Scale Drawings and Scale Factor - Beth Mathis | Library | Formative - Free Printable

Let's solve each problem step by step to determine the scale factor of each scale drawing. The scale factor is the ratio of the dimensions of the scale drawing to the original image.

We use the formula:

$$
\text{Scale Factor} = \frac{\text{Dimension of Scale Drawing}}{\text{Dimension of Original Image}}
$$

We’ll simplify fractions where possible.

---

Problem 1

- Original Image: 1.25 in
- Scale Drawing: 0.75 in

$$
\text{Scale Factor} = \frac{0.75}{1.25}
$$

Convert to fractions:
$$
= \frac{3/4}{5/4} = \frac{3}{4} \times \frac{4}{5} = \frac{3}{5}
$$

✔ Scale Factor = $ \frac{3}{5} $

---

Problem 2

- Original Image: 2 inches
- Scale Drawing: 3.5 inches

$$
\text{Scale Factor} = \frac{3.5}{2} = \frac{7/2}{2} = \frac{7}{2} \div 2 = \frac{7}{2} \times \frac{1}{2} = \frac{7}{4}
$$

Or directly:
$$
\frac{3.5}{2} = \frac{35}{20} = \frac{7}{4}
$$

✔ Scale Factor = $ \frac{7}{4} $

---

Problem 3

- Original Image: 1.75 in
- Scale Drawing: 0.75 in

$$
\text{Scale Factor} = \frac{0.75}{1.75}
$$

Convert to fractions:
$$
= \frac{3/4}{7/4} = \frac{3}{4} \times \frac{4}{7} = \frac{3}{7}
$$

✔ Scale Factor = $ \frac{3}{7} $

---

Problem 4

- Original Image: 4 cm
- Scale Drawing: 6 cm

$$
\text{Scale Factor} = \frac{6}{4} = \frac{3}{2}
$$

✔ Scale Factor = $ \frac{3}{2} $

---

Problem 5

- Original Image: 12 cm
- Scale Drawing: 6 cm

$$
\text{Scale Factor} = \frac{6}{12} = \frac{1}{2}
$$

✔ Scale Factor = $ \frac{1}{2} $

---

Problem 6

- Original Image: 3 cm
- Scale Drawing: 5 cm

$$
\text{Scale Factor} = \frac{5}{3}
$$

✔ Scale Factor = $ \frac{5}{3} $

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✔ Final Answers:

| Problem | Scale Factor |
|--------|--------------|
| 1 | $ \frac{3}{5} $ |
| 2 | $ \frac{7}{4} $ |
| 3 | $ \frac{3}{7} $ |
| 4 | $ \frac{3}{2} $ |
| 5 | $ \frac{1}{2} $ |
| 6 | $ \frac{5}{3} $ |

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🔍 Explanation Summary:

- Scale factor > 1: Enlargement (drawing is bigger than original)
- Scale factor < 1: Reduction (drawing is smaller than original)
- Scale factor = 1: Same size

So:
- Problems 2, 4, and 6 are enlargements
- Problems 1, 3, and 5 are reductions

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