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Adding Positive and Negative Integers

This guide teaches the fundamental concepts of adding positive and negative integers using various methods, including zero pairs, number lines, and rules for adding integers of differing signs. Students will learn to identify variables, variable expressions, and the absolute value of numbers, crucial for solving problems. The content encourages practical applications through examples, making the concepts accessible and engaging for learners. Whether you're a beginner or looking to refine your skills, this resource will enhance your understanding of integer addition.

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Adding Positive and Negative Integers

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  1. AddingPositiveand Negative Integers Confidential

  2. WARM-UP • Order from least to greatest 7, -3, 0, -1, 3 2) Insert a) -15 -16 b) 1 2 3) Find the sum: 748 + 93 = Confidential

  3. Review A variable is a letter that stands for a number We use variables when we don’t know the number A variable can be any letter Confidential

  4. Review We can also write VARIABLE EXPRESSIONS such as s + 9 8 n 16 x h A VARIABLE EXPRESSION contains a variable and an operation such as addition, subtraction, multiplication, division. Confidential

  5. Word phrases can be translated into VARIABLE EXPRESSIONS Word Phrase Variable Expression 2 more than n 2 + n k times 8 k x 8 Confidential

  6. Absolute Value The absolute value of a number is its distance from zero on the number line The absolute value of 4 is written as 4 The absolute value is always positive! Confidential

  7. Opposites Confidential

  8. When we add an integer and its opposite, the sum is zero EXAMPLES: (-5) + 5 = 0 98 + (-98) = 0 Opposites are also called ADDITIVE INVERSES. Confidential

  9. Today we are going to learn how to add integers. We will explore 3 different METHODS METHOD 1 - ZERO PAIRS + + - - - + - The red chips are NEGATIVE. The grey chips are POSITIVE Confidential

  10. Zero Pair - + + = 0 1 red chip 1 grey chip We call 1 red chip and 1 grey chip a ZERO PAIR Confidential

  11. Lets take an Example If we want to add 3 + 2 + + + We begin with 3 grey chips + + And we add 2 more grey chips 3 + 2 = 5 FOR A TOTAL OF 5 GREY CHIPS Confidential

  12. If we want to add -2 + (-4) Remember red chips are negative We begin with 2 red chips - - And we add 4 more red chips - - - - -2 + (-4) = -6 FOR A TOTAL OF 6 RED CHIPS. Do you have any questions so far???? Confidential

  13. Adding integers with different signs BUT if we want to add integers with different signs, we must use ZERO PAIRS - + These 2 chips form a ZERO PAIR. These 2 chips equal zero. Confidential

  14. Lets see with an Example Let's add (-5) + 3 - - - We begin with 5 red chips - - And we add 3 grey chips + + + Confidential

  15. Adding (-5) + 3 - - We begin with 5 red chips - - - And we add 3 grey chips + + + We circle the Zero Pairs and remove them! (Remember a ZERO PAIR equals zero.) Confidential

  16. Result We begin with 5 red chips - - And we add 3 grey chips We are now left with 2 red chips OR -2 Therefore, (-5) + 3 = -2 Confidential

  17. You try a few. Use your red and black pens to make your chips. (-3) + 1 = 4 + (-5) = Confidential

  18. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 METHOD 2 - Number Line We can use a number line to find the sum of 2 integers. WE ALWAYS START AT ZERO! Confidential

  19. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Lets add 3 + 4 by number line 2. 1. 1. Start at zero and move to the right (in a positive direction) 3 spaces. 2. Next, move further to the right 4 spaces. 3 + 4 = 7 3. Your answer is 7. Confidential

  20. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Now, let's add (-2) + (-8) 1. Start at zero and move to the left (in a negative direction) 2 spaces. 2. Next, move further to the left 8 spaces. 3. Your answer is -10. (-2) + (-8) = -10 Confidential

  21. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Let's see what happens when we add a positive AND a negative number. (-6) + 8 = • Start at zero and move to the left (in a negative direction) • 6 spaces. 2. Next, move to the RIGHT 8 spaces. 3. Your answer is 2. as (-6) + 8 = 2 DO YOU HAVE ANY QUESTIONS?? Confidential

  22. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 You try a couple..... Start at zero and draw your arrows! 4 + (-7) = (-2) + (-5) = Confidential

  23. Method 3 - Rules for adding integers Adding the The sum of 2 positive numbers is POSITIVE. Same sign The sum of 2 negative numbers is NEGATIVE. Example: 4 + 7 = 11 (-3) + (-6) = (-9) 11 + 8 = (-9) + (-1) = Confidential

  24. Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Example: (-2) + 9 = Absolute Values Step 1.) 2 9 Step Subtract 2.) 9 - 2 Sign of the larger number Step 3.) +7 Confidential

  25. Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Try (-11) + 5 = Step 1.) Absolute Values 11 , 5 Subtract Step 2.) 11 – 5 = 6 Sign of the larger number - 6 Step 3.) Confidential

  26. 1.) The temperature in Minneapolis was 7 degrees F at noon. By 8 pm, the temperature had dropped 15 degrees F. What was the temperature at 8 pm? Confidential

  27. 2.) You have $60 in your bank account. You withdraw (or take out) $45 to buy new tires for your bike. You then deposit (or add in) your babysitting money of $18.What is the new balance in your bank account? Confidential

  28. 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Let's see how well we understood the lesson today. Use a number line to find each sum. 1.) (-7) + 12 = 2.) 4 + (-10) = Confidential

  29. Find each sum. Remember your Addition Rules! 3.) (-7) + (-11) = 4.) 12 + (-5) = 5.) 22 + 7 = 6.) (-9) + 5 = 7.) 3 + (-10) = 8.) (-8) + 20 = 9.) 1 + (-30) = 10.) (-15) + (-5) = 11.) Opposites are also called A_________ I__________. Confidential

  30. Let's Review... There are 3 METHODS we can use to Add Integers. METHOD 1 We can add integers using ZERO PAIRS. Confidential

  31. To add (-5) + 3 = Then we are left with 2 red chips. Therefore, (-5) + 3 = -2 Confidential

  32. METHOD 2 We can also use a number line to find the sum of 2 integers. . Confidential

  33. METHOD 3 Rules Adding the Same Sign – The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE. Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Confidential

  34. You had a great lesson today! Be sure to practice what you learned! Confidential

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