Download Unit 3: Ratios and Proportional Relationships

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Real world Problems
There are examples of finding the cost of flooring using proportional relationships
and given information.
There are questions like using proportions to modify a recipe to create a different
number of servings.
The next unit is about percentages and will go in depth with percentage problems. In
this unit we will “plant the seed” on discounts, markups and changes based on
fractions. This will then tie into the percentages for the next unit.
Scale Drawings
Scale drawings are reductions or enlargements of a two-dimensional picture. The
dimensions from the original to the scale drawing are proportional and have a scale
factor. The scale factor is a constant of proportionality.
Scale Drawings
When the units are the same:
The scale factor is the same as the constant of proportionality.
𝑛𝑒𝑤
= 𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙
When the scale factor is greater than one, it is an enlargement.
When the scale factor is less than one, it is a reduction
When the units are different:
The scale is a ratio. i.e. 1 in. = 4 ft. You set up proportions to find the missing length.
For example: 2 ½ in = _____ft.
1
2 2 𝑖𝑛
𝑥 𝑓𝑡
=
1𝑖𝑛
4𝑓𝑡
Method 1: You multiply 1 x 2 ½ to get 2 1/2 , so multiply 4 x 2 ½ to get 10ft.
Method 2: Use cross products (multiplication) to get the answer.
1
2
2
𝑥
=
1
4
1(x) = 2 ½ (4)
X = 10
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