# Search Results for: distributive

## Commutative, distributive, illustrative-ly

Here they all are, apart from associative, as it belongs to algebra.

Filed under abstract, arithmetic, language in math, operations, teaching

## The Distributive Law, again !

The formal statement of the distributive law should read as follows: If a, b, c and d are numbers, or algebraic expressions (same thing really) and b = c + d then ab = ac + ad It is a … Continue reading

Filed under abstract, algebra, arithmetic, language in math, teaching

## Commutative, associative, distributive – These are THE LAWS

Idly passing the time this morning I thought of a – b = a + (-b). Fair enough, it is the interpretation of subtraction in the extended positive/negative number system. I then thought of a – (b + c) Sticking … Continue reading

Filed under abstract, algebra, arithmetic, education, language in math, teaching

## Subtraction and Negative Numbers : Part_2

Using the and connective. In “apple words” we have start with 7 apples subtract 3 apples result 4 apples or as a single “sentence”, Starting with 7 apples and subtracting 3 apples gives the result 4 apples or without the apples, … Continue reading

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## Geometry and Numbers – negative ones – “a minus times a minus is a plus”

To accommodate positive and negative numbers we need two extended number lines, with their zeros at the same place Then multiplication of two negative numbers will always give a positive result, following the same geometrical structure. The start, where the multiplier … Continue reading

Filed under arithmetic, education, geometry, geostruct, negative numbers, Number systems, Uncategorized

## Adding fractions – phew!

Who needs LCM ? First, three views of LCM with no comments : 1: Change them to equivalent fractions that will have equal denominators. As the common denominator, choose the LCM of the original denominators. Then the larger the numerator, … Continue reading

Filed under algebra, arithmetic, fractions, Uncategorized

## More bad language in math

Here is another horror which I found recently: The distributive law of addition: a(b + c) = ab + ac (OK, it’s a definition) The current school math explanation: You take the a and distribute it to the b to … Continue reading

Filed under abstract, arithmetic, language in math, teaching

## Subtraction in algebra – let’s use algebra !

I have seen some heavy handed ways of explaining the identity a – (b + c) = a – b – c Let us use algebra. Give the left hand side a name, say d .Then a – (b + … Continue reading

Filed under algebra, arithmetic, teaching

## -1 x -1 = 1, but some need convincing

Here is a popular argument: -1 x -1 has to be 1 or -1 If it was equal to -1 then -1 x -1 = -1 x -1 x 1 = -1 x1 and so dividing both sides by -1 … Continue reading

Filed under abstract, algebra, arithmetic