# Basic Multiplication and Division (Curious Concepts Precalculus 1.3)

Updated on September 4, 2013 ## Self-explain Learning Technique

Self-explain Learning Technique helps people to better comprehend, and remember any thing they want to learn. It my sound strange, but it is many times more effective then re-reading. To use this technique, give short answers to the prompted questions. Incorporate previous knowledge-and-life experience into your answer will make this learning technique more effective. On average it improves learning by over 2.5 standard deviations; the difference between a C student and an A student.

Multiplication is adding the same number so many times. 5 times, 4; is were we get that times saying. What is being said, in any of the ways to express it; (5)4, 5∙4, 0r even the confusing 5x4; is that 5 is being added together 4 times, like this: 5+5+5+5.

0 had it's turn of being special with addition and subtraction. Now it's 1, that has a very special relationship with all other numbers. 1 is the Multiplicative Identity, because a(1) = a; for every real number a. Except for 0, every real number has an inverse, 1/a. This satisfies a(1) = a

a(1) = a a(1/a) = 1

## Self-expain Learning Technique

How are the expressions a/b and a÷b similar (think on, / and ÷)?

## Division

Division is the implied operation in every fraction, and it undoes multiplication. To divide by a number, we simply make it an inverse.

a/b = a(1/b)

We call a/b the quotient of a and b, or as the fraction a over b. a is the Numerator and b is the Denominator. We can use the following properties to combine real numbers using division.

Numberator / Denominator

## Self-explain Learning Technique

How could you use the distributive property "disturbingly"

We can use the Distributive Property as a quick way to find a common denominator. We do not leave fractions were the numerator and the denominator can both be divided by a single number. This process can be simplified by using the smallest possible common denominator, Least Common Denominator (LCD).

Example:

7/9 + 5/30

Instead of multiplying 9 by 30, we can find the first multiple of 30 that is divisible by 9. 90 is 30∙3 and is divisible by 9. 9∙10 = 90 and 30∙3 = 90, so now we need to make the fractions proportionate to 90 as the denominator.

7/9 + 7/30 = (7∙10)/(9∙10) + (7∙3)/(30∙3) = 70/90 + 21/ 90 = 91/90

Practice Problem:

In a third world country there are 2 bands of guerrilla fighters. The first group is a group of child soldiers that kill to eat. 15 out 36 of of the child recruits last the first year. The other 8 of 11 were eaten by the remaining boys. The second group are pygmy tribes men that are experts with their blow guns, but they have a serious problem with malaria. 25 out of 48 of the blow gun warriors last through the first year after training. Both groups start with the same number of recruits each year, at least how many do they start with? What is the fraction of those that make it and those that started for both groups combined?

## Not a joking matter I use child soldiers and malaria as story problem references to remind people that these are real world problems | Source