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# Algebra ii

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### Algebra ii

1. 1. Algebra II
2. 2. Definitions <ul><li>Equation – A mathematical sentence stating that 2 expressions are equal. </li></ul><ul><li>12 – 3 = 9 </li></ul><ul><li>8 + 4 = 12 </li></ul>
3. 3. Definitions <ul><li>Equation – A mathematical sentence with an equals sign. </li></ul><ul><li>16 – 5 = 11 </li></ul><ul><li>14 + 3 = 17 </li></ul>
4. 4. Definitions <ul><li>Equals Sign (=) Means that the amount is the same on both sides. </li></ul><ul><li>4 + 2 = 6 </li></ul><ul><li>5 – 2 = 3 </li></ul>
5. 5. An Equation is like a balance scale. Everything must be equal on both sides. 10 5 + 5 =
6. 6. When the amounts are equal on both sides it is a true equation. 12 6 + 6 =
7. 7. When the amounts are unequal on both sides it is a false equation. 8 2 + 2 =
8. 8. When an amount is unknown on one side of the equation it is an open equation. 7 n + 2 =
9. 9. When you find a number for n you change the open equation to a true equation. You solve the equation. 7 n + 2 = 5
10. 10. Are these equations true, false or open? <ul><li>11 - 3 = 5 </li></ul><ul><li>13 + 4 = 17 </li></ul><ul><li>N + 4 = 7 </li></ul><ul><li>12 – 3 = 8 </li></ul><ul><li>3 + v = 13 </li></ul><ul><li>15 – 6 = 9 </li></ul>false true open false open true
11. 11. Definitions <ul><li>Inverse operation – the opposite operation used to undo the first. </li></ul><ul><li>4 + 3 = 7 7 – 4 = 3 </li></ul><ul><li>6 x 6 = 36 36 / 6 = 6 </li></ul>
12. 12. How to solve an addition equation <ul><li>Use the inverse operation for addition which is subtraction </li></ul><ul><li>m + 8 = 12 12 - 8 = 4 </li></ul><ul><li>m = 4 4 + 8 = 12 </li></ul>
13. 13. How to solve a subtraction equation <ul><li>Use the inverse operation for subtraction which is addition </li></ul><ul><li>m - 3 = 5 5 + 3 = 8 </li></ul><ul><li>m = 8 8 - 3 = 5 </li></ul>
14. 14. Solve these equations using the inverse operations <ul><li>n + 4 = 7 </li></ul><ul><li>n – 5 = 4 </li></ul><ul><li>n + 4 = 17 </li></ul><ul><li>n – 6 = 13 </li></ul><ul><li>n + 7 = 15 </li></ul><ul><li>n – 8 = 17 </li></ul>3 9 13 19 8 9
15. 15. Commutative Property <ul><li>5 + 4 = 9 4 + 5 = 9 </li></ul><ul><li>a + b = c b + a = c </li></ul><ul><li>6 + 3 = 9 3 + 6 = 9 </li></ul><ul><li>x+ y = z y + x = z </li></ul><ul><li>3 + 4 + 1 = 8 1 + 3 + 4 = 8 </li></ul>
16. 16. Solve these equations using the commutative property <ul><li>n + 7 = 7 + 4 </li></ul><ul><li>m + 2 = 2 + 5 </li></ul><ul><li>z + 3 = 3 + 9 </li></ul><ul><li>g + 6 = 6 + 11 </li></ul><ul><li>s + 4 = 4 + 20 </li></ul><ul><li>c + 8 = 8 + 32 </li></ul>n = 4 m = 5 z = 9 g = 11 s = 20 c = 32
17. 17. The Identity Property of Addition <ul><li>7 + 0 = 7 </li></ul><ul><li>a + 0 = a </li></ul><ul><li>8 + 0 = 8 </li></ul><ul><li>c + 0 = c </li></ul><ul><li>2 + 0 = 2 </li></ul>
18. 18. Use the Identity Property of addition to solve these problems <ul><li>n + 0 = 8 </li></ul><ul><li>b + 0 = 7 </li></ul><ul><li>m + 0 = 3 </li></ul><ul><li>v + 0 = 5 </li></ul><ul><li>w + 0 = 4 </li></ul><ul><li>r + 0 = 2 </li></ul>n = 8 b = 7 m = 3 v = 5 w = 4 r = 2
19. 19. Subtraction Rules of zero <ul><li>7 – 7 = 0 </li></ul><ul><li>n – n = 0 </li></ul><ul><li>4 – 0 = 4 </li></ul><ul><li>n – 0 = n </li></ul>
20. 20. Find the value of n using the rules of subtraction <ul><li>n - 8 = 0 </li></ul><ul><li>n – 9 = 0 </li></ul><ul><li>n – 0 = 7 </li></ul><ul><li>n – 0 = 9 </li></ul><ul><li>n – 7 = 0 </li></ul><ul><li>n – 0 = 5 </li></ul>n = 8 n = 9 n = 7 n = 9 n = 7 n = 5
21. 21. Write an equation for these problems using a variable <ul><li>Timothy got 72 right on his timed test in July. He got 99 right on this same test in November. </li></ul><ul><li>Jasmin runs 15 minutes before school and 30 minutes after school. </li></ul><ul><li>One zinger costs 25 cents. Issak bought 4. </li></ul>72 + n = 99 or 99 – 72 = n 15 + 30 = n 4 x 25 = n