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Foundations & Pre-Calculus 10 Imperial System

Lesson focus: To be able to convert between different imperial units.

• the imperial system is a measurement system that is still in use in industry and the trades in Canada as well as in the United States

• as compared to the metric system, there is no consistent multiple between the units

• the relationships between common imperial units are given below

a) 1 foot (ft) = ______ inches (in)

b) 1 yard (yd) = ______ feet (ft) = ______ inches (in)

c) 1 mile (mi) = ________ yards (yd) = ________ feet (ft)

• when converting between imperial units, there are two different methods we can use

i.e. proportional reasoning or unit analysis

e.g. Convert 98 inches into feet.

a) Proportional reasoning b) Unit analysis

• remember to cross-multiply and divide when converting by proportional reasoning

• remember to cross cancel the same units when converting by unit analysis

e.g. Convert 5 yards into inches. (two different methods)

e.g. Convert the following. Leave all answers in to the nearest tenth (when necessary).

1) 36 ft = ___________ yd 2) 7 mi = _____________ ft

3) 42 in = _____________ ft 4) 6.3 yd = _____________ in

• we can also use proportional reasoning when solving problems involving map scales

e.g. If a map has a scale of 1:500 000 (drawing size : actual size), what would a distance of 3 ½ inches represent (to the nearest mile)?

• a referent is used to estimate a measure

e.g. a referent for a length of 1 mm is the thickness of a dime

• you can use the table below to help your remember your imperial length referents

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