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. 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. 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. 521 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, 6,302,115 Illinois. 4,821,550 4,157,545 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 10. The principle of multiplication. The principle of multiplication is the same for all numbers. In each case the number of units is the same. The results 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 5 6 7 8 9 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. Multiply, writing the number of minutes required for Exs. 9-33: 11. Multiplying by fractions. In multiplying by fractions. we may use the following forms to show the similarity, although we have shorter ones for actual work. In multiplying 69 by we simply think that of 69 is 23, and we multiply (mentally) 23 by 2. In multiplying 6.9 by .2 we simply think that tenths multiplied by tenths is hundredths, and we multiply 69 by 2 and express the result as hundredths. 31. How much will ğ yd. of silk cost at 64 a yard? 32. How much will yd. of velvet cost at $1.60 a yard? |