9. Factors and Multiples E
... 4 Find the HCF of these pairs of numbers. a 8 and 10 b 6 and 15 c 18 and 30 d 7 and 29 e What can you say about the numbers in part d? 5 True or false? Explain your answers. a The smallest factor of any number is 1. b All numbers except 1 have an even number of factors. c Any multiple of 8 is also a ...
... 4 Find the HCF of these pairs of numbers. a 8 and 10 b 6 and 15 c 18 and 30 d 7 and 29 e What can you say about the numbers in part d? 5 True or false? Explain your answers. a The smallest factor of any number is 1. b All numbers except 1 have an even number of factors. c Any multiple of 8 is also a ...
3. Number theory
... 8. A positive integer is wrtten at each integer point in the plane (Z2 ), in such a way that each of these numbers is the arithmetic mean of its four neighbors. Prove that all of the numbers are equal. 9. A triangular number is a positive integer of the form n(n + 1)/2. Prove that m is the sum of tw ...
... 8. A positive integer is wrtten at each integer point in the plane (Z2 ), in such a way that each of these numbers is the arithmetic mean of its four neighbors. Prove that all of the numbers are equal. 9. A triangular number is a positive integer of the form n(n + 1)/2. Prove that m is the sum of tw ...
ES Content Scope and Sequence - International School of Kenya
... Generalize place value understanding for multidigit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous u ...
... Generalize place value understanding for multidigit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous u ...
Chapter One Notes
... algebraic expression: A mathematical phrase containing variables, numbers and operational symbols. evaluate: To find the number that an algebraic expression names by replacing a variable with a given number. (Solve) substitution: To put something in another’s place or replace the variable with a nu ...
... algebraic expression: A mathematical phrase containing variables, numbers and operational symbols. evaluate: To find the number that an algebraic expression names by replacing a variable with a given number. (Solve) substitution: To put something in another’s place or replace the variable with a nu ...
Core Algebra I
... Addition and Subtraction of Rational Numbers Changing an improper fraction to a mixed numeral ...
... Addition and Subtraction of Rational Numbers Changing an improper fraction to a mixed numeral ...
Curriculum 2.0 Algebra 2: Unit 2-Topic 1, SLT 6 Name: Operations
... Adding: Because the imaginary terms of complex conjugate pairs are always opposite, by definition, their sum is 0. This eliminates the imaginary part of the complex number, leaving only the sum of the real parts. The sum of the real parts will always be double the real part in the original complex n ...
... Adding: Because the imaginary terms of complex conjugate pairs are always opposite, by definition, their sum is 0. This eliminates the imaginary part of the complex number, leaving only the sum of the real parts. The sum of the real parts will always be double the real part in the original complex n ...
Subtraction of Real Numbers
... To follow the rule • Change the subtraction operation to addition • and the positive 6 to a negative 6. • The result is 3 +(-6). • Now follow the addition rules to get a result of –3. ...
... To follow the rule • Change the subtraction operation to addition • and the positive 6 to a negative 6. • The result is 3 +(-6). • Now follow the addition rules to get a result of –3. ...
Scientific Notation Shorthand method of writing very large
... Opener: • When you’re taking notes, if you have to write the same big word or words over and over again….do you write it out every time? How do you make it quicker? • If some random person looked at your notes would they be able to read them? Why or why not? ...
... Opener: • When you’re taking notes, if you have to write the same big word or words over and over again….do you write it out every time? How do you make it quicker? • If some random person looked at your notes would they be able to read them? Why or why not? ...
The Fibonacci Sequence
... The third month, the first pair creates another pair (so there are 3 pairs now). The fourth month the first 2 create new pairs (so 5 exist now). Etc. ...
... The third month, the first pair creates another pair (so there are 3 pairs now). The fourth month the first 2 create new pairs (so 5 exist now). Etc. ...
Arithmetic (93.9 KB)
... The order of addition does not matter, e.g. 5 + 3 = 8 = 3 + 5. The order of subtraction does matter, e.g. 5 − 3 = 2, but 3 − 5 = −2. Addition and subtraction exercises 1.1: (i) −3 + 4 (ii) 3 − 3 (iii) 3 − 7 (iv) −3 + 8 − 2 (v) −3 − 4 − 2. Answers at the end of topic. ...
... The order of addition does not matter, e.g. 5 + 3 = 8 = 3 + 5. The order of subtraction does matter, e.g. 5 − 3 = 2, but 3 − 5 = −2. Addition and subtraction exercises 1.1: (i) −3 + 4 (ii) 3 − 3 (iii) 3 − 7 (iv) −3 + 8 − 2 (v) −3 − 4 − 2. Answers at the end of topic. ...
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.