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. |
Reciprocal of Fractions
Here is an example (repeated from above)
| 1 | = |
25 cm5 9 gm9 sec4 |
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| 9 gm9 sec4 25 cm5 |
In general the reciprocal of
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a |
unit1 unit2 |
= | a unit1 b unit2 |
is
| 1 | = | b unit2 a unit1 |
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| a unit1 b unit2 |
Division of Quantities and Units
Division by a "fraction" is given by multiplication by the reciprocal of the fraction.
| 72
sec3 3 gm5 |
= | 72
sec3 3 gm5 |
* |
25 cm5 9 gm9 sec4 |
= |
175 |
cm7 |
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| 9 gm9 sec4 25 cm5 |
In general, we divide one fraction involving quantities by another fraction involving quantities as follows
| c unit1 d unit2 |
= |
c unit1 d unit2 |
* |
b unit2 a unit1 |
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| a unit1 b unit2 |
Here the middle and thicker fraction bar is used as a division sign.
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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.