Checklist
Notes
Review of fractions.
Unit conversions.
Problem solving with units.
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M 1030 §2A
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Assignment
Notes
Assignment:
1. p 92 Quick Quiz
2. p 93-95 Excercises 27, 38, 39, 45, 51, 54, 57, 63, 67,
69, 75
3. If you need a review on fractions, Exercises 13 - 18
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Key Words
Notes
Units - a quantity describing what is being measured or
counted
Unit conversion - converting one set of units to another
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Fractions - Inductive Testing
Notes
There are several rules about operations (+, −, ×, ÷) for
fractions:
Add / subtract with common denominators.
Add / subtract with different denominators.
Multiplication.
Reciprocals.
Division (invert and multiply).
Conversion to decimals.
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Fractions - Inductive Testing
Notes
To remember some rules, it helps to inductively test a
claim.
Does the value of a fraction change when you add the
same amount to the numerator and denominator? For
instance, is it true that, for every real number a,
2 2+a
=
?
3 3+a
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Unit conversions
Notes
Unit conversions between simple units is possible through
many ways of writing a conversion factor. For example,
we say 1 foot = 12 inches, or 1 foot per 12 inches, or 12
inches per foot:
1 ft = 12 in. or
(Math 1030)
1 ft
12 in.
or
12 in.
1 ft
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Unit conversions
Notes
Our examples include distances, time, areas, volumes, and
currencies in 2A. We’ll be able to answer questions like,
which is larger, 1 franc or 1 dollar? how many francs are
in a dollar? how many dollars are in a franc? what is the
price in dollars per pound for prices in francs per
kilograms?
Section 2B also has conversions between temperatures,
energy, density, and concentrations.
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Problem solving
Notes
Identifying the units aids problem solving. With the units
properly laid out, the method of approach can be planned
and the answer can have a form that is expected. Then,
carry out and operations on the numbers and units (keep
in mind you cannot add or subtract quantities with
different units). Then the answer can be checked if it has
the proper units.
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Notes