Thus, When no coefficient is expressed, 1 is understood. Where no sign is expressed, + is understood. 7. + 3x 8. -5xу 9. 9 abc 10. -24 xyz NEGATIVE QUANTITIES. 536. Suppose three men as follows: The first man has $5 and owes nothing. The third man has nothing and owes $5. The second man is worth nothing. The third man is worth 5 less than nothing. say he is worth — $5. So we may 537. Quantities like -$5, -17, and -2 a are called negative quantities. What sign precedes a negative quantity? Quantities with a plus sign expressed or understood are called positive quantities. 538. Oral Exercises. 1. A man bought a horse for $100. He sold it for $110. What was his gain? 2. A man bought a horse for $200. He sold it for $175. What was his gain? Ans. $25. 3. A man earned $60 during November. He spent $45. How much did he save? 4. A man earned $60 during December. He spent $70. How much did he save? 5. A man went north from a starting point 10 miles. He then went south 8 miles. How far north of his starting point was he then ? 6. A man went north from a starting point 10 miles. He then went south 14 miles. How far north of his start ing point was he then? 7. What is meant by a gain of — $5? 9. What is the meaning of this statement? is - 3 inches taller than her husband. A woman 10. John is 3 years older than Mary. Mary is how many years older than John? ADDITION OF POSITIVE AND NEGATIVE QUANTITIES. 539. Preliminary Exercises. 1. On Monday an agent makes $6 above his expenses; $3; on Wednesday, $4; on Thursday, $8; $2; on Saturday, $7. on Tuesday, on Friday, 2. Another agent's profits for the days of the week are -$3, $2,$2, $4, $1, $2. In the first example we add all the positive quantities, $6 + $4 + $8+ $7= $25. Then we add all the negative quantities, - $2 = = -$5. Adding $25 and - $5 the result is $20. - $3 In the second example we add all the positive quantities, and get $6. The sum of the negative quantities is $8. Adding $6 and -$8 the result is — $2. Can you give the rule for addition where the quantities have different signs? Which sign does the sum take? 6. 3x+14, -7x+9, -23, 4x-5, -2x, and 3x+11. Write like quantities in the same column. Find the sum of the positive terms, also the sum of the negative terms; subtract the less from the greater, and prefix the sign of the greater. 3x+14 -7x+9 - 23 4x - 5 - 2x 3x+11 7. 4a+3x, 2a, -7x-3a, -5x, -9a+x. 8. 9. 3b+c, 4a+6b, 5b-9c, 3a, -2a-3b+ 4 c. x8, x+4, -4x-3, 7x+16, -5x-10. 10. 4x+23, -8x+21, − z x + 11, −x + 5, 9x — 3. SUBTRACTION OF ALGEBRAIC QUANTITIES. 541. Preliminary Exercises. 1. A man sold a horse for $100 at a gain of $25. Find the cost. (Cost = selling price - gain.) 2. A man sold a horse for $100 at a gain of In the first of the above examples, subtracting + $25 is the same as adding $25. In the second of the above examples, subtracting - $25 is the same as adding + $25. We changed the first example from subtraction to addition by changing the sign of the subtrahend from + to −. We changed the second example from subtraction to addition by changing the sign of the subtrahend from to +. To subtract in algebra, change the sign of the subtrahend and proceed as in addition. 9. Subtracting -- 7 is the same as adding what? - 7. 10. Is a positive quantity increased or decreased by subtracting a negative quantity? NOTE. - When you become familiar with the process of subtraction it will not be necessary to write the subtrahend with a changed sign. You can conceive the sign changed and add. 542. Sight Exercises. 1. What is the difference between + 52° and +33°? 2. Between + 90° and 10° ? Show by a diagram. 3. A has $600, B owes $400. What are they worth together? (+ $ 600)+(− $ 400) = ? 4. How much better off is A than B? (+ $ 600) − (− $ 400) = ? 16. From 7y-2z+b take 8y+6b-z. 17. From c de take c+d-f. |