Ex. 9. What is the sum of -3a, -7a, -11a, and -8a? Ans. -29a. Ex. 10. What is the sum of -2bc, -12bc, -5bc and -bc? Ans. -20bc. Ex. 11. What is the sum of -3ax, −6ax, −15ax and -4ax? (42.) When the quantities are similar, but have dif ferent signs. RULE. Add all the positive coefficients together, and alsı all those that are negative; subtract the least of thes results from the greater; to the difference annex the common letter or letters, and prefix the sign of the greater sum. Thus, instead of 7a-4a, we may write 3a, since these two expressions obviously have the same value. Also, if we have 5a-2a+3a-a, this signifies that from 5a we are to subtract 2a, add 3a to the remainder, and then subtract a from this last sum, the result QUEST. What is case second? Give the rule. of which operation is 5a. But it is generally most convenient to take the sum of the positive quantities, which in this case is 8a; then take the sum of the negative quantities, which in this case is 3a; and we have Sa-3a, or 5a, the same result as before. The pupil must continually bear in mind the remark of Art. 21, that when no sign is prefixed to a quantity, plus is always to be understood. Ex. 1. What is the sum of 6a, −4a, 3a, and a? Ans. 6a. Ex. 2. What is the sum of 4xy-2xy+7xy—xy? Ans. 8xy. Ex. 3. What is the sum of 3abm+2abm-4abm a2x+7a 7x2-2ac -16h+2y -7ab2—3mx (43.) When some of the quantities are dissimilar. QUEST.-What is the third case? RULE. Collect all the like quantities together, by taking their sums or differences as in the two former cases, and set down those that are unlike, one after the other, with their proper signs. Unlike quantities can not be united in one term. Thus, 2a and 36 neither make 5a nor 56. Their sum can only be written 2a+3b. Ex. 1. What is the sum of 3ab+6ax and 5ab-2ax +m? Ans. 8ab+4ax+m. Ex. 2. What is the sum of 4a2-2ab and 5a2+y +ab? Ans. 9a-ab+y. Ex. 3. What is the sum of 8ax+2ac and 6ax-ac +4ac? Add together the following terms: Ans. 14ax+5ac. 2mn- x xxy -3xy+3ax -2bc+8y 4x-3xy -8xy- ax 2y +4bc-4abc+5mn (44.) When several quantities are to be added together, it is most convenient to write all the similar terms under each other, as in the following example. Ex 8 Add together the following terms: 11bc+4ad-8x 8x+7bc-2ad QUEST.-Give the rule. What is the most convenient mode of ar ranging the terms? |