174. The city of Holyoke was taxed for school purposes $73,500 on property valued at $24,500,000. What was the tax on a dollar?

175. The city of Brockton was taxed $76,196.04 on property valued at $19,049,010. What was the tax on a dollar?

143. Forms of Examples in Division.

176. Divide 72,864 by 11.

177. If a dividend is 46,008 and the divisor is 24, what is the quotient?

178. 72,864 ÷ 6624 = ? 3456 ÷ what = 144?

179. $85 multiplied by what number gives a product of $20,825?

180. What number multiplied by 59 gives a product of $8673?

181. 5460 is 52 times what number? 100 times what? 182. 71 times what sum of money equals $ 2556 ?

183. What is the quotient of 49,008 ÷ 73?

184. Divide 684,000 by 10, by 1000, by 100, and add the quotients?

185. How many are 3,654,321 ÷ 39,090 ?

186. The product of two factors is $7448, one of them is 98. What is the other?

187. The product of three factors is 11,904; two of them are 24 and 31. What is the third ?

188. What is 1 eighth of $ 13?

189. Find 1 eleventh of $7.062. 190. of 864.42 what number? 191. Divide $8.75 by $1.25.

192. $545 ÷ $3.87

=

? $1468.46 what $86.38? 193. A quotient is 16 men; the dividend 15,552 men. What was the divisor?

194. A dividend being 58,329 miles, the remainder 249 miles, and the quotient 11, what was the divisor?

144. Examples for Written Work.

195. How many sheets of paper are required for a book of 768 pages, 24 pages to a sheet?

196. How many square miles are there in a township of 5168 acres, 640 acres making 1 square mile?

197. Mr. Pratt put 1980 bushels of apples into barrels each holding 2 bushels 3 pecks. How many barrels did he use?

198. Mr. Granger received $2548 in payment of a debt, took $275 from the savings bank, and added to this $ 177 of his earnings. With the money he bought 160 acres of land. What was the price per acre?

199. Mr. Adams bought a house for $6200, paid $1500 down, and the remainder in four equal payments. How much was each payment?

200. If an oil well yields 6664 barrels of oil in 8 weeks, what is its daily yield?

201. Mr. Prince has 56,168 acres of pasture land, 1 seventh as much meadow land, and 1 eighth as much wood land as pasture. How many acres has he in all?

202. Charles is to keep 1 twentieth of all he receives from the sale of peaches. How much in dollars and cents will he keep if he sells $35 worth on Friday and $47 worth on Saturday?

203. A broker let a store for $240, and received for his services $19.20. How much did he get on a dollar?

204. In 1892 there were 133,683 students in the different colleges in the United States, with 9326 teachers. Find the average number of students to a teacher.

205. The United States in 1892 maintained schools for Indians, accommodating 13,588 pupils, at a total cost of $1,600,313. Find the cost for each pupil.

206. An operative can weave 30,000 yards of sheeting in 52 weeks. How much is that a week?

207. What is the sum of 36.84÷4 and 1 tenth of 568.72?

208. The readings of a thermometer kept by a school boy in Lowell for 4 successive days were as follows:

Find the averages for 6 A.M., 12 m., the highest average for one day.

and 4 P.M.; also

209. Very heavy cannonading has been heard at a distance of 475,000 feet. What is the distance in miles and feet?

210. If the earth is 92,800,000 miles from the sun, and the moon at its full is 224,000 miles farther on, and if light travels at the rate of 186,350 miles a second, how many seconds is it in passing from the sun to the moon and back to the earth? (Answer to tenths.)

211. The limit of perpetual snow at Quito, on the equator, is 15,800 feet above the level of the sea. Find the height in miles, carrying the answer to hundredths.

212. The National debt of the United States in 1890 was $891,960,104, and the number of inhabitants was 62,622,250. How much was the debt to each inhabitant?

What is Division? What is the dividend? the divisor? the quotient? the remainder? Perform and explain an example in short division; prove the work. Perform and explain an example in long division. Give the rule; the proof. How do you divide by 10, 100, 1000, etc.? How do you divide when the expression of the divisor contains zeros at the right?

Make examples to illustrate the measuring form of division; the partitive form.

When the dividend and quotient are given, how can you find the divisor? When the divisor and quotient are given, how can you find the dividend? When the multiplier and product are given, how can you find the multiplicand? When the multiplicand and product are given, how can you find the multiplier ?

DRILL TABLE No. 4. (See Supplement, Art. 1.) 145. For supplementary practice in division.

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SECTION VI.

MISCELLANEOUS AND REVIEWS.

SYMBOLS OF OPERATION.

146. The signs indicating the different arithmetical processes are sometimes used in the same expression.

Thus 83 x 2 = 2. 12 x 2 + 8 ÷ 4 = 26.

In every such case the multiplying and dividing indicated should be done first, the adding and subtracting afterwards. If, however, the terms to be operated upon are joined by a parenthesis () or vinculum the expression joined is

treated as if it denoted a single number.

To illustrate: 8 3 × 2 means that 3 x 2 is to be taken from 8; result 2. But (83) × 2, or 8 3 x 2, means that 3 is to be taken

from 8, and the remainder multiplied by 2; result 10.

Again, 8+ 3 x 2 = 14; but (8 + 3) × 2, or 8 + 3 x 2 = 22.

[(4+8) × 36] 5 means that the sum of 4 and 8 is to be multiplied by 3, the product to be diminished by 6, and the remainder divided by 5.

24÷4×2=12; but 24÷ (4×2)=3.

147. In performing a series of operations indicated by signs,

First, operate on the numbers that are joined by a paren thesis or vinculum as indicated by the signs. Next, multiply and divide, using the signs and in order as they occur. Finally, add and subtract as indicated by the signs + and