Generally, for Mondays, as far as my themes go, I’m opting for Musing Mondays, however, up until today I haven’t been having any math to contribute to Mathematical Mondays – or at least, I haven’t had the steady learning supply of Math lessons.
During these I’ll basically be laying out what we learned during the week in my math 97 class. For now, I’m going over terms. More will come, but with pictures, eventually.
Rational Numbers – Ratio of integers
Irrational numbers – cannot write as a ratio of integers. Such as Pi, the square root of 2 or 3, and so on
Integers – whole and negative numbers
Absolute value – the distance from zero on the number line. Usually the number is written with a vertical line on either side of it, signifying it’s being asked for the absolute value. Unfortunately, I don’t know how to do that on my iPad keyboard, so you’ll just have to take my word for this one.
EXAMPLE – the absolute value of 5 is 5 because it is 5 from zero on the number line.
The absolute value of -3 is 3 because it is 3 spaces from zero on the number line.
The absolute value of 8.34 is 8.34 because it is 8.34 spaces from zero on the number line.
Commutative Properties – the ability to move real numbers around in an expression without changing the outcome. This only applies to addition and multiplication.
EXAMPLE – a+b <– by applying the commutative property, it becomes b+a.
3+2 = 2+3 = 5
4×5 <—by applying the commutative property, it becomes 5×4
6×11 = 11×6 = 66
NOTE – Commutative Properties do NOT hold true for subtraction and division.
Associative Properties – AKA the Grouping Property – being able to regroup parts of the expression without effecting the outcome.
EXAMPLE: (a+b)+c = a+(b+c) <–the variables have been regrouped but it will still equal out to be the same.
(1+2)+3 = 1+(2+3) = 6
(ab)c = a(bc) <–the variables have been regrouped, but it will still equal the same.
(2×3)4 = 2(3×4) = 24 —> 2x3x4 = 6×4 = 2
Distributive Property – When using an expression with associative properties, it is distributing the number directly on the outside of the parentheses to the numbers inside the parentheses.
EXAMPLE: a(b+c) <—-distributing the a to multiply by the numbers inside
a(b+c) = ab+ac
2(y+4) = 2y+2×4 = 2y+8 <—that is as simplified as it can get without knowing what y represents.
Additive Inverse – Zero, when it does nothing to the identity of the number it is being added to.
EXAMPLE – x+0 = x+0 = x <—-0 had no effect on x when added to it
Multiplicative Identity – 1, when it does nothing to the identity of the number it is being multiplied with.
EXAMPLE: x1 = 1x = x <—-when 1 was multiplied with x, x remained x
Similar Terms (Like Terms) – terms that contain the same variables and the same exponents
EXAMPLE – 3x-4y-7x+2y <—- the Like terms are 3x and 7x, 4y and 2y.
2a+3b <—-these are NOT Like Terms because they have a different variable.
There’s the first bout of math vocabulary of math 97. Soon will be a review as to what in the world to do with negatives when applying them to operations as well as going over the order of operations