# Number and Operations

Fractions

Terminology
o Numerator: top number of a fraction
o Denominator: bottom number of a fraction
o Simplest terms: simplify both numbers (divide both numerator and denominator by common factor)

Ordering a sets of Fractions
o When ordering a set of fractions from least to greatest, you need to have common denominators to compare the value of the numerators.

o Another way to order a set of fractions is to use 0, ½, and 1 as benchmark numbers to make informed decisions about where the numbers from the list fall.

Comparing Fractions
o Strategy: When comparing fractions, find the LCD (least common denominator) to compare numerator values of the same fractional parts.

o In order to add or subtract fractions, you must have same fractional parts, meaning that the fractions need to have the same denominator in order to add or subtract the numerators.

Multiplying Fractions
o Multiplying fractions is one of the easiest operations of fractions. Simply multiply the numerators and then multiply the denominators. Be sure to put fraction in simplest terms.

Dividing Fractions
o The customary practice is to change the division problem into a multiplication problem. Keep the first fraction the same, and multiply by the reciprocal of the second fraction (reciprocal = inverse fraction).

Decimals

Ordering and Comparing Decimals
o Understanding place value of numbers less than 1 is very important in using decimals.
o To order and compare decimals, be sure to compare the place value of each number, and remember to add zeroes for missing places behind the decimal point to line up numerals.

o To add and subtract decimals, simply line up the decimals and continue with the operation of addition or subtraction. If some numerals have blank spaces behind the decimal point, you can simply add zeroes to fill in the missing wholes – this makes it easier to line up the numerals.

Prime Numbers and Composite Numbers

Prime Numbers
o Prime numbers are those numbers that only have two factors – 1 and itself. Examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 . . .

Composite Numbers
o Composite numbers are those numbers that have more than two factors. Examples include 4, 6, 8, 9, 10, 12, 15 . . .
o
Important: 0 and 1 are considered neither a prime number nor a composite number.

Squares and Square Roots
Perfect Squares
o Perfect Squares are the whole numbers multiplied by themselves.
1^2 = 1, where ^ means to square
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25 . . .

Square Roots
o The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so the square root of 16 is 4.

Order of Operations

The rules of “order of operations” explain how to evaluate mathematical expressions and/or equations
o Always use the following order when evaluating a mathematical expression or equation
 Parenthesis – complete the operations inside the parenthesis first
 Exponents – compute the exponents next
 Multiply and Divide – next, multiply and divide, from left to right
 Add and Subtract – finally, add and subtract, from left to right