What is Zeckendorf`s Theorem?
... While uniqueness can perhaps be more easily directly proven, this contradiction is more in the traditional spirit. ...
... While uniqueness can perhaps be more easily directly proven, this contradiction is more in the traditional spirit. ...
A number is divisible by
... 3 if the sum of the digits is divisible by 3 4 if the last to digits of the number is divisible by 4 5 if the number ends in 0 or 5 6 if the number is divisible by 2 AND 3 9 if the sum of the digits is divisible by 9 10 if the number ends in 0 ...
... 3 if the sum of the digits is divisible by 3 4 if the last to digits of the number is divisible by 4 5 if the number ends in 0 or 5 6 if the number is divisible by 2 AND 3 9 if the sum of the digits is divisible by 9 10 if the number ends in 0 ...
surds - Hinchingbrooke
... rounded to a certain number of decimal places can only be an approximation. For example, the length of x in the triangle below is exactly 21 , and this can be used in further calculations, for example to find y. ...
... rounded to a certain number of decimal places can only be an approximation. For example, the length of x in the triangle below is exactly 21 , and this can be used in further calculations, for example to find y. ...
Note taking
... completing homework, and preparing for exams. Leave plenty of space between key points and examples. Crowded notes are difficult to review. It is always good to have two examples: one very easy to understand when home alone with your notes and one more complex for you to apply to harder applications ...
... completing homework, and preparing for exams. Leave plenty of space between key points and examples. Crowded notes are difficult to review. It is always good to have two examples: one very easy to understand when home alone with your notes and one more complex for you to apply to harder applications ...
Boolean Algebra
... The binary operator + defines addition. The additive identity is 0. The additive inverse defines subtraction. The binary operator defines multiplication. The multiplicative identity is 1. The multiplicative inverse of a = 1/a defines division, i.e., a 1/a = 1. The only distributive ...
... The binary operator + defines addition. The additive identity is 0. The additive inverse defines subtraction. The binary operator defines multiplication. The multiplicative identity is 1. The multiplicative inverse of a = 1/a defines division, i.e., a 1/a = 1. The only distributive ...
Absolute Value
... Lesson 1-2 Absolute Value Integers - the set of whole numbers and their opposites. Which are examples of Integers? ...
... Lesson 1-2 Absolute Value Integers - the set of whole numbers and their opposites. Which are examples of Integers? ...
Chapter 5 Notes - Dripping Springs ISD
... Simplify before multiplying if possible Change any mixed numbers to improper fractions before multiplying!!! Reduce if necessary ...
... Simplify before multiplying if possible Change any mixed numbers to improper fractions before multiplying!!! Reduce if necessary ...
4-3: Alternating Series, and the Alternating Series Theorem
... • Clearly none of the tests we’ve developed so far can help us (I dare you to try them). So how can we determine if this series converges? P k+1 • Idea: let’s look at Sn = nk=1 (−1)k for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. • Obviously, if we continue, we find the “hopping” behavior continues infinite ...
... • Clearly none of the tests we’ve developed so far can help us (I dare you to try them). So how can we determine if this series converges? P k+1 • Idea: let’s look at Sn = nk=1 (−1)k for n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. • Obviously, if we continue, we find the “hopping” behavior continues infinite ...
Significant Figure Rules
... Here are two more examples where the significant zeros are in red: 2.30 x 10-5 4.500 x 1012 ...
... Here are two more examples where the significant zeros are in red: 2.30 x 10-5 4.500 x 1012 ...
3,1
... Identity of Addition: a + 0 = a Identity of Multiplication: a x 1 = a Multiplicative Property of Zero: a x 0 = 0 Inverse of Multiplication: (a/b) x (b/a) = 1 Inverse of Addition (zero pair) : -a + a = 0 ...
... Identity of Addition: a + 0 = a Identity of Multiplication: a x 1 = a Multiplicative Property of Zero: a x 0 = 0 Inverse of Multiplication: (a/b) x (b/a) = 1 Inverse of Addition (zero pair) : -a + a = 0 ...
2 Matrix Supplement 2-2 - 2-3 and 2-5
... What would be a great way to use Associative and Communitive properties to do these mentally? ...
... What would be a great way to use Associative and Communitive properties to do these mentally? ...
Common Core Math Standards
... Apply properties of operations as strategies to multiply and divide. EX: If 6 x 4 = 24 is known, then 4 x 6 = 24 3.OA.6 Understand division as an unknown-factor problem. Find 32/8 by finding the number that makes 32 when multiplied by 8. 3.OA.7 Fluently multiply and divide within 100, using strategi ...
... Apply properties of operations as strategies to multiply and divide. EX: If 6 x 4 = 24 is known, then 4 x 6 = 24 3.OA.6 Understand division as an unknown-factor problem. Find 32/8 by finding the number that makes 32 when multiplied by 8. 3.OA.7 Fluently multiply and divide within 100, using strategi ...
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.