conversion Factors Used:

- 1 yard = 3 feet
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters
- 1 meter = 100 centimeters

We use dimensional analysis (also called unit cancellation), where we multiply by fractions that equal 1 (so they don’t change the value), but cancel out unwanted units.

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## ✔ Problem-by-Problem Breakdown & Explanation

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1. 1 yard as centimeters

$$
1 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 91.44 \text{ cm}
$$

- Cancel: yd → ft → in → cm
- Calculation:
$$
1 \times 3 \times 12 \times 2.54 = 91.44 \text{ cm}
$$

✔ Correct.

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2. 10 feet as meters and centimeters

$$
10 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{1 \text{ m}}{100 \text{ cm}} = 3 \text{ m } 4.8 \text{ cm}
$$

- Convert feet → inches → cm → meters
- Total cm:
$$
10 \times 12 \times 2.54 = 304.8 \text{ cm}
$$
- Convert to meters: $304.8 \div 100 = 3.048$ m → 3 m and 4.8 cm

✔ Correct.

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3. 9 yards as meters and centimeters

$$
9 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{1 \text{ m}}{100 \text{ cm}} = 8 \text{ m } 22.96 \text{ cm}
$$

- Step-by-step:
- 9 × 3 = 27 ft
- 27 × 12 = 324 in
- 324 × 2.54 = 822.96 cm
- 822.96 ÷ 100 = 8.2296 m → 8 m and 22.96 cm

✔ Correct.

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4. 50 feet as meters and centimeters

$$
50 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{1 \text{ m}}{100 \text{ cm}} = 15 \text{ m } 24 \text{ cm}
$$

- 50 × 12 = 600 in
- 600 × 2.54 = 1524 cm
- 1524 ÷ 100 = 15.24 m → 15 m and 24 cm

✔ Correct.

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5. 6 feet as centimeters

$$
6 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 182.88 \text{ cm}
$$

- 6 × 12 = 72 in
- 72 × 2.54 = 182.88 cm

✔ Correct.

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6. 70 feet as meters and centimeters

$$
70 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} \times \frac{1 \text{ m}}{100 \text{ cm}} = 21 \text{ m } 33.6 \text{ cm}
$$

- 70 × 12 = 840 in
- 840 × 2.54 = 2133.6 cm
- 2133.6 ÷ 100 = 21.336 m → 21 m and 33.6 cm

✔ Correct.

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7. 10 feet as meters and centimeters (Repeated)

Same as #2 → 3 m 4.8 cm

✔ Correct.

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8. 4 feet as centimeters

$$
4 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 121.92 \text{ cm}
$$

- 4 × 12 = 48 in
- 48 × 2.54 = 121.92 cm

✔ Correct.

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9. 10 feet as meters and centimeters (Repeated again)

Again, same as before → 3 m 4.8 cm

✔ Correct.

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10. 1 foot as centimeters

$$
1 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} \times \frac{2.54 \text{ cm}}{1 \text{ in}} = 30.48 \text{ cm}
$$

- 12 × 2.54 = 30.48 cm

✔ Correct.

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## 📌 Summary of Key Concepts:

- Cross-cancelling units ensures only desired units remain.
- Always use exact conversion factors:
- 1 inch = 2.54 cm (exact)
- 1 ft = 12 in
- 1 yd = 3 ft
- 1 m = 100 cm
- When converting to meters and centimeters, divide total cm by 100:
- Whole number = meters
- Remainder = centimeters

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## ✔ Final Answer Check:
All answers on the worksheet are correct and properly calculated using dimensional analysis.

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📘 How to Use This Method:

For any length conversion:
1. Start with your original measurement.
2. Multiply by conversion fractions (e.g., 12 in / 1 ft).
3. Cancel units step-by-step.
4. Multiply numerators and divide by denominators.
5. Convert final cm to meters if needed.

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