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Adding Integers

Adding Integers. Section 2.2 and 2.3. The Concept. Today’s subject is not new to you, but rather a revisiting of an important topic from years previous Understanding the adding positive and negative numbers (integers) is imperative to the process of solving basic algebraic equations.

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Adding Integers

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  1. Adding Integers Section 2.2 and 2.3

  2. The Concept • Today’s subject is not new to you, but rather a revisiting of an important topic from years previous • Understanding the adding positive and negative numbers (integers) is imperative to the process of solving basic algebraic equations

  3. The number line • The basic premise of adding these numbers is that the first number is plotted on the number line and then the answer is developed by moving either right or left • e.g. 4+5=9 • e.g. -3+10=7 Axis of symmetry Vertex

  4. Solve the following Add • 5+10 • -4+1 • -10+3 • 3+-10 • (4+3)+-3 • 4+(3+-3) • 3+0 • 4+-4

  5. Commutative Associative a + b = b + a (ab)c = a(bc) Properties

  6. Identity This will always make something equal to it’s self a · 1 = a & a + 0 = a Properties

  7. Inverse This will make something go to 1 or zero a + (-a) = 0 & a · = 1 Properties

  8. Commutative Associative Identity Inverse Distributive a + b = b + a (ab)c = a(bc) a · 1 = a & a + 0 = a a + (-a) = 0 & a · = 1 a(b + c) = ab + ac Properties Lastly

  9. Example • What property is illustrated here?

  10. Example • What property is illustrated here?

  11. Example • What property is illustrated here?

  12. Example • What property is illustrated here?

  13. The number line • The basic premise of subtracting is the addition of the opposite number • e.g. 4-5= • 4+(-5)=-1 • e.g. -3-9= • -3+(-9)=-12 Axis of symmetry Vertex

  14. Re write using the Cm. property • X+Y • 5-4 • -4-4 • 9- -4

  15. Solve the following subtract • 5-10 • -4-1 • -10--3 • 3--10 • (4-3)-3 • 4-(3--3) • 3-0 • 4--4

  16. example • 2-(-4) • 2+(-5) • -3-5

  17. Evaluate the expression • X=-9 Y=4 • X+4-Y • -x-y • -y-x-5

  18. Practical Example • This past weekend you started with $20 in your pocket. Over the course of the three days you did the following things • Went to the movies for $6.50 • Bought candy for $2.50 • Found $2 in the parking lot • Went to the football game for $1 • Stopped at QT on the way home and bought a pop and M&M’s for $3.25 • Gave a homeless person $1 and all the coins you had in your pocket • Bought a cookie at a coffee shop for $1.43 How much money do you have left?

  19. Most Important Points • Addition on the number line • Properties of addition

  20. Homework you must do both 2.2 Pg. 75 3-17, 26-31, 38-41 2.3 Pg. 83 3-10, 17-22, 32-34, 42,43

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