2-2

... times the sum of a second and a third equals the product of the first and second numbers plus the product of the first and third numbers. ...

... times the sum of a second and a third equals the product of the first and second numbers plus the product of the first and third numbers. ...

Integers and Absolute Value

... The number one less than zero would be written as -1. This is an example of a negative number. A negative number is a number less than zero. Negative numbers are members of the set of integers. Integers are the set of all positive and negative whole numbers and can be represented as points on a numb ...

... The number one less than zero would be written as -1. This is an example of a negative number. A negative number is a number less than zero. Negative numbers are members of the set of integers. Integers are the set of all positive and negative whole numbers and can be represented as points on a numb ...

Logic and Proof Exercises Question 1 Which of the following are true

... Use an algebraic proof to prove each of the following true statements. (a) The product of two odd numbers is an odd number. (b) The product of two square numbers is a square number. (A square number is an integer which is the result of squaring another integer. For example, 4 is a square number beca ...

... Use an algebraic proof to prove each of the following true statements. (a) The product of two odd numbers is an odd number. (b) The product of two square numbers is a square number. (A square number is an integer which is the result of squaring another integer. For example, 4 is a square number beca ...

Here is the algorithm example for the week 8 discussion

... Example 2: (to be worked out in the discussion). Write and analyze a pseudocode algorithm that finds the product of the largest and smallest even integers in the list a 1, a2, …, an. The algorithm should return -1 (or some other negative value) if there are no even numbers. If there is just one even ...

... Example 2: (to be worked out in the discussion). Write and analyze a pseudocode algorithm that finds the product of the largest and smallest even integers in the list a 1, a2, …, an. The algorithm should return -1 (or some other negative value) if there are no even numbers. If there is just one even ...

Some Simple Number Problems

... 2. Show that a whole number is divisible by 9 if its digits add up to a multiple of 9. So, for example 972 is divisible by 9 as 9 7 2 18 , which is a multiple of 9.2. 3. Show that a whole number is divisible by 4 if its last two digits are divisible by 4.3 4. Prove that the sum of two odd numb ...

... 2. Show that a whole number is divisible by 9 if its digits add up to a multiple of 9. So, for example 972 is divisible by 9 as 9 7 2 18 , which is a multiple of 9.2. 3. Show that a whole number is divisible by 4 if its last two digits are divisible by 4.3 4. Prove that the sum of two odd numb ...

Dividing with Significant Figures

... result is limited by the least accurate measurement involved in the calculation. • Division ▫ After dividing the numbers, you then round the result off so it has the same number of significant figures as the component with the smallest number of significant figures. ...

... result is limited by the least accurate measurement involved in the calculation. • Division ▫ After dividing the numbers, you then round the result off so it has the same number of significant figures as the component with the smallest number of significant figures. ...

94 Ninety-Four XCIV

... The number 94 has four divisors: 1, 2, 47, 94. The number 94 is the seventy-second deficient number: s(94) = 1 + 2 + 47 = 50 < 94. As a sum of four or fewer squares: 94 = 22 +32 +92 = 32 +62 +72 = 12 +22 +52 +82 = ...

... The number 94 has four divisors: 1, 2, 47, 94. The number 94 is the seventy-second deficient number: s(94) = 1 + 2 + 47 = 50 < 94. As a sum of four or fewer squares: 94 = 22 +32 +92 = 32 +62 +72 = 12 +22 +52 +82 = ...

Multiplication and Division of Whole Numbers

... Notice that both the divisor and the quotient are factors of the dividend. To find the factors of a number, try dividing the number by 1, 2, 3, 4, 5, … Those numbers that divide into the number evenly are its factors. Continue this process until the factors start to repeat. A prime number is a natur ...

... Notice that both the divisor and the quotient are factors of the dividend. To find the factors of a number, try dividing the number by 1, 2, 3, 4, 5, … Those numbers that divide into the number evenly are its factors. Continue this process until the factors start to repeat. A prime number is a natur ...

Properties of Multiplication Associative Property of Multiplication

... Distributive Property The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example: a x (b + c) = a x b + a x c ...

... Distributive Property The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example: a x (b + c) = a x b + a x c ...

3 Three III

... an arbitrary angle into 3 equal parts using just a straightedge and compass. A closed polygon with 3 sides is called a triangle. That’s what Euclid called it, a figure with three angles. Why do we all say that it is a figure with three sides? The word is 3 dimensional, or so it appears. The third Pr ...

... an arbitrary angle into 3 equal parts using just a straightedge and compass. A closed polygon with 3 sides is called a triangle. That’s what Euclid called it, a figure with three angles. Why do we all say that it is a figure with three sides? The word is 3 dimensional, or so it appears. The third Pr ...

Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. The simplest way to prove that zero is even is to check that it fits the definition of ""even"": it is an integer multiple of 2, specifically 0 × 2. As a result, zero shares all the properties that characterize even numbers: 0 is divisible by 2, 0 is neighbored on both sides by odd numbers, 0 is the sum of an integer (0) with itself, and a set of 0 objects can be split into two equal sets.Zero also fits into the patterns formed by other even numbers. The parity rules of arithmetic, such as even − even = even, require 0 to be even. Zero is the additive identity element of the group of even integers, and it is the starting case from which other even natural numbers are recursively defined. Applications of this recursion from graph theory to computational geometry rely on zero being even. Not only is 0 divisible by 2, it is divisible by every power of 2, which is relevant to the binary numeral system used by computers. In this sense, 0 is the ""most even"" number of all.Among the general public, the parity of zero can be a source of confusion. In reaction time experiments, most people are slower to identify 0 as even than 2, 4, 6, or 8. Some students of mathematics—and some teachers—think that zero is odd, or both even and odd, or neither. Researchers in mathematics education propose that these misconceptions can become learning opportunities. Studying equalities like 0 × 2 = 0 can address students' doubts about calling 0 a number and using it in arithmetic. Class discussions can lead students to appreciate the basic principles of mathematical reasoning, such as the importance of definitions. Evaluating the parity of this exceptional number is an early example of a pervasive theme in mathematics: the abstraction of a familiar concept to an unfamiliar setting.