Scale factors and similarity

1
Scale factors and similarity

• Ratios Proportions
• Scale
• Scale diagrams

2
Ratios???

• Ratios are basically a comparison of two
  quantities with the same units.
• Ratios can be expressed
• as a fraction ?
• as a comparison ratio 1 3

3
Proportions???

• A proportion is simply two ratios that are
  equivalent to each other. 
• Proportions are usually used in Algebra to solve
  for some missing information.
• Proportions are solved using cross multiplication

4
Scale

• Scale is a comparison between the actual size of
  an object and the size of the diagram
• The first number in the scale represents the
  drawing, while the second number represents the
  actual measurement of the object
• So, a scale of 1 45 means that 1 unit on the
  drawing represents 45 units on the actual
  object. The size of the unit depends on the
  information provided. It could be cm, m, km,
  thousands of miles..
• Scale can also be stated
• as a percent - for example the diagram
  represents a 66 reduction
• or in words the diagram is two thirds the size
  of the actual object

5
From scale diagrams to actual measurements

• When provided with a scale diagram, it will state
  the scale.
• This diagram of a skateboard uses a scale of 1
  14
• 5.5 cm
• To determine actual size, either use the scale
  ratio provided and multiply (5.5cm x 14 77cm)
• or use a proportion and cross multiply
• 1 5.5
• 14 x x 77

6
Determining scale factor

• Scale diagram measurement
• actual measurement
• If you are given a diagram, and know the actual
  measurement of an object, you can determine the
  scale factor!
• Example an actual Canadian quarter has a
  diameter of 23.88 mm. Measure the diagram of the
  quarter that you have been given.
• Set up the proportion for scale 14
• 23.88 o.586 0.6 scale factor

7
Practice makes perfect

• Homework
• Page 143 1 10, 13, 18, 19