Real Numbers
... To describe your pay, we use real numbers. • In fact, we use real numbers everyday—to describe how tall we are, how much money we have, how cold (or warm) it is, and so on. • In algebra, we express properties of the real numbers by using letters to stand for numbers. ...
... To describe your pay, we use real numbers. • In fact, we use real numbers everyday—to describe how tall we are, how much money we have, how cold (or warm) it is, and so on. • In algebra, we express properties of the real numbers by using letters to stand for numbers. ...
Document
... Definition: Two sets A and B have the same cardinality if and only if there exists a bijection (or a one-to-one correspondence) between them, A ~ B. We split infinite sets into two groups: 1. Sets with the same cardinality as the set of natural numbers 2. Sets with different cardinality as the set o ...
... Definition: Two sets A and B have the same cardinality if and only if there exists a bijection (or a one-to-one correspondence) between them, A ~ B. We split infinite sets into two groups: 1. Sets with the same cardinality as the set of natural numbers 2. Sets with different cardinality as the set o ...
Chapter 2
... 2.11 Comparing and Ordering Rational Numbers Comparing fractions: If necessary, rewrite fractions to have the same denominator, and then order by comparing numerators. Order from least to greatest: 1/7, 3/9, -3/5, 11/14, 5/7, 3/7 ...
... 2.11 Comparing and Ordering Rational Numbers Comparing fractions: If necessary, rewrite fractions to have the same denominator, and then order by comparing numerators. Order from least to greatest: 1/7, 3/9, -3/5, 11/14, 5/7, 3/7 ...
Big Ideas: Chapter 1
... 8. The temperature at noon is 12 F. The temperature at midnight is 8 F. Which temperature is closer to 0 F? 9. Write an integer whose absolute value is greater than itself. Suggested Homework for 8/5/16 – Adding Integers_______________________________________ Add. ...
... 8. The temperature at noon is 12 F. The temperature at midnight is 8 F. Which temperature is closer to 0 F? 9. Write an integer whose absolute value is greater than itself. Suggested Homework for 8/5/16 – Adding Integers_______________________________________ Add. ...
File
... Marco gained 5 pounds over the summer. He lost 7 pounds and then gained 3 pounds over the holidays. What was Marco’s total change in weight? Show your work. ...
... Marco gained 5 pounds over the summer. He lost 7 pounds and then gained 3 pounds over the holidays. What was Marco’s total change in weight? Show your work. ...
a * b
... 1. Multiply on both sides to clear the equation of fractions or decimals. (This is optional, but can ease computations.) Not a fan of this one. 2. If parentheses occur, multiply to remove them using the distributive laws. 3. Collect like terms on each side, if necessary. 4. Get all terms with variab ...
... 1. Multiply on both sides to clear the equation of fractions or decimals. (This is optional, but can ease computations.) Not a fan of this one. 2. If parentheses occur, multiply to remove them using the distributive laws. 3. Collect like terms on each side, if necessary. 4. Get all terms with variab ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.