ADDITION REVIEWED 8. The principle of addition. The principle of addition is the same whether we add integers, fractions, denominate numbers, or expressions containing letters. In each case the number of units is the same. In each the addition 7 + 8 requires us to add 1 to the next higher order. In oral addition, as of 68 and 97, it is usually better to begin at the left. In this case say: "97, 157, 165"; that is, 97 +60 = 157, 157 + 8 = 165. 16. Add 2 in., 3 in., 3 in., 7 in., 11 in. Express the result also as feet and a fraction; as feet and inches. 17. What do we mean by addition? by addends? by the sum? How do we check (or prove) our additions? Give examples. WRITTEN EXERCISE Add, checking (proving) the work by adding in reverse 5. Reduce , 2, to twelfths and add. Also reduce to twenty-fourths and add. 6. Reduce,, to eighths and add. Also reduce to decimal fractions and add, checking by reducing the result to an integer plus a common fraction. 7. Add,,, by reducing to sixths; to twelfths; to eighteenths. Show that the results are equal. 8. Add 1,, t, 3, 7. (Which is the better plan in this case, to reduce to the denominator 120, or to decimal fractions?) 9. Add 3, 2, 1, §, 1o. (To what common denominator may these fractions be reduced? Is it better to reduce to decimal fractions? Why?) Notice that the first of these results reduces to the second if x = 100 and y = 1; to the third if x = = 1 ft., y = 11⁄2 ft., or 1 in.; to the fourth if x = 1 lb., y = lb., or 1 oz. 27. The following are some recent statistics of the great industries of the United States. Wool Manuf. Cotton Manuf. Iron and Steel Meat Industry Lumber Flour 2,636 $415,075,713 264,021 $92,499,262 $250,805,214 $427,905,020 1,051 467,240,157 302,861 661 573,119,275 222,264 921 189,198,264 68,534 33,035 611,611,524 283,260 25,258 218,714,104 37,073 Boots and Shoes 1,600 101,795,233 142,922 Publishing 15,305 192,443,708 94,604 86,689,752 176,551,527 339,198,619 120,723,092 522,071,772 803,344,591 33,457,013 683,583,577 786,603,670 104,640,591 317,923,548 566,832,984 17,703,418 475,826,345 560,719,063 59,175,883 169,604,054 261,028,580 50,214,051 50,214,904 222,983,569 Find the sums of the various columns. Pupils should be timed in all such work, and accuracy should be insisted upon by requiring checks. 28. The following are some of the wealthiest countries in the world according to recent statistics, with the approximate money which each has. Add the columns. Fill the last column by adding the three preceding columns crossways to the right. How will you check the work? SUBTRACTION REVIEWED 9. 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, 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"? 3 ct. from $2? Can you not subtract |