· Natural or counting numbers: 1, 2, 3, 4,...
· Whole numbers: 0, 1, 2, 3,...
· Integers: ...-3, -2, -1, 0, 1, 2, 3,
· Rational numbers: Integers and fractions.
· Irrational numbers: Cannot be written as fractions: or π.
· Prime numbers: Divisible only by 1 and itself: 2, 3, 5, 7, 11, 13, . . .
. (0 and 1 are not prime or composite.)
· Composite numbers: Divisible by more than just 1: 4, 6, 8, 9, 10, 12, .
. . .
· Closure: All answers fall into original set.
· Commutative: Order does not make any difference: a + b = b + a, ab = ba.
· Associative: Grouping does not make any difference: (a + b) + c = a + (b
+ c), (ab)c = a(bc).
· Identity: 0 for addition, 1 for multiplication.
· Inverse: Negative for addition, reciprocal for multiplication.
1. Work within parentheses ( ),
brackets [ ], and braces { } from innermost and work outward.
2. Simplify exponents and roots
working from left to right.
3. Do multiplication and division, whichever
comes first left to right.
4. Do addition and subtraction, whichever comes
first left to right.
1. Underline the place value to
which you're rounding off.
2. Look to the immediate right (one
place) of your underlined place value.
3. Identify the number (the one to the right).
If it is 5 or higher, round your
underlined place value up 1 and change all the other numbers to its right to
zeros. If less than 5, leave your underlined place value as it is and change
all the other numbers to the right to zeros.
· To add or subtract decimals, simply line up the decimal points and then
add or subtract as usual.
· To multiply decimals, just multiply as usual and then count the total
number of digits above the line that are to the right of all decimal points.
Place the decimal point in your answer so that there are the same number of
digits to the right of the decimal point as there are above the line.
· To divide decimals, if the number you're dividing by has a decimal, move
the decimal to the right as many places as possible and then move it under the
division sign just as many places (add zeros if necessary). Move the decimal up
to your answer.
To add or subtract fractions, you
must have a common denominator.
· If two fractions have a common denominator (like fractions), you simply
add or subtract the numerator and keep the same denominator. (For example, 1/5
+ 2/5 = 3/5.)
· If two fractions do not have a common denominator (unlike fractions),
find a lowest common denominator (LCD), change each of the fractions to
equivalent fractions with the new denominator, and then add or subtract the numerators
and keep the same denominator. (For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6
· When subtracting mixed numbers, you may have to "borrow" from
the whole number. When you borrow 1 from the whole number, the 1 must be
changed to a fraction.
· To multiply fractions, simply multiply the numerators and then multiply
the denominators. (For example, 2/3 × 1/5 = 2/15.) Reduce to lowest terms if
necessary.
· To divide fractions, invert the second fraction and then multiply. (For
example, 1/5 ÷ 1/4 = 1/5 × 4/1 = 4/5.)