Videos on Operations with Fractions

Refer to methods for obtaining Prime Factorization, GCDs, LCDs as needed in the other video pages.

[Play Video] 3-4 minutes. Equivalent fractions - Lowering and raising terms (the values of numerators and denominators) to obtain equivalent fractions. Simplification involves lowering terms - cancelling common factors or divisors on top and bottom. Addition & subtraction of fractions may involve raising terms to obtain a common denominators. See below.
[Play Video] 2-3 minutes A few examples of Simplifying Fractions - lowering terms by canceling common factors until there are no more common factors, so that the numerator and denominator are relatively prime, that is there prime decompositions have no primes in common.
[Play Video] 2-3 minutes. Multiplying Fractions with cancellation of common factors done first (recommended) or not, with more simplification to be done later.
[Play Video] 5 minutes. How to add fractions using common denominators. Here the common dominators is the lowest or least common denominator (LCD) and its given by the least common multiple (LCM) of the denominators in the fractions added together. Here the listing multiples method is used to compute the LCM. The alternative of not using the LCD for the fractions is explored to show what happens when the LCD is not used.
[Play Video] 3 minutes Another example of how to add fractions with and without the least common denominators with an explanation that not using the LCD (least common denominator) leads to ratios that can be simplified. So use of LCDs is promoted.
[Play Video] 3 minutes - Comparison of Fractions Size or Magnitude, and more examples of the use of common denominators in addition and subtraction.
[Play Video] 3 minutes - Another example of the listing multiples method to find the LCM and thus the LCD for the sum of two fractions.
[Play Video] 4 minutes - Factorization method to obtain a common denominator, here the LCM and thus the LCD for the sum of two fractions. See if you can recognize the GCD of the denominators here. It is not mentioned here. In this example, the LCD is given by a product that does not have to be evaluated explicity due to cancellation of common terms after addition of fractions.
[Play Video] 2 minutes - Fraction Simplification using Prime Decomposition (factorization) to identify common factors for cancellations.
[Play Video] 5 minutes - Product Simplification using Prime Decomposition by Canceling Common Primes, thus avoiding some denominator and numerator multiplication. An alternative common factors as they appear, more opportunistic, is given and is to be recommended.
[Play Video] 5 minutes - How to use Prime Factorization or Decomposition for LCM and LCD for a pair of denominators, an example.

The simplification, multiplication and addition of Fractions may depend on recognition and cancellation of common factors, prime or not. See how GCDs and LCMs (or LCDs) may be used in the addition and multiplication of fractions.

Euclid's Algorithm for computing the GCD of a pair of whole numbers provides a method for simplifying fractions, quickly without using prime decomposition of numerators and denominators.How should appear in a future video.

Three Skills
For
Algebra
Volume 2

Videos - Operations with Fractions

Three Skills For Algebra Volume 2

Videos - Operations with Fractions

Three Skills
For
Algebra
Volume 2