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Bell Ringer

Bell Ringer. 58,021.349 What is the place value of the 8? What is the place value of the 4? What is the place value of the 2? What is the place value of the 9 ? What is the place value of the 3?. Integer Operations. The Incredible Number Line!!!.

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Bell Ringer

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  1. Bell Ringer 58,021.349 • What is the place value of the 8? • What is the place value of the 4? • What is the place value of the 2? • What is the place value of the 9? • What is the place value of the 3?

  2. Integer Operations

  3. The Incredible Number Line!!! • The number line contains an infinite amount of points. • 5, -6, 3.2, 1.115, 9.9 are all on the number line. • We will deal specifically with integers, which are the whole numbers on the number line.

  4. What is an Integer? • A number with no fractional part. • Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...} • Examples of integers: -16, -3, 0, 1, 198 • Basically integers are all positive and negative whole numbers and zero!

  5. Adding Integers • Number Line – Start at the first number and move forwards or backwards. -4 + 5 = ? • Counters -4 Your answer is 1!!! 5

  6. Subtracting Integers • Number Line – This can get confusing, but the subtraction sign changes the direction you travel in. 3 – (-4) = • Counters – This isn’t much better! 3 -4 How did I get here? Huh??

  7. Adding Integers • Rules for adding integers • Adding (when signs are the same) • Keep the sign • Add • Ex. 3 + 4 = 7 • Ex. (-9) + (-4) = -13 • Adding (when signs are different) • Keep the sign of the bigger digit • Subtract • Ex. -3 + 5 = 2 • Ex. 4 + -7 = -3

  8. Sample Additions • -5 + 9 = • -7 + -8 = • 6 + (-12) = • 1. The signs are different, so I find the difference, which is 4. The 9 is the bigger digit, so my answer is positive. • 2. The signs are the same, so I add, which gives me 15. The signs are the same, so I keep the answer negative. • 3. The signs are different, so I find the difference, which is 6. The -12 is the bigger digit, so my answer is negative.

  9. Subtracting Integers • Rules for subtracting integers • ALL subtraction problems: • Change the subtraction sign to an addition sign. • Change the sign of the second number. • Follow addition rules • Ex: 3 – (- 7) = 3 + (+7) = 10

  10. Sample Subtraction • 6 – 9 = • -5 – (-3) = 1. Change the subtraction to addition and change the sign of the second digit. 6 – 9 = 6 + (-9) = Follow addition rules. 6 + (-9) = -3 2. Change the subtraction to addition and change the sign of the second digit. -5 – (-3) = -5 + 3 = Follow addition rules. -5 + 3 = -2

  11. Multiplying and Dividing Integers • Rules for multiplying and dividing integers • Multiply/Divide • If the signs are the SAME…the answer will be POSITIVE • If the signs are DIFFERENT …the answer will be NEGATIVE • Ex. -4 • (-7) = 28 • Ex. 5 • (-3) = -15 • Ex. 25 ÷ (-5) = -5 • Ex. -15 ÷ (-3) = 5

  12. Sample Multiplying and Divding • 5 • -8 = • -3 • -6 = • -25 ÷ 5 = • -6 ÷ -2 = 1. The signs are different, so the answer will be negative. 5 • -8 = -40 2. The signs are the same, so the answer will be positive. -3 • -6 = -18 3. The signs are different, so the answer will be negative. -25 ÷ 5 = -5 4. The signs are the same, so the answer will be positive. -6 ÷ -2 = 3

  13. Samples • 1. -4 + 5 = • 2. -6 – (-9) = • 3. 5 • -9 = • 4. -12 ÷ -3 = 1 3 -45 4

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