YOU are better than YOU think. Show yourself how:
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Logic
Mastery Do not leave here without it - Logic mastery will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.
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-/[]\- After logic, (a) continue reading Three Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes & More Math, chapters 2 to 6; For online automated help in senior high school maths & calculus, visit quickmath.com For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com With overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck. |
Slopes with Units - Rates of Change
For a straight line graph of a first quantity Q1 versus a
second quantity Q2, the slope
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That is, the units of slope is the ratio given by the unit of
rise (vertical axis) over the units of run (the horizontal axis).
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Improper Units
The unit 1 is an improper unit. The units 1 radian = 1. So the degree = [(p)/180] and the one percentage 1.0% = [1/100] are further examples of improper units, that is units that are multiples of real numbers. (The discussion of improper units is unique to this author.
Units in computations have been a concern for chemists and physicists but not so far for mathematicians. The codification of mathematics needs to be extended to include units as a service to other disciplines.
Cost Versus Quantity -Rates
The metric BWGZ gravel supply business charges the amount
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For w = 2000 lbs of gravel, the cost would be
since 1 kg = 2.2046 lbs at the surface of the earth.
C
=
$20.00 + 2000 lbs·
$15.00
50 kg
=
$20.00 + 2000 ·
15.00
50
$·
lbs
kg
=
$20.00 + 2000 ·
15.00
50
$·
lbs
2.2046 lbs
=
$20.00 +
æ
ç
è
2000·
15.00
50
·
1
2.2046
ö
÷
ø
$
=
$20.00 + $272.16 = $292.16
FOOTNOTE: At the earth surface, a one pound mass and one pound
weight are identical measures of material. There is a distinction
between mass and weight that has to be considered for calculations
away from the earth surface. Students of physics should know
why.
In computations, we follow the
convention that units can appear before or after the number
in it. In contrast, in the presentation of results, the
placement of the unit before or after depends on
grammatical or cultural preferences of a cosmetic nature.
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www.whyslopes.com
Fractions, Ratios, Units, Rates
& Proportionality
Fraction
Starter Lesson
(simplify, multiply, divide & then add or subtract)
An Alternative Starter
Lesson
(take your pick, or try both)
Arithmetic Videos - Real Player Format
Decimal Addition
Methods
Decimal
Subtraction Methods
Decimal
Multiplication Methods
Decimal Division
Methods
Fractions
Primes
Greatest Common
Divisors
Least Common Multiples
Square Root
Simplification
Area Content Summary
- Fraction Starter Lesson
- Real Player Videos on Operations with Primes and Fractions
- Continuous Ruler & Line Segment
model for fractions and operations on fractions - Number Theory Area points to the general model. - Distinction between Ratios and Fractions, a nuance: While binary ratios a:b may be identified with a fraction, triple ratios a:b:c and further multiple ratios cannot.
- Saying how to add and subtract like monomials in units and their powers, and saying how multiply and divide like and unlike monomials leads to fraction like expressions involving units and a framework for discussion rates - ratios of quantities - a framework for handling proportionality constants, and framework for carrying units through calculation in quantitative disciplines
Hint: See site area on solving linear equations to strengthen fraction sense and algebra skills together. Good luck.