Properties of Numbers & Fractions

If we are adding two or more numbers together, we can combine any two at a time, and the final result will be the same. Example: (3 + 5) + 8 = 3 + (5 + 8) 8 + 8 = 3 + 13 16 = 16 In both cases, the sum is 16. This is called the _________. We can "associate" the 5 with either the 3 or the 8.

Associative Property of Addition

If we are multiplying two or more numbers together, we can combine any two at a time, and the final result will be the same. Example: (3 x 5) x 8 = 3 x (5 x 8) 15 x 8 = 3 x 40 120 = 120 In both cases, the product is 120. This is called the _______. We can "associate" the 5 with wither the 3 or the 8.

Associative Property of Multiplication

It doesn't matter in what order we add two numbers, the sum will be the same. Example: 3 + 5 = 5 + 3 In both cases, the sum is 8. This is called the ________.

Commutative Property of Addition

It doesn't matter in what order we multiply two numbers, the product will be the same. Example: 3 x 5 = 5 x 3 In both cases, the product is 15. This is called _________.

Commutative Property of Multiplication

The _____ combines both addition & multiplication and introduces a new way of expressing multiplication. When you write a number directly next to a set of parenthesis, you multiply whatever is inside the parenthesis by that number. Example: 2(3 + 2 + 5) = 2(10) 20 = 20

Distributive Property

When subtracting mixed numbers you might have to _____. In the problem 7 3/8 - 3 5/8, you are not able to subtract 5/8 from 3/8, so you must borrow from the 7.

borrow

___ is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in this acronym tells you what to calculate first, second, etc., until the calculation is complete.

PEMDAS

Sometimes its is possible to reduce before multiplying fractions. This is called ______ (see pic).

canceling

In order to add/subtract fractions, they must have the same denominator. If the denominators are not the same, the fractions must be _______ to equivalent fractions with the same denominator. Example: 5/7 + 2/5 = ?/35 + ?/35 = 25/35 + 14/35 = 39/35 = 1 4/35

changed

A ______ is a fraction whose numerator or denominator, or both, are fractions themselves. Example: 5/8/3/5 = 5/8÷ 3/5 = 5/8 x 5/3 = 25/24 = 1 1/24

complex fraction

In order to add/subtract fractions, they must have the same ______. If the denominators are the same, add the numerators, keep the denominator and reduce the fraction, if possible. Example: 3/8 + 5/8 = 3 + 5/8 = 8/8 = 1

denominator

_______ are fractions that are equal in value. These types of fractions are found by multiplying or dividing the numerator and denominator of a fraction by the same non-zero number. Example (see picture): a) 1/2 x 2/2 = 2/4 and 2/4 x 2/2 = 4/8 b) 4/8 ÷ 2/2 = 2/4 and 2/4 ÷ 2/2 = 1/2

equivalent fractions

If you are adding/subtracting mixed numbers you can either: 1) change the mixed numbers to ______ fractions, then add (subtract) OR 2) Add (subtract) the whole numbers, then add/subtract the fractions part (shown in the pic).

improper

An _____ is a fraction whose numerator is larger than or equal to the denominator. Thus, this type of faction has a value greater than or equal to 1. Example: 6/5, 9/7, 5/3, 4/4

improper fraction

To divide fractions, _____ the divisor (second fraction), the proceed as in multiplication. Example: 5/2 ÷ 2/1 = 5/2 x 1/2 = 5/4 = 2 1/2

invert

A _____ is a fraction whose numerator is smaller that its denominator. Thus, this type of fraction has a value less that 1. Example: 5/6, 7/9, 2/3, 17/18

proper fraction

Divided the numerator and denominator of a fraction by the same number is called _____. To reduce fractions to lowest terms, divide the numerator and denominator by the largest whole number that divided evenly.

reducing

A ______ can be expressed as an improper fraction by using 1 as the denominator. Example: 8 = 8/1

whole number

A way of adding/subtracting fractions _____ a common denominator is: 1. Multiply the numerator of the first fraction times to denominator of the second. 2. Multiply the denominator the the first fraction times the numerator of the second. 3. Add the totals in steps 1 and 2. This the numerator of the sum. 4. Multiply the denominators. This is the denominator. 5. Reduce if possible. Example: 5/6 + 2/7 = (5x7) + (6x2)/6x7 = 35 + 12/42 = 47/42 = 1 5/42

without

To multiply fractions, multiply the _______ together, multiply the _______ together, and then reduce, if possible. Example: 3/5 x 2/9 = 3x 2/5x9 = 16/45 = 2/15

numerators, denominators

A ______ is a whole number and a fraction. To change this pair into an improper fraction, add the numerator of the fraction part to the product of the denominator and the whole number. The result is the numerator. Keep the denominator of the original fraction part.

mixed number