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# 2 5math Laws

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### 2 5math Laws

1. 1. Math Laws Properties of Addition, Multiplication, and Equalities
2. 2. Warm-Up
3. 3. Warm-Up
4. 4. What’s the Deal? <ul><li>In these lessons we will use the commutative, associative, and distributive properties of addition and multiplication. </li></ul><ul><li>We will use the reflexive, symmetric, transitive, and substitution properties of equality. </li></ul><ul><li>We will be reminded of the additive inverse and identity properties. </li></ul>
5. 5. Properties of Addition and Multiplication <ul><li>Commutative </li></ul><ul><li>Associative </li></ul><ul><li>Examples: </li></ul><ul><li>4+3=3+4 </li></ul><ul><li>71*25 = 25*71 </li></ul><ul><li>(6+7)+9=6+(7+9) </li></ul><ul><li>(8*10)*73=8*(10*73) </li></ul>
6. 6. Nicknames <ul><li>Commutative Property </li></ul><ul><li>Associative Property </li></ul><ul><li>Order Property </li></ul><ul><li>Grouping Property </li></ul>
7. 7. Complete each step and name the property used <ul><li>24+(27+56) = </li></ul><ul><li>(27 +__) + 56 = </li></ul><ul><li>27 + (24 + __ ) = </li></ul><ul><li>27 + __ = ____ </li></ul><ul><li>Given </li></ul><ul><li>Commutative Property </li></ul><ul><li>Associative Property </li></ul><ul><li>Addition </li></ul>
8. 8. Identity Properties <ul><li>208 = 208 </li></ul><ul><li>What number can we add to 208 to get the same answer? (208) </li></ul><ul><li>208+0 = 208 </li></ul><ul><li>Identity Property of Addition </li></ul><ul><li>98 = 98 </li></ul><ul><li>What number can we multiply by 98 to get the same answer? (98) </li></ul><ul><li>98*1 = 98 </li></ul><ul><li>Identity Property of Multiplication </li></ul>
9. 9. What is the opposite? <ul><li>15x – 8y + 7 </li></ul><ul><li>Two Ways: </li></ul><ul><ul><li>Change all signs or, </li></ul></ul><ul><ul><li>Multiply all terms by -1 </li></ul></ul><ul><li>One way: </li></ul><ul><li>-1(15x-8y+7) = </li></ul><ul><li>-15x + 8y – 7 </li></ul><ul><li>OR </li></ul><ul><li>+15x – 8y +7 </li></ul><ul><li>-15x +8y -7 </li></ul>
10. 10. I MUST GET PAID! <ul><li>Nora has two part-time jobs. She gets paid \$8 per hour at the retail store and \$12 per hour typing term papers for college students. How much will she be able to deposit into her piggy bank after working 7 hours at the store and 5 hours of typing? </li></ul>(8*7)+(5*12) \$56+\$60=\$106
11. 11. <ul><li>Copyright D DAHLBERG </li></ul>Woodard Bay WIldlife Sanctuary Olympia, Washington
12. 12. <ul><li>Pg. 86: </li></ul><ul><li>12; 15-21; 43, 44 </li></ul>Assignment
13. 13. Distributive Property & Properties of Equality
14. 14. Transitive Property of Equality <ul><li>a = a </li></ul><ul><li>Looks pretty straightforward. </li></ul>
15. 15. Symmetric Property of Equality <ul><li>If b = a, then a = b </li></ul><ul><li>If n = 99, then 99 = ____. </li></ul>
16. 16. Transitive Property of Equality <ul><li>If a = b, and a=c, then a = c </li></ul><ul><li>If x = 42, and n=(42), then x = ____. </li></ul><ul><li>Hint: any time you see trans- in part of a word, the meaning usually involves “across”. </li></ul>
17. 17. Substitution Property of Equality <ul><li>If b = a, then a = b </li></ul><ul><li>If x = (44-2), and n=(40+2), then x = __. </li></ul>42
18. 18. Distributive Property of Multiplication <ul><li>35(20 + 9) </li></ul><ul><ul><li>means 35 x everything in the parentheses. </li></ul></ul><ul><li>35*20 + 35 *9 = </li></ul><ul><li>700 + 315 =1015 </li></ul><ul><li>755 * 45 = (700 + 50 + 5)•45 </li></ul><ul><ul><li>(700•45)+ (50•45)+ (5•45) </li></ul></ul>
19. 19. Try Some <ul><li>9 (5+y)= </li></ul><ul><ul><li>45 + 9y </li></ul></ul><ul><li>14(x-5)= </li></ul><ul><ul><li>14x - 70 </li></ul></ul><ul><li>3(n+2)= </li></ul><ul><ul><li>3n + 6 </li></ul></ul><ul><li>3p(r+2)= </li></ul><ul><ul><li>3pr+3p2 </li></ul></ul>
20. 20. Write these using the Distributive Property <ul><li>rs+rq </li></ul><ul><li>4bk + sk </li></ul><ul><li>9xy – 21xyz </li></ul><ul><li>10fg – 2kg </li></ul><ul><li>Start by finding the factors that are common to both terms. </li></ul><ul><li>The first one shows r is common to both. </li></ul><ul><li>r(s+q) </li></ul><ul><li>k(4b + s) </li></ul><ul><li>3xy(3 – 7z) </li></ul><ul><li>2g(5f – 2k) </li></ul>
21. 21. assignment <ul><li>Pg 86: 24-31; 33-37; 45, 47 all </li></ul>