Sidebilder
PDF
ePub

What is reduction descending? (80.) Analyze an example at the blackboard. (100., a.) Repeat the rule. (100., b.). What is reduction ascending? (81.) Analyze an example at the blackboard. (101., a.) Repeat the rule. (101., b.)

LESSON XVI.

161. A grocer bought five tubs of butter, each containing 64.37 lbs., at 18.5 cts. per pound; 7 cheeses, each weighing 46.34 lbs., at 9.3 cts. per pound: how much did the whole cost?

162. If a clerk receiving $4440.25 spends $1472.22 for board, and twice as much for clothes, books, and other expenses, how much will he have left?

163. B has 457.2 lbs. of sugar, C has three times as many as B, and D has as many as B and C together; how many pounds of sugar has D?

164. A has 43.2 tubs of butter, B has 2.4 times as many as A, and C has twice as many as A and B together; how many tubs have they in all?

165. A has 371.5 yards of cloth, B has .4 as many yards as A, and C has 3.7 as many yards as A and B together; what is the value of all the cloth, at $2.42 per yard?

166. There are 75.7 tubs of butter, each tub weighing 37.4 lbs.; the tubs which contain the butter weigh .14 as many lbs. as the butter they contain; how many pounds of butter do the tubs contain?

167. A farmer sold 19.3 tubs of butter weighing 78.3 lbs. each; the tubs which contain the butter weigh each .12 as many pounds as the butter they contain: how much is the butter worth, at 29.3 cts. per pound?

QUESTIONS.-Analyze at the blackboard an example in the addition of denominate numbers. (102., a.) Analyze at the blackboard

an example in the subtraction of denominate numbers? (103., a.) Give the rule. (103., g.).

LESSON XVII.

178. DIVISION OF DECIMALS.

Divide 2.460 by 14.24.

MODEL OPERATION.

14.24)2.460(.1727+ Ans.

1.424

1.0360

9968

3920

2848

10720

.9968

ANALYSIS.-1. For convenience write the divisor, dividend, and quotient, as in simple division.

2. 14.24 are equal to 1424 hundredths; and 2.460 are equal to 2460 thousandths.

3. 1424 hundredths are contained in 2460 thousandths 1 tenth of a time, with a remainder of 1036 thousandths, equal to 10360 ten thousandths. Write the 1 tenth in the place of tenths in the quotient.

4. 1424 hundredths are contained in 10360 ten-thousandths 7 hundredths of a time, with a remainder of 392 ten-thousandths, equal to 3920 hundred-thousandths. Write the 7 hundredths in the place of hundredths in the quotient.

5. 1424 hundredths are contained in 3920 hundred-thousandths 2 thousandths of a time, with a remainder of 1072 hundred-thousandths, equal to 10720 millionths. Write the 2 thousandths in the place of thousandths in the quotient.

*

1424 hundredths are contained in 10720 millionths 7 tenthousandths of a time, with a remainder, &c.

NOTES.-1. The analysis should be carried as far as the teacher may deem advisable. 2. The sign+annexed to the quotient shows that the division is not exact.

179. PROPOSITIONS IN DIVISION OF DECIMALS.

(a.) Any denomination divided by units gives the same denomination for a quotient; as, hundredths divided by units give hundredths; thousandths give thousandths; hundreds give hundreds, &c.

(b.) Any denomination divided by tenths gives a denomination ten times larger than the denomination divided; as, units divided by tenths give tens; tenths give units; hundredths give tenths, &c.

(c.) Any denomination divided by hundredths gives a denomination one hundred times larger than the denomination divided; as, units divided by hundredths give hundreds; thousandths give tenths; millionths give ten thousandths, &c.

(d.) Any denomination divided by thousandths gives a denomination one thousand times larger than the denomination divided; as, thousandths divided by thousandths give units, &c.

(e.) GENERAL LAW.-Any denomination divided by any denomination less than a unit, gives for a quotient a denomination as many times larger than the denomination divided, as the denomination of the divisor is less than a unit.

NOTE. For the use of teachers who prefer the old method of pointing, we give the following:

(f) RULE.-Divide as in simple division, making the number of decimal places in the dividend at least equal to those in the divisor; then subtract the number of decimal places in the divisor from the number of decimal places in the dividend, and the remainder will denote the number of

decimal places in the quotient. Should there not be as many fig ures in the quotient, supply the deficiency by prefixing ciphers.

QUESTIONS.-Analyze at the blackboard an example in the multiplication of denominate numbers. (104.) Analyze at the blackboard an example in the division of denominate numbers? (105.) What is an integer? (106.) What is an odd number? (107.) What is an even number? (108.) What is a prime number? (109.) What is a composite number? (110.) When are numbers said to be prime to each other? (111.) What is a prime factor? (112.) What is a composite factor? (113.)

LESSON XVIII.

EXAMPLES FOR PRACTICE.

168. Divide 463. by 38. 169. Divide 417. by 47. 170. Divide 347. by 59. 171. Divide 24.374 by 73. *172. Divide 2.432 by 97. 173. Divide .6712 by 39.

[ocr errors]

|181. Divide 4 by 72.
182. Divide 40 by 973.
183. Divide 63.1 by 25.
184. Divide 12 by 376.
185. Divide 864 by .3.
186. Divide 642 by .4.

[blocks in formation]

QUESTIONS.-IS a unit considered a factor? (113., a.) Separate a composite number into its prime factors. (114.) Give the rule. (114., d.) Give the proof. (114., e.) What is the use of a parenthesis or vinculum? (116.) What is cancellation? (117.) What is a common divisor of two or more numbers? (118.) What is the greatest common divisor? (119.) What is a common multiple of two or more numbers? (121.)

*NOTE.-Continue the division to five decimal places in the quotient.

LESSON XIX.

194. Divide .463 by .4.
195. Divide .437 by 4.6.
196. Divide 3.07 by 46.3.
197. Divide 4.07 by 916.3.
198. Divide .6703 by 571.2.
199. Divide 46.72 by 3712.3.

200. Divide 427.1 by .03. 201. Divide 467 by .07. 202. Divide 417 by .09. 203. Divide 387 by .07. 204. Divide 868 by .04. 205. Divide 407 by .23.

206. Divide 91.63 by .47.

$207. Divide 46.72 by .32.
208. Divide 46.47 by .43.
209. Divide 96.876 by .43.
210. Divide 47.236 by .97.
211. Divide 37.26 by 4.38.
212. Divide 67.43 by 37.46.
213. Divide 21.3 by 467.23.
214. Divide 9 by 3724.86.
215. Divide 4 by 6712.43.
216. Divide 1 by 6738.41.
217. Divide .007 by 3672.49.
218. Divide .00006 by 7189.48.
219. Divide .000302 by 5763.43.

QUESTIONS.-What is a multiple of a number? (120.)

the least common multiple? (122.)

What is a common fraction? (124.)

What is

What is a fraction? (123.)

What is a decimal fraction?

(125.) What are the terms of a fraction? (126.) What is the denominator of a fraction? (127.)

LESSON XX.

220. Divide 307.464 by 34; by 3.4; by .34. 221. Divide 407.673 by 46.3; by 50.72; by .467. 222. Divide 876.4123 by 864.3; by 8.67; by 4.673. 223. Divide 896.437 by 967.3; by 5.703; by 6.934. 224. Divide 43.2 by 467.2; by 59.634; by 2.6734. 225. Divide 46.73 by 947.32; by 47.286; by 4.4834. 226. Divide 46.37 by 46.37; by 4.637; by .4637. 227. Divide 9 by 83; by 3.67; by 9876.

228 Divide 8.3 by 6.72; by 9.183; by 671.83. 229. Divide 4.7 by 9.1864; by 9.1372; by 8.6493. 230. Divide .87 by .89672; by .03496; by .0089672.

QUESTIONS.-What does the numerator of a fraction show? (128.) What is a proper fraction? (129.) What is an improper fraction?

« ForrigeFortsett »