Pepperell Middle School
... • understand p+q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. • show that a number and its opposite have a sum of 0 (are additive inverses). • interpret sums of rational numbers by describing real-world contexts. • ...
... • understand p+q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. • show that a number and its opposite have a sum of 0 (are additive inverses). • interpret sums of rational numbers by describing real-world contexts. • ...
Caesar, Shift and Affine Ciphers
... (P = C – 1 )(mod 26)), a is encrypted by B, b is encrypted by C, etc.) Shift back by 02: paa du vpja xh sxkxsts xcid iwgtt epgih (P = (C – 2) (mod 26)), a is encrypted by C, b is encrypted by D, etc) ...
... (P = C – 1 )(mod 26)), a is encrypted by B, b is encrypted by C, etc.) Shift back by 02: paa du vpja xh sxkxsts xcid iwgtt epgih (P = (C – 2) (mod 26)), a is encrypted by C, b is encrypted by D, etc) ...
CC Investigation 3: Integers and the Coordinate Plane
... • How can you use these distances to tell how long the line segment connecting points C and D is? (Add the distances.) After Problem 3.4, ask: What general rule can you use to find the distance between two points on a horizontal line? (Find the number of units between the x-coordinates.) between two ...
... • How can you use these distances to tell how long the line segment connecting points C and D is? (Add the distances.) After Problem 3.4, ask: What general rule can you use to find the distance between two points on a horizontal line? (Find the number of units between the x-coordinates.) between two ...
Lecture 2. How computer work? - Department of Computer Science
... • To convert a decimal integer into binary, keep dividing by 2 until the quotient is 0. Collect the remainders in reverse order. • To convert a fraction, keep multiplying the fractional part by 2 until it becomes 0. Collect the integer parts in forward order. • Example: 162.375: ...
... • To convert a decimal integer into binary, keep dividing by 2 until the quotient is 0. Collect the remainders in reverse order. • To convert a fraction, keep multiplying the fractional part by 2 until it becomes 0. Collect the integer parts in forward order. • Example: 162.375: ...
Factoring Polynomials
... In this section, we discuss how to “undo” this process. There are times when the expression on the right is much simpler to work with. However, the left side can provide valuable information as well. We want to be able to take an expression in either form, and convert it to the other. In this sectio ...
... In this section, we discuss how to “undo” this process. There are times when the expression on the right is much simpler to work with. However, the left side can provide valuable information as well. We want to be able to take an expression in either form, and convert it to the other. In this sectio ...
Multiply a polynomial
... It is also advantageous to multiply polynomials without rewriting them in a vertical format. Though the format does not change, we must still distribute each term of one polynomial to each term of the other polynomial. Multiply: (x + 2)(x – 5) ...
... It is also advantageous to multiply polynomials without rewriting them in a vertical format. Though the format does not change, we must still distribute each term of one polynomial to each term of the other polynomial. Multiply: (x + 2)(x – 5) ...
Math 15 - Chapters 3 and 4 Test Show your work for each problem
... Use induction to prove that if the two piles initially each contain the same number of sticks, the second player can always guarantee a win. SOLN: Let denote the statement, “the second player wins when there are initially n sticks in each pile. Basis Step: P(1) is true because in this case there is ...
... Use induction to prove that if the two piles initially each contain the same number of sticks, the second player can always guarantee a win. SOLN: Let denote the statement, “the second player wins when there are initially n sticks in each pile. Basis Step: P(1) is true because in this case there is ...
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.