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# Chapter 8: Proportional Reasoning

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## Chris Mok

on 27 January 2015

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#### Transcript of Chapter 8: Proportional Reasoning

Chapter 8: Proportional Reasoning (First Half)
Chapter Focuses
8.1: Comparing and Interpreting Rates

8.2: Solving Problems That Involve Rates

8.3: Scale Diagrams
8.1 Comparing and Interpreting Rates
Key Idea:
Rates can be represented in a variety of ways. The representation should depend on your purpose.
Example
Julia can buy a 7 kg turkey from Superstore for \$25.52. Costco has turkeys advertised in its weekly
flyer for \$1.27/lb. There are about 2.2 lbs in 1 kg. Which store has the lower price?
8.2: Solving Problems That Involve Rates
Key Idea:
When you are given a rate problem that involves an unknown, you can solve the problem using a variety of strategies.
Example
A faucet leaks 1 mL per minute. How many litres are wasted in a week?
Superstore: \$25.52÷7kg= \$3.64/kg

Costco: (\$1.27÷1lb)x(2.2lb÷1kg)= \$2.79

Costco sells Turkeys at a lower price

*1mL= .001L

(.001÷1min)x(60min÷1hr)x(24hrs÷1Day)x(7Days÷1Week)= 10.08L/Week

In one week, the faucet will leak 10.08 litres.
8.3: Scale Diagrams
Key Ideas:
Scale diagrams can be used to represent 2-D shapes. To create a scale diagram, you must determine an appropriate scale to use. This depends on the dimensions of the original shape and the size of diagram that is needed.
The scale factor represents the ratio of a distance measurement of a shape to the corresponding distance measurement of a similar shape, where both measurements are expressed using the same units.
Example
Using the scale factor of 2/5 what is the new dimensions of a rectangle with the length of 21 metres and a width of 13 metres?
L: (21)x(2/5)= 8.4m
W: (13)x(2/5)= 5.2m

The reduced rectangle is now 8.4m x 5.2m
21m
13m
5.2m
8.4m
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