Scale Factor of Scale Drawings

Determining Scale Factor

• The scale factor of a scale drawing is typically determined using the formula:
  \frac{\text{model or scale}}{\text{actual or original}}

Example 1

• Model or scale: 0.75

• Actual or original: 1.25

• Ratio setup: \frac{0.75}{1.25}

• Dividing 0.75 by 1.25 results in 0.6.

• 0. 6 is equivalent to six tenths, which simplifies to \frac{3}{5}.

Example 2

• Scale or model: 3.5

• Original: 2

• Ratio setup: \frac{3.5}{2}

• Dividing 3.5 by 2 results in 1.75.

• 1. 75 is equivalent to one and seventy-five hundredths, or 1 \frac{3}{4}.

• Converting 1 \frac{3}{4} to an improper fraction gives \frac{7}{4}.

Example 3

• Scale: 0.75

• Original: 1.75

• Ratio setup: \frac{0.75}{1.75}

• Dividing 0.75 by 1.75 results in a decimal.

• Converting \frac{0.75}{1.75}to a fraction gives \frac{3}{7}.

Example 4

• Scale: 6

• Original: 4

• Ratio setup: \frac{6}{4}

• Simplifying \frac{6}{4} gives \frac{3}{2}.

• Converting \frac{3}{2} to a decimal gives 1.5.

Key Considerations

• Pay attention to whether the question asks for the answer as a decimal, fraction, or ratio.

• Use division to convert fractions to decimals.

• Convert to improper fractions when necessary to express the ratio in the desired format.