SUBTRACTION REVIEWED 339. The principle of subtraction. The principle of subtraction is the same whether we subtract integers, fractions, denominate numbers, or expressions containing letters. The general principle is seen in the following: In each case the number of units is the same. In each case the subtraction 1 - 3 requires us to increase the 1 by a unit of the next higher order before subtracting. In oral subtraction, as of 23 from 61, it is usually better to begin at the left. In this case say: "61, 41, 38"; that is, 61 20 41, 41 - 3 = 38. = 16. What is meant by saying that " only units of the same kind can be added"? Can you not add $2 and 3 ct.? 17. What is meant by saying that "only units of the same kind can be subtracted"? Can you not subtract 3 ct. from $2? WRITTEN EXERCISE Subtract, checking each result by adding the subtrahend and remainder. Time yourself. Notice the similarity of the figures used in Exs. 13-15. Notice the similarity of the figures used in Exs. 16-18. 19. $1,725,342,628 - $632,487,129. 31. Write out in your own way a statement of your method of adding numbers. 32. Write out in the same way a statement of your method of subtracting numbers. 41. 426 gal. 13 qt. – 197 gal. 31 qt. 42. 1345.25 +1753 +375 — (3 + 3 + 3). 43. 234 sq. ft. 93 sq. in. - 175 sq. ft. 983 sq. in. 44. 148 cu. ft. 5211 cu. in. 69 cu. ft. 8273 cu. in. New York. . 7,268,894 48. The five states having the largest population are here given, with the population according to a recent census. The population of New York was how much more than that of each other state? 49. By the table of Ex. 48, Illinois. Ohio. Missouri 4,821,550 4,157,545 3,106,665 the population of Pennsylvania was how much more than that of Illinois? of Ohio? of Missouri? 50. By the same table, the population of Illinois was how much more than that of Ohio? of Missouri? MULTIPLICATION REVIEWED 340. The principle of multiplication. The principle of multiplication is the same for all numbers. The results In each case the number of units is the same. differ because the first number is on the scale of 10, the second on the scale of 12. The principle is the same: Multiply the denominations or orders separately. Then add the partial products, simplifying when possible. In oral multiplication, as of $7.50 by 9, it is usually better to begin at the left. In this case we say: "$63, $4.50, $67.50." 11. $2.50 12. $7.50 13. $8.20 14. $3.30 15. $5.50 16. What is meant by saying that the multiplier must always be an abstract number? Illustrate. 17. What is meant by saying that the product must always be of the same denomination as the multiplicand? WRITTEN EXERCISE Multiply as indicated, noticing the similarity in the figures of the multiplicands: 1. By 7: 175, 17 ft. 5 in., 1 mi. 75 ft. 2. By 37: 3. By 13 4. By 25: 427, 42 lb. 7 oz., 4 mi. 27 rd. 936, $9.36, 93 ft. 6 in., 9036. 428, 4 sq. ft. 28 sq. in., 4028. 8. By 625 1728, 17 sq. ft. 28 sq. in., 17,028. : Multiply, writing the number of minutes required for Exs. 9-33: |