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267. Exercises upon the Table.

124. Find the prime factors of each | 164. What number is that from which numerator in D. f

if you take A the remainder 125. Find the prime factors of each

will be B? denominator in D.

165. What number is that to which 126. Find the g. c. f. of the terms if you add C of F the sum will of each fraction in D.

be G? 127. Find the l. c. m. of F, G,* and 166. What number multiplied by F H.

will give G for a product ? 128. Change D to lowest terms. 167. What number divided by E will 129. Change the mixed numbers in give D for a quotient?

G to improper fractions. 168. What divisor will give E for a 130. Find the sum of A and C.

quotient, H being the divi131. A+B+C. 146. GxF.

dend? 132. C+D+E. 147. G* E.

169. What number is that to which 133. E+F+G 148. A:B.

if A of itself be added the sum +H. 149. C:E.

will equal H? 134. A-B. 150. C:F.

170. What number is that from which 135. H-G. 151. H:A.

if B of itself be subtracted, the 136. G-E. 152. E:F.

remainder will be F? 137. H+A-G. 153. G:E.

171. Divide into three such parts 138. A - B of C. 154. A of F:E.

that the 2d shall be twice the 139. Difference 155. A of C

1st, and the 3d F more than of C and D. • B of E.

the 2d. What is the 3d part ? 140. C of E 156. (A + B) 172. At E dollars a yard, what will - A of B. •(BRC).

F yards of cloth cost? 141. Simplify 157. (A - B)

173. At E dollars a yard, how many A of B of C. • (B+C).

yards of cloth can be bought 142. Simplify 158. A+C-B.

for F dollars ? A of B of 159. ExF+G. 174. If B pounds of tea cost H cents, C of E. 160.

what will E pounds cost ? 143. A ~ B.

A of E, A - B. 175. John can do a piece of work in 144.* C F. B+CG:F.

E days, and James can do the 145. C x E.

same work

F days. In what 161. If G is B of some number, what time can both together do it?

is C of the same number? 176. If George and Albert can do a 162. H is C of how many times E?

piece of work in E days, and 163. C of E is B of how many times A?

Albert can do it alone in F

days, in what time can George * Omitting fractions.

do it alone ?

† See page 57, for Explanation of the Use of the Drill Tables.

SECTION X.

DECIMAL FRACTIONS.

268. Articles 30 to 36 treat of a series of fractions, tenths, hundredths, thousandths, etc., - each of which has for a denominator 10, or a number made by using 10's only as factors. Such fractions are decimal fractions.

NOTE. Decimal fractions are usually called decimals.

To read and write Decimals.

269. The method of reading and of writing decimals has been explained in Articles 34 to 36. These the pupil

may review.

270. Exercises.

a. Read 5.368; 0.406; 2.007; 0.039; 105.105. b. Read 0.4721; 7.0497; 10.010; 15.0015.

Read the following: c. 30.0094

e. 120.250049 d. 17.01845

f. 1.001025

g. 200.005
h. 0.205

Note. To distinguish 200.005 (Example g) from 0.205 (Example h), use the word decimal before reading the decimal part. Thus, 200.005 may be read “two hundred and the decimal five thousandths ”; while 0.205 may be read “ decimal two hundred five thousandths."

Read the following: i. 0.315

m. 500.0074 j. 300.015

n. 4700.0065 k. 36000.00018

0. 430.06 1. 0.36018

p. 43000.06

q. 1000.00001 r. 14.00375 s. 0.0000027 t. 0.1000012

271. To write a decimal: Write the number as an integer, and place the decimal point so that the right-hand figure shall stand in the place required by the denomina. tion of the decimal.

NOTE. When the given number does not fill all the decimal places, supply the deficiency with zeros.

For other exercises in reading and for exercises in writing decimals, see

page 135.

The pupil may now review addition and subtraction of decimals (Articles 45, 50, 61, and 65).

REDUCTION OF DECIMALS.

To change the Denomination of a Decimal Fraction.

272. Exercises.

a. What is the denominator of the fraction 0.5 ? 0.25 ? 0.075 ? 7.3? 4.86 ?

b. What is the numerator of the fraction 0.4 ? 0.04 ? 0.075 ? 0.0101 ? 0.000007 ? 0.25 ? 0.1125 ?

c. Write as a common fraction 0.3; 0.08; 0.375; 0.0204.

273. ILLUSTRATIVE EXAMPLE. Change 0.5 to thousandths.

WRITTEN WORK.

0.5 = 0.500

Explanation.— Multiplying both numerator and denominator of x by 100, we have 30000 which is expressed decimally by writing 0.500.

274. From the written work above we derive the following

Rule.

To express a decimal fraction in any lower denomination: Annex zeros to the given expression until the place of the required denomination is filled,

275. Examples for the Slate. 1. Change 0.07 to thousandths. 2. Change 0.4, 0.75, 2.5, and 1.06 to thousandths. 3. Express 0.003, 1.75, and 0.006 as ten-thousandths.

4. Express 3 as tenths; as hundredths; as thousandths; as ten-thousandths; etc.

Answers. 3.0; 3.00; etc. NOTE. Read the above answers : *Thirty tenths; three hundred hundredths”; etc.

5. Express 7, 40, and 37 as tenths; as hundredths; as tenthousandths.

To change a Decimal Fraction to a Common Fraction.

WRITTEN WORK.

276. ILLUSTRATIVE EXAMPLES. Change 0.25 and 0.333 to common fractions in their simplest forms.

Explanation. - After writing these frac0.25 = * = ?

tions with their denominators, we find that 0.33} = 2030 = 388 = }

the first can be changed to smaller terins

(Art. 198), and that the second may be changed to a simple fraction (Art. 252) and then to its smallest terms.

277. From the examples above we derive the following

Rule.

To change a decimal fraction to a common fraction : Write the decimal in the form of a common fraction, and then change the result, if necessary, to its simplest form.

278. Examples for the Slate. Change the following to common fractions in their simplest forms: (6.) 0.4 (11.) 0.3 (16.) 0.750

(21.) 0.0625 (7.) 0.80 (12.) 0.377 (17.) 0.368

(22.) 0.0333 (8.) 0.35

(13.) 0.62} (18.) 0.663 (23.) 0.147 (9.) 0.75 (14.) 0.87} (19.) 0.6663

(24.) 7.5 (10.) 0.71 (15.) 0.875

(20.) 0.072

(25.) 1.163

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