1.2 Adding **Integers** Adding 3 or more terms Strategy You can add everything going from left to right Or you can use Commutative and Associative Properties to help make the numbers easier to add together Helpful Hints Look for **Additive** Inverse Property (sum is 0) Add the /) Commutative Property Allows you to add in any order as long as the problem is all **addition** Associative Property Allows you to regroup numbers by putting parenthesis around them. You may use the Associative Property when there is all/

Applied Algebra B Lesson: 2 – 3 Adding **Integers** Objective: Learn to add **integers**. Adding **Integers** Like Signs Add numbers and keep the sign 3 + 4 = 7 -6 – 8 = -14 Unlike Signs Subtract numbers, take the sign **of** the bigger number -4 + 11 = 7 5 – 13 = -8 Find/11 + 6 =17 Opposites Also called **Additive** Inverses or Zero Pair Examples 3 & -3 3 + -3 = 0 or 3 – 3 = 0 -10 & 10 -10 + 10 = 0 or 10 – 10 = 0 Property **Additive** Inverse Property The sum **of** any number and its **additive** inverse is 0. Simplify each expression 5x/

justify the rules for…subtracting…**integers**. Preview **of** MA.7.A.3.2 Subtract…**integers**,…including solving problems in everyday contexts. Sunshine State Standards 11-5 Subtracting **Integers** Move left on a number line to subtract a positive **integer**. Move right on a number line to subtract a negative **integer**. Subtracting **Integers** on a Number Line 11-5 Subtracting **Integers** **Additional** Example 1: Writing **Integer** Subtraction Write the subtraction modeled/

Pre-Algebra 09/7/10 OBJECTIVE – Solve **integer** **addition** and subtraction by identifying the terms and applying the rules HOMEWORK – P27-28 #6,22,27,36,53,55 – P32-33 #13,30,31,49,53 – Due 9/13 TAKS Tune-Up p6 WARMUP On back **of** **Integer** Investigation paper from last week write: What pattern do you see for each quadrant? – All positive-- All negative/

Contents Example 1Add **Integers** on a Number Line Example 2Add **Integers** with the Same Sign Example 3Add **Integers** on a Number Line Example 4Add **Integers** with Different Signs Example 5Use **Integers** to Solve a Problem Example 6Add Three or More **Integers** Example 2-1a /hike he gained an altitude **of** 29 feet. At what altitude did Dave complete his hike? Answer:Dave completed his hike at 3 feet below sea level. Example 2-6a Commutative Property **Additive** Inverse Property Identity Property **of** **Addition** Answer: –4 Find. /

Dept www.mathsrevision.com Learning Intention Success Criteria 1.To be put **integers** in order **of** size. 1. To understand how to add positive and negative numbers using the thermometer as an aid. S3 3/Intention Success Criteria 1.To be able to write down mathematically the **addition** and subtraction **of** both positive and negative **integers**. 1. To explain how to write down mathematically **addition** and subtraction **of** negative **integers**. Negative Numbers **Addition** & Subtraction S3 3 17-Apr-15Created by Mr. Lafferty Maths/

2 3 4 5 Negative **integers** Positive **integers** 0 is neither positive nor negative The **integers** are the set **of** whole numbers and their opposites. -The whole numbers are the counting numbers and zero: 0, 1, 2, 3, …. -**Integers**: …,-3, -2, -1, 0, 1, 2, 3,… Remember! Graph the **integer** –7 and its opposite on a number line. **Additional** Example 1: Graphing **Integers** and Their Opposites on a/

a positive **integer**. Move left on a number line to add a negative **integer**. Adding **Integers** on a Number Line Parentheses are used to separate **addition**, subtraction, multiplication, and division signs from negative **integers**. –2 + (–5) = –7 Writing Math Example 1 Write the **addition** modeled on/13 B. –13 C. 23 D. –23 4. The basement **of** a building is 10 feet below the ground level. The height **of** the building including the basement is 69 feet. What is the height **of** the building from the ground level? A. 79 ft B. 69/

set **of** positive whole numbers, their opposites, and zero. (Ex: -2, -1, 0, +1, +2) Adding and Subtracting **Integers** 3R 3L Adding and Subtracting **Integers** Reflection Observe, Question, Comment 08/16/1308/15/13 Warm-Up: Standard: Objective: Notes/Examples: Practice: Party or War? The **addition** symbol does not always mean to ADD! The subtraction symbol does not always mean to SUBTRACT! Problems to/

BEDMAS -36/-6 -154+56= -7x-9= Introduction What is BEDMAS? Brackets Exponents Division Multiplication **Addition** Subtraction When working out an **Integers** equation follow the BEDMAS rules. I can show you how to do that in 2 easy steps. Step 1 When /change the plus and negative sign into a minus sign like this 8 – 10 =. Now try some **of** these examples Now all you have to do is stick all that together and that is how you do BEDMAS with **integers**. Now try some **of** these examples (7 x -9) + 38 = (8²+7) – 45= 78 x 3 /

combining like terms and substituting. 1)-5x + 14x + (-6x) when x = 2 2)8x + (-7) + (-5x) when x = 2 Adding **Integers** You can use **integer** **addition** in real-life situations when you know the direction and the amount **of** change in a quantity. Adding **Integers** 1) The temperature at 4 pm Tuesday was 14° Fahrenheit. By 6 am Wednesday, the temperature had dropped 21°. What/

There are 3 switches downstairs, each corresponding to one **of** the light bulbs upstairs. How can you figure out which light switch goes to which light bulb by only making 1/ Lesson 1.02- Thinking About Negative Numbers Vocabulary: Number line Opposite Homework: Book: pg. 15; 4 Goals: Identify patterns in the **addition** table. Perform **integer** **addition**. Explain rules **of** **integers**. Lesson 1.03 **Addition** Table 1. Fill in the missing numbers For You to Explore: 2. Find and explain patterns you see. 1. What are the /

September 20, 2012 Modeling **integer** **addition** with counters: represents a positive **integer** and represents a negative **integer** Add the number **of** counters represented by each **integer** When modeling **integers** a create a zero pair and cancel each other out The remaining counters signify your answer Modeling **Integer** **Addition** with Counters + + Modeling **integer** **addition** with a number line Moving right on the number line represents a positive **integer** and moving left on the/

solve real-life problems. N8 Develop and analyze algorithms for computing with **integers** and demonstrate fluency in their use. Subtracting **Integers** 3-5 (pgs 128 -131) Well, I mean the RULE **of** Subtraction!Well, I mean the RULE **of** Subtraction! –To Subtract an **integer**… you add its opposite. –Change the problem to **addition**, and use SAK or DSL. Examples Subtracting 5 - 2 = ? This is the same/

(+) = [11 + (–11)] + (–4)Associative Property (+) = 0 + (–4)**Additive** Inverse Property = –4Additive Identity Property Answer: The solution is –4. Example 7 CYP A.–12 B.–10 C.–7 D.–2 Find 5 + (–7) + (–5). Example 8 FINANCIAL LITERACY Small businesses manage their inventory using **integers**. The cost **of** goods sold is calculated as starting inventory plus cost **of** items bought during the year plus a/

always positive or zero. Holt CA Course 1 2-1 Introduction to **Integers** The symbol | | is read as “the absolute value **of**.” For example, |–3| means "the absolute value **of** –3." Reading Math Holt CA Course 1 2-1 Introduction to **Integers** Graph the **integer** –7 and its opposite on a number line. **Additional** Example 1: Graphing **Integers** and Their Opposites on a Number Line The opposite/

Different Signs Example 8:Real-World Example Five-Minute Check Main Idea/Vocabulary Add **integers**. opposites **additive** inverse NGSSS MA.7.A.3.1 Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value **of** **integers**. Also addresses MA.7.A.3.2. Example 1 Add **Integers** with the Same Sign Find –6 + (–3). Start at 0. Move 6 units/

–12 is to the left **of** –10, –12 < –10. Graph –12 and –10 on the same number line. **Additional** Examples Use five as the number line unit. –35, –10, –2, 16, 68 Write the numbers in order from left to right. Comparing and Ordering **Integers** LESSON 6-2 Order from/a. 16, –2, –35, 68, –10 In order from least to greatest, the numbers are –35, –10, –2, 16, 68. **Additional** Examples Comparing and Ordering **Integers** LESSON 6-2 (continued) b. –87, –14, 41, –104, 78 In order from least to greatest, the numbers are –104, –87, /

’t there. Add the numbers and then put the sign **of** the addends in front **of** your answer. 9 + 5 = 14 -9 + -5 = -14 **Integer** **Addition** Rules Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger and put the sign **of** the larger in front **of** your answer. -9 + 5 = 9 - 5 = 4 Larger number Answer/

-17 Created by Mr. Lafferty Maths Dept Created by Mr. Lafferty Maths Dept Negative Numbers **Addition** & Subtraction Learning Intention Success Criteria 1 We are learning how to write down mathematically **addition** and subtraction **of** negative **integers**. To be able to write down mathematically the **addition** and subtraction **of** both positive and negative **integers**. www.mathsrevision.com 5-Apr-17 Created by Mr. Lafferty Maths Dept Created by/

**integers**. Preview **of** MA.7.A.3.2 Subtract…**integers**,…including solving problems in everyday contexts. Subtracting **Integers** on a Number Line Move left on a number line to subtract a positive **integer**. Move right on a number line to subtract a negative **integer**. Confused??? Subtracting **Integers**/, Change KEEP, CHANGE, CHANGE Some teachers teach Slash/Slash or Slash/Dash as KEEP, CHANGE, CHANGE **Additional** Example 1: Writing **Integer** Subtraction Write the subtraction modeled on each number line. A. B. –4 –3 –8 –7 /

when the signs **of** **integers** are different, their product or quotient is negative. The patterns also suggest that the product or quotient **of** two negative **integers** is positive. 2-4 Multiplying and Dividing **Integers** MULTIPLYING AND DIVIDING TWO **INTEGERS** If the signs are:Your answer will be: the same different positive negative 2-4 Multiplying and Dividing **Integers** Find each product. **Additional** Example 2: Multiplying **Integers** A. –6 · (–5/

- 2 Using Counters We can also use and to represent positive and negative numbers. For each **of** our positive numbers, we will use a + sign and for all **of** our negative numbers, we will use a – sign. Let’s try a few… + - **Integer** RULES List the **integer** **addition** and subtraction rules you have been taught in years prior to 8th grade. What IS a rule/

suggest that when the signs **of** **integers** are different, their product or quotient is negative. The patterns also suggest that the product or quotient **of** two negative **integers** is positive. Course 2 2-4 Multiplying and Dividing **Integers** MULTIPLYING AND DIVIDING **INTEGERS** If the signs are:Your answer will be: the same different positive negative Find each product. **Additional** Example 2: Multiplying **Integers** Course 2 2-4 Multiplying/

= –600 –400 + 200 –200 0 200 400 600 + 200 The product **of** two negative **integers** is a positive **integer**. Multiplying and Dividing **Integers** 1-7 Multiplying and Dividing **Integers** 1-7 **Additional** Example 1: Multiplying and Dividing **Integers** A. –6(4) B. –8(–5) 40 –24 Signs are / –24 3 D. 6 Signs are the same. Answer is positive. –12 –2 Multiplying and Dividing **Integers** 1-7 **Additional** Example 2: Using the Order **of** Operations with **Integers** A. 3(–6 – 12) –54 3(–18) Subtract inside the parentheses. Think: The/

to unsigned !! Carnegie Mellon 41 Today: Bits, Bytes, and **Integers** Representing information as bits Bit-level manipulations **Integers** Representation: unsigned and signed Conversion, casting Expanding, truncating **Addition**, negation, multiplication, shifting Summary Carnegie Mellon 42 Sign Extension Task: Given w-bit signed **integer** x Convert it to w+k-bit **integer** with same value Rule: Make k copies **of** sign bit: X = x w–1,…, x w/

/Divide unit Lec 13Systems Architecture3 Support for SLT and Overflow Detection Lec 13Systems Architecture4 MIPS ALU Lec 13Systems Architecture5 MIPS **Integer** Multiply and Divide Hi and Lo registers –mfhi –mflo Signed and unsigned multiply –mult –multu Divide instructions –div/ Architecture Fast Multiplication Hardware Unroll the **addition** “loop” Use 32 32-bit adders Each adder produces 32-bits and a carry-out The least significant bit **of** each intermediate sum is a bit **of** the product. The other 31 bits/

– 1 + + 3 – 1 + + 3 3 – 1 3 – 1 2 + 2 + 2 1.Change the subtraction to **addition**, then... 2....change the sign **of** the 2 nd **integer**. 3.Signs are DIFFERENT. 4.SUBTRACT the absolute values. 5.Write down that number. 6.The answer is NEGATIVE because the bigger – 10 /values. 5.Write down that number. 6.The answer is NEGATIVE because both **integers** are negative. 1.Change the subtraction to **addition**, then... 2....change the sign **of** the 2 nd **integer**. 3.Signs are DIFFERENT. 4.SUBTRACT the absolute values. 5.Write down /

Minus Higher” Student Outcome: I will learn different strategies to use **addition** to subtract **integers**.. ( ) – ( ) The morning temperature is - 5°C. This afternoon it will reach a temperature **of** +6°C. How much lower is the morning temperature than (/ day. Applying **Integer** Operations Student Outcome: I will decide when to add and subtract **integers**. Applying **Integer** Operations What are some words we use to know whether we should add or subtract **integers**? Subtraction to **Addition** **of** **Integers** Page 339-340/

or divide. –24 3 D. 6 Signs are the same. Answer is positive. –12 –2 Evaluating Algebraic Expressions 1-6Multiplying and Dividing **Integers** **Additional** Example 2: Using the Order **of** Operations with **Integers** A. 3(–6 – 12) –54 3(–18) Add the opposite **of** 12 inside the parentheses. Think: The signs are different. The answer is negative. Simplify. B. –5(–5 + 2) 15 –5(–3/

or divide. –24 3 D. 6 Signs are the same. Answer is positive. –12 –2 Evaluating Algebraic Expressions 1-6Multiplying and Dividing **Integers** **Additional** Example 2: Using the Order **of** Operations with **Integers** A. 3(–6 – 12) –54 3(–18) Add the opposite **of** 12 inside the parentheses. Think: The signs are different. The answer is negative. Simplify. B. –5(–5 + 2) 15 –5(–3/

the rules for adding…**integers**. Preview **of** MA.7.A.3.2 Add…**integers**,…including solving problems in everyday contexts. Sunshine State Standards 11-4 Adding **Integers** Move right on a number line to add a positive **integer**. Move left on a number line to add a negative **integer**. Adding **Integers** on a Number Line 11-4 Adding **Integers** Parentheses are used to separate **addition**, subtraction, multiplication, and division/

number1 & number2 Inputs: How we did it. We then initialized (gave an initial value to) number1 & number2 by the lines number1 = **Integer**.parseInt ( firstNumber ); number2 = **Integer**.parseInt ( secondNumber ); These lines convert the String values **of** firstNumber and secondNumber into int values and store them as number1 and number2. **Addition**.java //read in second number from user as a String secondNumber = JOptionPane.showInputDialog ( “Enter second/

**additional** information! 2 Forms On the first form, Next will bring up the second form. On the second form, Previous will bring up the first form. 2 Forms prSrchCr First I entered the course number that I want to search for. The retrieval is successful and comes back with the name **of**/ the call is made to Load_file it is executing Load_File which is part **of** FileHandlr2.bas. Private Sub cmdRetrieve_Click() Dim wrkInd As String, ptr As **Integer** Dim AddCrsResp As **Integer** wrkInd = "N" ptr = 1 Do While wrkInd = "N" /

= 3 Start at 0. Move right 4 spaces. To subtract 1, move to the left. 2-3 Subtracting **Integers** Rules for Subtracting **Integers**: Add the opposite 1. copy 2. change 3. opposite 4. Follow the Rules **of** Adding **Integers**. 2-3 Subtracting **Integers** **Additional** Example 1B: Modeling **Integer** Subtraction 1 2 –6–5–4 –3 –2–1 0 Use a number line to find each difference. –3/

are the counting numbers and zero: 0, 1, 2, 3, …. Remember! Holt CA Course 1 2-1 Introduction to **Integers** Graph the **integer** –7 and its opposite on a number line. **Additional** Example 1: Graphing **Integers** and Their Opposites on a Number Line The opposite **of** –7 is 7. 1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0 7/

feet. The whole numbers are the counting numbers and zero: 0, 1, 2, 3,.... Remember! Course 2 2-1 **Integers** Graph the **integer** 7 and its opposite on a number line. **Additional** Example 1: Graphing **Integers** and Their Opposites on a Number Line The opposite **of** –7 is 7. 1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0 7/

signs are different, SUBTRACT and use the sign **of** the larger number. (-2) + 4 = 2 2 + (-4) = -2 Song **Addition** Rule: Sung to the tune **of** “Row, row, row, your boat” Same signs add and keep, different signs subtract, keep the sign **of** the higher number, then it will be exact! Another way to Add **Integers** Is With a Number Line 0123456-2-3-4/

Objectives#8 MUST add two 8-bit binary **integers** SHOULD explain overflow errors COULD provide solutions to limit overflow errors GCSE Computing#BristolMet Adding binary numbers Adding binary numbers uses the same method as **addition** in Base10 where you carry 1 across e./ 1 1 Requires another bit GCSE Computing#BristolMet Overflow Overflow – when a number becomes too large to fit into the number **of** bits allocated it is said to ‘overflow’ and some bits are ‘lost’ leaving an incorrect value. For example: 1 /

Line A number line can also be used to model the **addition** **of** **integers** An arrow can be drawn above the number line to model each **of** the **integers** in the **addition** expression The second arrow is started at the finishing point **of** the first arrow Ex. The arrow above the number line represents (-6) Adding **Integers** With A Number Line Ex. Evaluate (+1) + (-6) Two arrows need/

similar to adding **integers** on a number line, but instead **of** adding, we will be subtracting. Place a circle on the number line to represent the first number in the problem. The second number will tell you how much to take away (this is different from **addition** because now we/Example 3 Model 5 – (-2) on a number line Start at 5 Move two spaces to the right (since 2 was negative) This is the opposite **of** what we did for example 1 Answer: 7 + Example 4 Model 3 – (-4) on a number line Answer: 7 + Example 5 Model 6 /

Represent Positive **Integers** Represent Negative **Integers** ANSWERS CornellNotes Goals: Warm up to the idea **of** the investigation Use an interactive approach to develop mathematical habits **of** mind. Lesson 1.01-Getting Started 1. What are the missing numbers in/ patterns you see. On Your Own: Homework: Book: pg. 11; 10 Goals: Perform **integer** **addition** Subtract using **integers** by adding the opposite Lesson 1.02- Thinking About Negative Numbers Vocabulary: Number line Opposite Homework: Book: pg. 15; 4 /

isolate the variable is to add the opposite **of** –3 to both sides. Because the sum **of** a number and its opposite is 0, the opposite **of** a number is also known as the **additive** inverse **of** the number. Holt CA Course 1 2-5 Solving Equations Containing **Integers** 3 + (–3) = 0 3 is the opposite, or **additive** inverse, **of** –3. Helpful Hint Holt CA Course 1 2/

2)1 = 2 (mod 5 ) Arithmetic Modulo m Definitions: Let Z m be the set **of** nonnegative **integers** less than m: { 0, 1, …., m −1 } The operation + m is defined as a + m b = (a + b) mod m. This is **addition** modulo m. The operation ∙ m is defined as a ∙ m b = (ab) mod/ ∙ 11 9 = (7 ∙ 9) mod 11 = 63 mod 11 = 8 Arithmetic Modulo m The operations + m and ∙ m satisfy many **of** the same properties as ordinary **addition** and multiplication. Closure: If a and b belong to Z m, then a + m b and a ∙ m b belong to Z m. Associativity/

the same sign: Keep the sign and add the numbers! -3 + (-7) = -10 4 + 9 = 13 ExitPreviousPrevious NextNext **Integer** Rules for **Addition** If two **Integers** have different signs: Subtract the two numbers and keep the sign **of** the number with the highest absolute value!absolute value -3 + 7 = 4 15 + (-9) = 6 -7 + 2 = -5 ExitPreviousPrevious NextNext You try now! Will the answer be/

bank. Hint If you don’t see a negative or positive sign in front **of** a number, it is ALWAYS positive. 9 + **Integer** **Addition** Rules Rule #1 – When adding two **integers** with the same sign, ADD the numbers and keep the sign. 9 + 5/+21 2. –22 + -11 = -33 3. 55 + 17 = +72 4. –14 + -35 = -49 **Integer** **Addition** Rules Rule #2 – When adding two **integers** with different signs, find the difference (SUBTRACT) and take the sign **of** the larger number. -9 + +5 = 9 - 5 = 4 Larger absolute value: Answer = - 4 Solve These Problems /

–1 0 1 2 3 4 5 E. Write the **integers** 8, –5, and 4 in order from least to greatest. **Additional** Example 2: Ordering **Integers** 8 > –5, 8 > 4, and –5 < 4 Compare each pair **of** **integers**. –5, 4, and 8. 1-3 **Integers** and Absolute Value Course 3 –5 is less than both 4/ and 8. F. Write the **integers** 7, –12, and 13 in order from least to greatest. Check It Out: **Additional** Example 2 13 > –12, 13 > 7, and –12 < 7 Compare each pair **of** **integers**. –12, 7, and 13. 1-3 **Integers** and Absolute Value Course 3 –12 is less /

fraction. They are decimals that are nonrepeating and nonterminating Examples 0.1567613491… Real Numbers is the set **of** all rational and irrational numbers. Real Numbers Rational NumbersIrrational Numbers **Integers** Whole Numbers 0 15 -13 -7 -35 -.37.823 -.37 29 2 5 6 Absolute/absolute value **of** the numbers. 7 + -5 =2-9 + 21= 6 + -15 = 12 - 2 nd step 21 – 92 nd step 7-5 2 nd step 15 - 6 9 - 23 + 16 = - 2 nd step 23 - 16 7 Subtraction Change the problem into an **addition** problem. To subtract an **integer**, add /

when the signs **of** **integers** are different, their product or quotient is negative. The patterns also suggest that the product or quotient **of** two negative **integers** is positive. 2-4 Multiplying and Dividing **Integers** MULTIPLYING AND DIVIDING TWO **INTEGERS** If the signs are:Your answer will be: the same different positive negative 2-4 Multiplying and Dividing **Integers** Find each product. **Additional** Example 2: Multiplying **Integers** A. –6 · (–5/

2 +3 +4 +5 Negative **Integers** Positive **Integers** 0 is neither negative nor positive. The set **of** whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember! **Additional** Example 2: Graphing **Integers** Graph each **integer** and its opposite on a number line/**of** **integers**. Write < or >. A. –2 1 B. 2 –3 C. –3 –4 –5 –4 –3 –2 –1 0 1 2 3 4 5 –2 < 1 –2 is to the left **of** 1 on the number line. 2 > –3 2 is to the right **of** –3 on the number line. –3 > –4 –3 is to the right **of** –4 on the number line. **Additional**/

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