Absolute value:
The absolute value of a number tells how far away the number is
from zero on a number line. For example, the absolute value of 7 is 7, because it is seven numbers away from zero.
The absolute value of -7 is also seven because it is also seven numbers away from zero. Absolute value is ALWAYS a positive
number!
Integers:
Addition - If the signs are the same,
simply add and give the sign of the two addends. For example, 5 + 4 = 9 and -5 + -4 = -9. If
the signs are different, subtract and give the sign of the number with the greater absolute value. For example, -9 +
3 = -6 and 9 + (-3) = 6.
Subtraction - To subtract an integer,
add its opposite.
For example, 8 - 3 = 8 + (-3), which equals 5. Makes sense, right? Okay, so -8
-3 = -8 + (-3), which equals -11. Another example might be a little trickier, but the rule stays the same. Here
goes: -6 - (-3) = -6 + 3, which equals -3.
Multiplication and division - This one
is EASY! If the two numbers have the same sign, then the answer is always a positive number. For example,
5 x 5 = 25 , -5 x -5 = 25, 72/8 = 9 and -72/-8 = 9. If the two numbers have signs that are different, then the
answer is ALWAYS negative. For example, -6 x 4 = -24 and 54/-9 = -6.
Exponents - are fun! The base (also known as the big number) tells you
which number to use and the exponent (the little number at the top right-hand side of the base) tells you how many times to
multiply it by itself. The only tricky part comes when you use integers. If the base is a negative number and
the exponent is a positive number, then the answer depends on whether the base is inside of parentheses or not. If the
base is a negative number and is NOT inside of parentheses,AND the exponent is a positive number, then the answer will
ALWAYS be a negative.
Order of Operations - To solve problems with
multiple steps, use this order:
1st Do the work inside of PARENTHESES or grouping symbols
2nd Simplify any
EXPONENTS
3rd
MULTIPLY OR DIVIDE in order from left to right
Last
ADD OR SUBTRACT in order from left to right.
Scientific Notation is a system used to write very large or very small numbers.
It is ALWAYS written as the product of two numbers. The first number MUST be at least "1" and less than "10."
The second number is a power of ten.
Example: 32,000,000,000,000 is written as 3.2 x 10 to the 13th power. Of course, the
"13" would be an exponent, but I am having trouble writing those with this webpage. More to follow.
