267. Exercises upon the Table. 124. Find the prime factors of each | 164. What number is that from which if you take A the remainder will be B? numerator in D.† 125. Find the prime factors of each 127. Find the 1. c. m. of F, G,* and 166. What number multiplied by F H. 128. Change D to lowest terms. 130. Find the sum of A and C. 132. C+D+ E. 133. E+F+G 147. GxE. 148. A÷B. + H. 149. C÷E. 134. A-B. 150. C÷F. 135. H-G. 151. H÷A. 136. G-E. 152. E÷F. 137. H+A-G. 153. G÷E. 154. A of F÷E. 138. AB of C. 139. Difference of C and D. 140. C of E 142. Simplify C of E. 143. Ax B. 144. C× F. 145. Cx E. will give G for a product? 167. What number divided by E will give D for a quotient? 168. What divisor will give E for a quotient, H being the dividend? 169. What number is that to which if A of itself be added the sum will equal H? 170. What number is that from which if B of itself be subtracted, the remainder will be F? 171. Divide H into three such parts that the 2d shall be twice the 1st, and the 3d F more than the 2d. What is the 3d part? 172. At E dollars a yard, what will F yards of cloth cost? 173. At E dollars a yard, how many yards of cloth can be bought for F dollars? 174. If B pounds of tea cost H cents, what will E pounds cost? A of EA-B. 175. John can do a piece of work in X E days, and James can do the same work in F days. In what time can both together do it? If George and Albert can do a piece of work in E days, and Albert can do it alone in F days, in what time can George 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. 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." 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 by 100, we have, 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. 276. ILLUSTRATIVE EXAMPLES. Change 0.25 and 0.33– to common fractions in their simplest forms. WRITTEN WORK. 0.25=2%= 0.3313188 = } Explanation. After writing these frac tions with their denominators, we find that 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: |