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Algebra II

Algebra II. Definitions. Equation – A mathematical sentence stating that 2 expressions are equal. 12 – 3 = 9 8 + 4 = 12. Definitions. Equation – A mathematical sentence with an equals sign. 16 – 5 = 11 14 + 3 = 17. Definitions.

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Algebra II

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  1. Algebra II

  2. Definitions • Equation – A mathematical sentence stating that 2 expressions are equal. • 12 – 3 = 9 • 8 + 4 = 12

  3. Definitions • Equation – A mathematical sentence with an equals sign. • 16 – 5 = 11 • 14 + 3 = 17

  4. Definitions • Equals Sign (=) Means that the amount is the same on both sides. • 4 + 2 = 6 • 5 – 2 = 3

  5. An Equation is like a balance scale. Everything must be equal on both sides. = 10 5 + 5

  6. When the amounts are equal on both sides it is a true equation. = 12 6 + 6

  7. When the amounts are unequal on both sides it is a false equation. = 8 2 + 2

  8. When an amount is unknown on one side of the equation it is an open equation. = 7 n + 2

  9. When you find a number for n you change the open equation to a true equation. You solve the equation. = 7 5 n + 2

  10. Are these equations true, false or open? false • 11 - 3 = 5 • 13 + 4 = 17 • N + 4 = 7 • 12 – 3 = 8 • 3 + v = 13 • 15 – 6 = 9 true open false open true

  11. Definitions • Inverse operation – the opposite operation used to undo the first. • 4 + 3 = 7 7 – 4 = 3 • 6 x 6 = 36 36 / 6 = 6

  12. How to solve an addition equation • Use the inverse operation for addition which is subtraction • m+ 8 = 12 12 - 8 = 4 • m = 4 4 + 8 = 12

  13. How to solve a subtraction equation • Use the inverse operation for subtraction which is addition • m- 3 = 5 5 + 3 = 8 • m = 8 8 - 3 = 5

  14. Solve these equations using the inverse operations 3 • n + 4 = 7 • n – 5 = 4 • n + 4 = 17 • n – 6 = 13 • n + 7 = 15 • n – 8 = 17 9 13 19 8 9

  15. Commutative Property • 5 + 4 = 9 4 + 5 = 9 • a + b = c b + a = c • 6 + 3 = 9 3 + 6 = 9 • x+ y = z y + x = z • 3 + 4 + 1 = 8 1 + 3 + 4 = 8

  16. Solve these equations using the commutative property n = 4 • n + 7 = 7 + 4 • m + 2 = 2 + 5 • z + 3 = 3 + 9 • g + 6 = 6 + 11 • s + 4 = 4 + 20 • c + 8 = 8 + 32 m = 5 z = 9 g = 11 s = 20 c = 32

  17. The Identity Property of Addition • 7 + 0 = 7 • a + 0 = a • 8 + 0 = 8 • c + 0 = c • 2 + 0 = 2

  18. Use the Identity Property of addition to solve these problems • n + 0 = 8 • b + 0 = 7 • m + 0 = 3 • v + 0 = 5 • w + 0 = 4 • r + 0 = 2 n = 8 b = 7 m = 3 v = 5 w = 4 r = 2

  19. Subtraction Rules of zero • 7 – 7 = 0 • n – n = 0 • 4 – 0 = 4 • n – 0 = n

  20. Find the value of n using the rules of subtraction • n - 8 = 0 • n – 9 = 0 • n – 0 = 7 • n – 0 = 9 • n – 7 = 0 • n – 0 = 5 n = 8 n = 9 n = 7 n = 9 n = 7 n = 5

  21. Write an equation for these problems using a variable • Timothy got 72 right on his timed test in July. He got 99 right on this same test in November. • Jasmin runs 15 minutes before school and 30 minutes after school. • One zinger costs 25 cents. Issak bought 4. 72 + n = 99 or 99 – 72 = n 15 + 30 = n 4 x 25 = n

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