Interactive Voting - Negative numbers
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The document discusses negative numbers on a number line. It explains that negative numbers are those to the left of 0 on the number line. It provides examples of adding negative and positive numbers using a number line by starting at the negative number and moving right the number of places indicated by the positive addend.
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Introduction to integers
Integers are defined as whole numbers that can be positive, negative, or zero, and are used to represent real-world situations involving amounts above and below zero like elevation, temperature, financial gains and losses, and distances. Integers are located on a number line and adding integers involves moving right on the number line while subtracting involves moving left, with examples provided of calculating distances between elevations represented as integers.
Miriam
The document discusses addition and subtraction of signed numbers on a number line. It explains that the + sign means to move to the positive side of the number line and the - sign means to move to the negative side. It provides examples of adding (+2) + (+4) = +6 and subtracting (-3) - (-1) = -5 on the number line. It also notes that when multiplying a number by a signed number, you add or subtract that number to itself the same number of times to the positive or negative side depending on the sign. Finally, it explains that you can use a number line to divide by splitting it into equal parts.
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Integers are the set of whole numbers (positive and negative) used to represent elevations and other quantities above or below a reference point like sea level. Positive integers are whole numbers greater than zero representing elevations above sea level, while negative integers are whole numbers less than zero representing elevations below sea level. For example, Mount McKinley's elevation of 20,320 feet above sea level can be written as the positive integer +20,320, while Death Valley's elevation of 282 feet below sea level can be written as the negative integer -282.
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Integers1a
The document defines positive and negative numbers and their properties. Positive numbers are greater than zero, while negative numbers are less than zero. Opposite numbers are the same distance from zero but in opposite directions. Integers include all whole numbers and their opposites on the number line. Negative numbers are used to represent temperatures below zero, depths under sea level, and amounts of debt. The document then explains the rules for adding integers, whether the signs are the same or different, and illustrates examples using a number line.
Introduction to Positive and Negative Numbers
The document provides an introduction to integers including:
- Definitions of positive and negative numbers and their representation on number lines
- Rules for comparing and ordering integers
- Real-world examples of how integers are used to represent things like temperature, sea level, and money
- Key concepts and rules for adding and subtracting integers including keeping the sign of the first integer the same and changing the operation and second integer's sign for subtraction
- Examples of using number lines to visually represent integer operations
- A method for proving that subtracting a negative number is the same as adding a positive number
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Introduction to integers
Integers are defined as whole numbers that can be positive, negative, or zero, and are used to represent real-world situations involving amounts above and below zero like elevation, temperature, financial gains and losses, and distances. Integers are located on a number line and adding integers involves moving right on the number line while subtracting involves moving left, with examples provided of calculating distances between elevations represented as integers.
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Integers are the set of whole numbers (positive and negative) used to represent elevations and other quantities above or below a reference point like sea level. Positive integers are whole numbers greater than zero representing elevations above sea level, while negative integers are whole numbers less than zero representing elevations below sea level. For example, Mount McKinley's elevation of 20,320 feet above sea level can be written as the positive integer +20,320, while Death Valley's elevation of 282 feet below sea level can be written as the negative integer -282.
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The document outlines rules of divisibility for determining if a number is divisible by numbers 2 through 9 without performing long division. It explains that a number is divisible by 2 if the ones digit is even, by 3 if the sum of the digits is divisible by 3, by 4 if the last two digits are divisible by 4, and so on, providing examples for each rule. It notes that understanding these rules allows one to quickly determine divisibility of even very large numbers without calculations.
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The document defines positive and negative numbers and their properties. Positive numbers are greater than zero, while negative numbers are less than zero. Opposite numbers are the same distance from zero but in opposite directions. Integers include all whole numbers and their opposites on the number line. Negative numbers are used to represent temperatures below zero, depths under sea level, and amounts of debt. The document then explains the rules for adding integers, whether the signs are the same or different, and illustrates examples using a number line.
Introduction to Positive and Negative Numbers
The document provides an introduction to integers including:
- Definitions of positive and negative numbers and their representation on number lines
- Rules for comparing and ordering integers
- Real-world examples of how integers are used to represent things like temperature, sea level, and money
- Key concepts and rules for adding and subtracting integers including keeping the sign of the first integer the same and changing the operation and second integer's sign for subtraction
- Examples of using number lines to visually represent integer operations
- A method for proving that subtracting a negative number is the same as adding a positive number
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The document explains the order of operations (PEMDAS) for solving math problems with multiple operations:
1) Perform operations inside parentheses first from left to right.
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3) Perform multiplication and division from left to right.
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Some example problems are worked out step-by-step to demonstrate how to follow PEMDAS.
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Integers are the set of whole numbers and their opposites. They include positive numbers to the right of zero on the number line and negative numbers to the left of zero. Positive integers are whole numbers greater than zero, while negative integers are whole numbers less than zero. Opposite integers are the same distance from zero but on opposite sides. The document provides examples of writing real-world situations as integers and using integers to solve a problem about elevation distances.
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Numberline notes
- Integers include whole numbers and their opposites on the number line including zero. Positive numbers are greater than zero, while negative numbers are less than zero.
- Integers can be compared and ordered on a number line, with numbers to the left being less than those to the right. Their absolute values represent distances from zero.
- Integers are used to represent real-world concepts like temperature, elevation, and financial amounts, with positive integers for gains and negative for losses or amounts owed.
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An integer is a whole number that can be positive or negative, including numbers like 12, -10, and -30,843. Fractions and decimals are rational numbers, not integers. Integers are plotted on a number line and can be ordered from least to greatest or greatest to least. The absolute value of a number represents its distance from zero on the number line and is always positive.
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1) Perform operations inside parentheses first from left to right.
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Integers are the set of whole numbers and their opposites. They include positive numbers to the right of zero on the number line and negative numbers to the left of zero. Positive integers are whole numbers greater than zero, while negative integers are whole numbers less than zero. Opposite integers are the same distance from zero but on opposite sides. The document provides examples of writing real-world situations as integers and using integers to solve a problem about elevation distances.
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Numberline notes
- Integers include whole numbers and their opposites on the number line including zero. Positive numbers are greater than zero, while negative numbers are less than zero.
- Integers can be compared and ordered on a number line, with numbers to the left being less than those to the right. Their absolute values represent distances from zero.
- Integers are used to represent real-world concepts like temperature, elevation, and financial amounts, with positive integers for gains and negative for losses or amounts owed.
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An integer is a whole number that can be positive or negative, including numbers like 12, -10, and -30,843. Fractions and decimals are rational numbers, not integers. Integers are plotted on a number line and can be ordered from least to greatest or greatest to least. The absolute value of a number represents its distance from zero on the number line and is always positive.
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This document discusses comparing and ordering integers. It defines integers as whole numbers and their opposites, and provides examples of integers on a number line. It explains that in golf, lower scores are better, so a score of 1 under par (-1) is better than a score of 2 over par (2). When comparing two integers on a number line, the integer farther to the left is smaller. The document demonstrates ordering lists of integers from least to greatest.
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In this I am going to you all about integers like operations which can be applied on them, absolute value , comparison , etc.
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Rounding whole numbers involves replacing a number with the closest number in tens, hundreds, or thousands. To round to the nearest ten, underline the digit in the tens place and if it is 5 or greater, round up the tens place digit. Then change all following digits to zero. The same process is followed to round to the nearest hundred or thousand, examining the hundreds or thousands place digit respectively. Examples show rounding 534 to 530 when rounding to tens, 500 when rounding to hundreds, and 1000 when rounding to thousands.
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2. An equation for the final position of an object is presented as the sum of its initial position and distance traveled. Examples are given of calculating the final position using different starting positions and distances.
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Wednesdayweek2
Okay, let's break this down step-by-step:
* The population is dropping at a rate of 255 people per year
* We want to know how long it will take for the change in population to be 2,040 people
* So we set up an equation: Rate x Time = Change
* Rate is -255 people/year
* Change is -2,040 people
* So the equation is: -255x = -2,040
* Solve for x: x = 2,040/-255 = 8 years
Therefore, it will take 8 years for the change in population to be 2,040 people.
Integers1.Ppt
The document defines positive and negative numbers and their relationships. It discusses how negative numbers are used to represent temperatures below zero, debt, and locations under sea level. The document then explains the rules for adding positive and negative integers, including counting right on a number line for positive numbers and left for negative numbers. Sample addition problems are shown applying these rules.
Subtracting Integers
1. To subtract integers, add the opposite of the second number instead of subtracting.
2. Adding a "zero pair" does not change the difference of a subtraction problem, but allows negatives to be subtracted by providing positive chips to remove.
3. The number line can be used to model integer subtraction by moving left for negatives and right for positives.
Add and subtract pos and neg numbers 4 parts
This document provides an introduction to integers through five parts:
Part I defines key integer vocabulary like positive and negative numbers. It discusses integer properties like opposites and compares/orders integers on number lines. Real world applications like temperature, sea level, and money are explored.
Part II covers integer addition rules - signs the same means keep the sign, signs different means subtract the numbers and keep the larger absolute value sign. Number lines demonstrate adding integers visually.
Part III explains that subtracting a negative number is the same as adding a positive number through changing operation and number signs. More examples solidify this rule.
Part IV proves this subtraction rule is true by using the same checking method as regular subtraction equations
The real number system
John scored 17 points (4x4 + 0x1 + -1x3 = 17)
Mary scored 20 points (4x5 = 20)
Adam scored 18 points (4x4 + -1x2 = 18)
Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30)
Kim scored 31 points (4x7 + 4x1 = 31)
Jenny scored 32 points (4x8 = 32)
Zack scored 27 points (4x6 + 4x1 = 27)
Amy scored 25 points (4x5 + 4x1 = 25)
The students sorted from highest to lowest scores are:
1
Chapter 1 Study Guide
The document discusses the order of operations (PEMDAS) and provides examples of how to evaluate expressions and solve equations. It explains that parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right have precedence based on the PEMDAS acronym. Integers, absolute value, adding, subtracting, multiplying, and dividing integers are also covered along with writing algebraic expressions and solving different types of equations.
Chapter 1 Study Guide
The document discusses the order of operations (PEMDAS) and provides examples of how to evaluate expressions and solve equations. It explains that parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right have priority in calculations. Algebraic expressions and equations are introduced along with rules for manipulating integers and solving different types of equations.
Math Chapter 1 - Integers
This chapter introduces integers and their operations. Students will learn to use negative numbers, draw integers on a number line, compare integers, and order integers in sequences. Key terms include integers, positive integers, negative integers, and number line. The chapter discusses representing temperatures below zero as negative numbers, finding opposites on the number line, and using properties like commutativity and associativity to simplify integer calculations mentally.
INNOVATIVE LESSON TEMPLATE
This document provides an overview of negative numbers and integer addition. It defines negative numbers as numbers less than zero, opposite numbers as having the same distance from zero in the opposite direction, and integers as including all whole numbers and their opposites on the number line including zero. It then presents two rules for integer addition: 1) if signs are the same, add the numbers and use that sign, and 2) if signs are different, subtract the smaller number from the larger and use the larger number's sign. Several examples are worked out using a number line to visually demonstrate integer addition.
Cha
This document provides an overview of negative numbers and integer addition. It defines negative numbers as numbers less than zero, opposite numbers as having the same distance from zero in the opposite direction, and integers as including all whole numbers and their opposites on the number line including zero. It then presents two rules for integer addition: 1) if signs are the same, add the numbers and use that sign, and 2) if signs are different, subtract the smaller number from the larger and use the larger number's sign. Several examples are worked out using a number line to visually demonstrate integer addition.
Grade 6 PPT_Math_Q2_W9.pptx
This document provides instruction and exercises on comparing and ordering integers from least to greatest. It includes examples of arranging integers in ascending and descending order on a number line. Students are asked to identify integers relative to other numbers on the number line, as well as insert comparison symbols like < and > to make statements true. The document also contains exercises for students to arrange lists of integers in ascending and descending order.
Absolute Value and the Fundamental Operations on Integers.pptx
This document discusses integers and fundamental operations on integers. It defines integers as positive and negative whole numbers and explains how to represent integers on a number line. Absolute value is defined as the distance from zero, which cannot be negative. Rules for addition, subtraction, multiplication and division of integers are provided, including keeping or changing the sign of the answer depending on the signs of the integers being operated on. Examples of each type of operation are worked out step-by-step.
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Absolute Value and the Fundamental Operations on Integers.pptx
Absolute Value and the Fundamental Operations on Integers.pptx
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Interactive Voting - Negative numbers
- 2. We can think of numbers being on a number line: 0 2 3 4 5 6 7 8 9 10 1 These numbers are all positive numbers. +
- 3. The number line can also continue on past 0: 0 2 3 4 5 6 7 8 9 10 1 These new numbers are negative numbers. - -1 -10 -9 -8 -6 -5 -7 -4 -3 -2
- 4. 0 2 3 4 5 6 7 8 9 10 1 -1 -10 -9 -8 -6 -5 -7 -4 -3 -2 We can use our number lines to work out the sums which include negative numbers. What is -3 plus 5? We start at -3 First we locate -3 on the number line.
- 5. 0 2 3 4 5 6 7 8 9 10 1 -1 -10 -9 -8 -6 -5 -7 -4 -3 -2 We can use our number lines to work out the sums which include negative numbers. What is -3 plus 5? We start at -3
- 6. 0 2 3 4 5 6 7 8 9 10 1 -1 -10 -9 -8 -6 -5 -7 -4 -3 -2 We can use our number lines to work out the sums which include negative numbers. What is -3 plus 5? We start at -3 Next we count on 5 places to the right. After 5 jumps we arrive at 2 =2
- 7. 0 2 3 4 5 6 7 8 9 10 1 -1 -10 -9 -8 -6 -5 -7 -4 -3 -2 Now try this one: What is -1 plus 3
- 8. 0 2 3 4 5 6 7 8 9 10 1 -1 -10 -9 -8 -6 -5 -7 -4 -3 -2 Now try this one: What is -1 plus 3 =2