Euclid`s Algorithm - Cleveland State University
... GCD(a, b) = GCD(a, r). Where a and b are integers, and q and r are integers such that b = q × a + r. We know that: GCD(a, b) | a and GCD(a, b) | b From the Division Theorem we know: GCD(a, b) | (1 × b – q × a) and r = (b – q × a) We can then replace the right side with r: GCD(a, b) | r From here we ...
... GCD(a, b) = GCD(a, r). Where a and b are integers, and q and r are integers such that b = q × a + r. We know that: GCD(a, b) | a and GCD(a, b) | b From the Division Theorem we know: GCD(a, b) | (1 × b – q × a) and r = (b – q × a) We can then replace the right side with r: GCD(a, b) | r From here we ...
Let’s Do Algebra Tiles
... Integer multiplication builds on whole number multiplication. Use concept that the multiplier serves as the “counter” of sets needed. For the given examples, use the algebra tiles to model the multiplication. Identify the multiplier or counter. Draw pictorial diagrams which model the multiplication ...
... Integer multiplication builds on whole number multiplication. Use concept that the multiplier serves as the “counter” of sets needed. For the given examples, use the algebra tiles to model the multiplication. Identify the multiplier or counter. Draw pictorial diagrams which model the multiplication ...
Grade 7
... drawings, similar figures using graphics, and constant speed involving only one unit of time 2. Identify a proportion used to solve a problem given figures with the same orientation in space 3. Solve one-step percent problems involving discounts, taxes, and tips, using whole-number percents only 4. ...
... drawings, similar figures using graphics, and constant speed involving only one unit of time 2. Identify a proportion used to solve a problem given figures with the same orientation in space 3. Solve one-step percent problems involving discounts, taxes, and tips, using whole-number percents only 4. ...
x, y
... to variable v if v is not given another value on any of the nodes or edges in the path Reach : If there is a def-clear path from li to lj with respect to v, the def of v at li reaches the use at lj du-path : A simple subpath that is def-clear with respect to v from a def of v to a use of v du (ni, n ...
... to variable v if v is not given another value on any of the nodes or edges in the path Reach : If there is a def-clear path from li to lj with respect to v, the def of v at li reaches the use at lj du-path : A simple subpath that is def-clear with respect to v from a def of v to a use of v du (ni, n ...
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.