Unit 3 - Linear Inequalities In One Variable
... What happens when you multiply both sides of the true statement -2 < 5 by 8? You get another true statement -16 < 40. What happens when you multiply both sides of the true statement -2 < 5 by -8? You get a false statement 16 < -40! To make it a true statement you must reverse the inequality symbol. ...
... What happens when you multiply both sides of the true statement -2 < 5 by 8? You get another true statement -16 < 40. What happens when you multiply both sides of the true statement -2 < 5 by -8? You get a false statement 16 < -40! To make it a true statement you must reverse the inequality symbol. ...
Document
... slide) is a partial function on N: for instance the couple 2,4 does not have an image in N. In order that the function minus were total, we’d have to extend the domain to integers. ...
... slide) is a partial function on N: for instance the couple 2,4 does not have an image in N. In order that the function minus were total, we’d have to extend the domain to integers. ...
Fractions and Rational Numbers
... Note. There is nothing "improper" about improper fractions. In some applications, it is often more appropriate to use an improper fraction than it is to use a mixed number. Examples would be problems involving rates of change, ratios, or odds. ...
... Note. There is nothing "improper" about improper fractions. In some applications, it is often more appropriate to use an improper fraction than it is to use a mixed number. Examples would be problems involving rates of change, ratios, or odds. ...
A characterization of all equilateral triangles in Z³
... The connection with Carmichael numbers goes a little further. Carmichael numbers have at least three prime factors and numerical evidence suggests that the following conjecture is true: Conjecture: The Diophantine equation (4) has degenerate solutions if and only if d has at least three distinct pri ...
... The connection with Carmichael numbers goes a little further. Carmichael numbers have at least three prime factors and numerical evidence suggests that the following conjecture is true: Conjecture: The Diophantine equation (4) has degenerate solutions if and only if d has at least three distinct pri ...
FP3: Complex Numbers - Schoolworkout.co.uk
... Finding the square root of a complex number In FP1, we considered one way to find the square roots of a complex number. There is an alternative way to find the roots using de Moivre’s theorem. Example: Find the square roots of 5 – 12i, giving your answers in the form a + bi. Solution: Write 5 – 12i ...
... Finding the square root of a complex number In FP1, we considered one way to find the square roots of a complex number. There is an alternative way to find the roots using de Moivre’s theorem. Example: Find the square roots of 5 – 12i, giving your answers in the form a + bi. Solution: Write 5 – 12i ...
ILLUSTRATING INTEGERS
... Move right on a number line to add a positive integer. Move left on a number line to add a negative integer. ...
... Move right on a number line to add a positive integer. Move left on a number line to add a negative integer. ...
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.