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Extra info for Algebra 04 Infinite groups, Linear groups
1. 6 Ϫ (Ϫ4) 4. Ϫ6 Ϫ (Ϫ4) 2. Ϫ6 Ϫ (4) 5. 0 Ϫ (Ϫ4) 3. 6 Ϫ (4) 6. ) Remember . . Just change the subtraction problem into an addition problem, and take the opposite of the number being subtracted. Then solve the new addition problem. Example: 6 Ϫ (Ϫ4) 6 Ϫ (Ϫ4) becomes 6 ϩ (ϩ4) after both signs are changed. 6 ϩ (+4) ϭ 10 MULTIPLYING INTEGERS Multiplying integers is easy. When you multiply two integers, there are four possible cases. Case 1: Both numbers are positive. Example: 6 и 4 52 algebra_ch2 5/4/06 9:30 AM Page 53 MULTIPLYING INTEGERS Case 2: Both numbers are negative.
3x divided by 3 ϭ ᎏ33ᎏ 8xy 7. 8xy divided by y ϭ ᎏ yᎏ ϭ 8x 33 algebra_ch1 5/4/06 9:27 AM Page 34 A PAINLESS BEGINNING Set # 3, page 18 1. 0 ϩ a ϭ a 5. (0)a ϭ 0 2. a(0) ϭ 0 6. a Ϫ 0 ϭ a 3. 0 Ϫ a ϭ Ϫa 7. ᎏ0aᎏ is undefined. 4. ᎏ0aᎏ ϭ 0 Set # 4, page 23 1. 4 Ϭ (2 ϩ 2) Ϫ 1 ϭ ᎏ44ᎏ Ϫ 1 ϭ 1 Ϫ 1 ϭ 0 2. 3 ϩ 12 Ϫ 5 и 2 ϭ 3 ϩ 12 Ϫ 10 ϭ 15 Ϫ 10 ϭ 5 3. 16 Ϫ 2 и 4 ϩ 3 ϭ 16 Ϫ 8 ϩ 3 ϭ 11 4. 6 ϩ 52 Ϫ 12 ϩ 4 ϭ 6 ϩ 25 Ϫ 12 ϩ 4 ϭ 23 5. (4 Ϫ 3)2(2) Ϫ 1 ϭ (1)2(2) Ϫ 1 ϭ 1(2) Ϫ 1 ϭ 2 Ϫ 1 ϭ 1 Set # 5, page 27 1. DM/A 3.
Add them. Place a negative sign in front of the answer. EXAMPLES: (Ϫ3) ϩ (Ϫ8) ϭ Ϫ11 (Ϫ2) ϩ (Ϫ4) ϭ Ϫ6 Ϫ5 ϩ (Ϫ5) ϭ Ϫ10 Case 3: One number is positive and one number is negative. Painless Solution: Pretend both numbers are positive. Subtract the smaller number from the larger number. Give the answer the sign of the number that would be larger if both numbers were positive. (Ϫ3) ϩ (ϩ8) ϭ ? Pretend both numbers are positive and subtract the smaller number from the larger number. 8Ϫ3ϭ5 Give the answer the sign of the larger number if both numbers were positive.