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By Ladislav Nebeský

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6. 7. 8. 9. 10. ) algebra_ch1 5/4/06 9:27 AM Page 33 BRAIN TICKLERS—THE ANSWERS BRAIN TICKLERS— THE ANSWERS Set # 1, page 9 1. 3x ϩ 7x ϭ 10x 2. 4x ϩ x ϭ 5x 3. 3x Ϫ 3x ϭ 0 4. 10x Ϫ x ϭ 9x 5. 6x Ϫ 4x ϭ 2x 6. 3x ϩ 2 ϭ 3x ϩ 2 The sum of these terms cannot be simplified because 3x and 2 are not like terms. 7. 10 Ϫ 4x ϭ 10 Ϫ 4x This expression cannot be simplified because 10 and 4x are not like terms. Set # 2, page 15 1. 3x times 4y ϭ 3x(4y) ϭ 12xy 2. 6x times 2x ϭ 6x(2x) ϭ 12x2 3. 2x times 5 ϭ 2x(5) ϭ 10x 7ᎏ x ϭ1 4.

The answer is always positive. EXAMPLES: Ϫ8 Ϭ (ϩ2) ϭ –4 Ϫ15 Ϭ (Ϫ3) ϭ ϩ5 55 algebra_ch2 5/4/06 9:30 AM Page 56 THE INTEGERS MATH TALK! Here’s how you change Math Talk into just Plain English. Ϫ9 Ϭ (Ϫ3) ϭ 3 Negative nine divided by negative three equals three. Case 3: One number is positive and the other negative. Painless Solution: Pretend the numbers are positive. Divide the numbers. The answer is always negative. EXAMPLES: Ϫ9 Ϭ 3 ϭ Ϫ3 15 Ϭ (Ϫ3) ϭ Ϫ5 Case 4: The dividend is zero. Painless Solution: Zero divided by any number (except 0) is zero.

Divide the numbers. The answer is always positive. EXAMPLES: Ϫ8 Ϭ (ϩ2) ϭ –4 Ϫ15 Ϭ (Ϫ3) ϭ ϩ5 55 algebra_ch2 5/4/06 9:30 AM Page 56 THE INTEGERS MATH TALK! Here’s how you change Math Talk into just Plain English. Ϫ9 Ϭ (Ϫ3) ϭ 3 Negative nine divided by negative three equals three. Case 3: One number is positive and the other negative. Painless Solution: Pretend the numbers are positive. Divide the numbers. The answer is always negative. EXAMPLES: Ϫ9 Ϭ 3 ϭ Ϫ3 15 Ϭ (Ϫ3) ϭ Ϫ5 Case 4: The dividend is zero.

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Algebraic properties of trees (Acta Universitatis Carolinae : Philologica monographia) by Ladislav Nebeský


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