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. |
Changing and Converting Units
Recall 1 metre = 100 centimetres and 1 decimetre = 10 centimetres. Here the unlike units metre, centimetre and decimetre are of the same type [L] for length. So
9 metres + 8 decimetres + 3 centimetres
= 9 x 100 centimetres + 8 x 10 centimetres + 13 centimetres
= (900 + 80 + 3) centimetres
= 983 centimetres.
Alternatively 983 centimetres = 98.3 decimetres = 9.83 metres.
In calculations involving lengths, we can replace
- metres by 100 centimetres or 10 decimetres;
- decimeters by 0.1 metres or 10 centimetres; and
- centimetres by 0.01 metres or 0.1 decimetres.
Here I have use decimal notation for the fractions (1/10) and (1/100) for convenience while typing this page. That is, we could use fraction notation and mixed number notation as well in the foregoing.
Similarly, we can use the equations
1 minute = 60 seconds,
1 hour = 60 minutes,
1 day = 24 hours
to go back and forward between unlike units of measurement of time [T].
Further examples could follow using units of mass and force or weight.
Remark - exceptional case: The equality sign is usually has the
reflective property that a = b when and only when b = a. Here may read
the equality sign to mean the same as or is equivalent to. For
writing
gives and comes from
But with a change of units we may write 3 apples + 4
bananas = 7 fruits and 2 apples + 5 oranges = 7 fruits The change of units here does not allow to conclude with out further information that
because we might also have
In discussing fruits of different types, 3 apples + 4 bananas = 7 fruits is equivalent to 7 fruits = 3 apples + 4 bananas when and only when we are situation where all individual fruits appearing are considered equivalent when and only when the equality sign means has the same value as and is not be interpreted as yields. |
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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.