YOU are better than YOU think. Show yourself how:
|
-/[]\-
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.
|
-/[]\- 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. |
4. Simple Fraction of a Simple Fraction
By definition or convention above, 4 fifths of an object is 4 times a fifth of the object. If the object itself is a simple fraction of another object, we would have 4 fifths of the simple fraction would be 4 times a fifth of the simple fraction. Examples follow.
| 1 4 |
of | 3 10 |
= | 3 4*10 |
So 7 quarters would be seven times the latter.
| 7 4 |
of | 3 10 |
= | 7* | 3 4*10 |
= | 7*3 4*10 |
= | 21 40 |
We may replace the word of by the times symbol * to get
| 7 4 |
* | 3 10 |
= | 7* | 3 4*10 |
= | 7*3 4*10 |
= | 21 40 |
In general, we may compute a simple fraction of a simple fraction as follows:
| A N |
of | B M |
= | A*B N*M |
or with a times symbol * instead of the word of, we write.
| A N |
* | B M |
= | A*B N*M |
In the resulting fraction, the the numerator (top) is a product of the numerators of the factors and the denominator (bottom) is a product of the denominator of the factors.
The foregoing describes the first method for multiplying fractions. After that, we would simplify the resulting fraction by canceling common factors in the products numerator and denominator. The rule here is multiply first and cancel second. But this order can be changed. Cancellation first leads to smaller numbers and a quicker way (usually more efficient) to compute the simplified form of the product.
More examples of products of simple fractions
A)
| 6 7 |
* | 8 9 |
= | 6*8 7*9 |
= | 48 63 |
B)
| 5 12 |
* | 9 10 |
= | 5*9 12*10 |
= | 45 120 |
= | 9 24 |
C)
| 2 3 |
* | 2 3 |
= | 2*2 3*3 |
= | 4 9 |
Here we are multiplying first and canceling common factors second following the general rule above. But a modification of it is more efficient. See below.
Do you see how the figure
3
42
3suggests or confirms
| 3 4 |
* | 2 3 |
= | 6 12 |
= | 1 2 |
|
|
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.