Scale Factor of Scale Drawings

Determining Scale Factor

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

Example 1

  • Model or scale: 0.75

  • Actual or original: 1.25

  • Ratio setup: 0.751.25\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 35\frac{3}{5}.

Example 2

  • Scale or model: 3.5

  • Original: 2

  • Ratio setup: 3.52\frac{3.5}{2}

  • Dividing 3.5 by 2 results in 1.75.

  • 1. 75 is equivalent to one and seventy-five hundredths, or 1341 \frac{3}{4}.

  • Converting 1341 \frac{3}{4} to an improper fraction gives 74\frac{7}{4}.

Example 3

  • Scale: 0.75

  • Original: 1.75

  • Ratio setup: 0.751.75\frac{0.75}{1.75}

  • Dividing 0.75 by 1.75 results in a decimal.

  • Converting 0.751.75\frac{0.75}{1.75}to a fraction gives 37\frac{3}{7}.

Example 4

  • Scale: 6

  • Original: 4

  • Ratio setup: 64\frac{6}{4}

  • Simplifying 64\frac{6}{4} gives 32\frac{3}{2}.

  • Converting 32\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.