3. Give rule and reason for addition of decimals.

SUBTRACTION OF DECIMALS.

1. Give rule and reason for subtraction of decimals. Art. 151. 2. How many places do you point off in remainder? Art. 151. 3. From two hundred and twenty-seven thousandths take ninety-seven and one hundred and twenty ten thousandths. Art. 151. Ex. 24.

MULTIPLICATION OF DECIMALS.

1. After multiplying, how many places do you point off in the product? Give an example. Art. 152.

2. When there are not so many places what do you do? Art.. 152.

3. Give rule and reason for multiplication of decimals. Art. 152.

4. Multiply two hundred and ninety-four millionths by one millionth. Art. 152. Ex. 13.

5 What effect does removing the decimal point one place to the right or left have on decimal fractions? Art. 154.

CONTRACTIONS IN MULTIPLICATION.

1. What is contraction in multiplication of decimals? Art. 153. 2. What is proposed in the example? Explain it. Art. 153. 3. How are the numbers written down for multiplication? Art. 153.

4. Give the rule and reason for this method. Art. 153.

5. Where is the first figure of every product to be written, and how do you compensate for the part omitted? Art. 153.

6. By this method multiply 4745.679 by 751.4549 and reserve only whole numbers in the product. Art. 153. Ex. 5.

DIVISION OF DECIMAL FRACTIONS.

1. Define division of decimal fractions. Art. 155.

2. How do you determine the number of decimal places in the quotient? Art. 155.

3. Give the rule for the division of decimals. Art. 155.

4. How do you divide a decimal by 10, 100, or 1000? Art. 156.

5. How many suits of clothes can be made from 34 yds. of cloth, allowing 4.25 yds. for each suit? Art. 156. Ex. 30.

6. If there are more decimal places in the divisor than in the dividend, what do you do? What will the figures of the quotient then be? Art. 157.

7. What do you do after you have brought down all the figures of the dividend? Art. 158.

CONTRACTIONS IN DIVISION.

1. What are contractions in division? Art. 160.

2. Explain the process of making the division. Art. 1C0. 3. What figures may be omitted in the contracted method? Art. 160.

4. Give the reasons for contractions in division. Art. 160. 5. Divide by this method 98.187437 by 8.4765618. Art. 160. Ex. 4.

REDUCTION OF COMMON AND DECIMAL FRACTIONS.

1. How do you change a common to a decimal fraction? Art.

161.

2. How do you change a decimal to the form of a common fraction?

22

3. A man owns of a ship; he sells of his share: what part is that of the whole, expressed in decimals? Art. 161. Ex.

19.

DENOMINATE DECIMALS.

1. Define a denominate decimal. Art. 163.

2. How do you find the value of a denominate number in decimals of a higher unit? Art. 164.

3. Give rule and reason for finding the value of a decimal in integers of less denominations. Art. 165.

4. What decimal part of a mile is 72 yards? Art. 164. Ex. 29.

CIRCULATING OR REPEATING DECIMALS.

1. How many cases are there of changing a vulgar to a decimal fraction? What are they? Art. 166.

2. What distinguishes one of these cases from another? Art.

166.

3. How can you tell when a vulgar fraction can be exactly expressed decimally? Art. 167.

4. How many decimal places will there be in the quotient? Art. 167.

5. Can be exactly expressed decimally? Art. 168.

6. To what does the value of this quotient approach? Art. 168.

7. When does it become equal to one third? Art. 168.

8. Define a circulating decimal. Art. 169.

9. What is a repetend? Give an example. Art. 170. 10. What is a single repetend? A compound repetend? Pure repetend? Mixed repetend? Similar repetend? Art. 171-175. 11. What are dissimilar repetends? Conterminous repetends? Art. 177.

12. What are Similar and Conterminous repetends? Art. 178. 13. Give the rule and reason for reducing a pure repetend to its equivalent common fraction. Art. 178.

14. How do you find the value of a mixed repetend? Art. 180.

15. How do you add circulating decimals? Art. 183.

16. Give the rules and reasons for Subtraction, Multiplication, and Division of circulating decimals.

17. Multiply 45.1'3 by '245′ and divide 3.753' by '24'. Art. 186. Ex. 8.

CONTINUED FRACTIONS.

1. What is a continued fraction? Art. 187.

2. Define an approximating fraction. Art. 188.

3. Place 7 under the form of a continued fraction and find the value of each approximating fraction. Art. 188. Ex. 5.

RATIO AND PROPORTION.

1. Define ratio. Proportion. Art. 189.

2. From how many terms is a ratio derived? Art. 190. 3. What is the first term called? The second?

tandard? Art. 190.

Which is the

4. How may the ratio of two numbers be expressed and read? Art. 191.

5. What are proportional terms? Art. 192.

6. Which are the extremes of a proportion? The means? Art. 193.

7. What is the product of the extremes equal to? Art. 194. 8. On what principle is the rule for proportion founded? Art. 194.

9. What is Simple ratio? Compound ratio? Art. 195.

10. Define and give the rule of Three, and reason for same. Art. 198.

11. How do you state a question by the rule of Three? Art.

199.

12. At what time between 6 and 7 o'clock will the hour and minute hands of a clock be exactly together? Art. 199. Ex. 46.

13. A can do a piece of work in 3 days; B, in 4 days; C, in 6 days: in what time will they all do it, working together? Art. 199. Ex. 49.

CAUSE AND EFFECT.

1. Define Causes, Simple and Compound. Art. 200.

2. What are Effects, Simple and Compound? Art. 201.

3. What do we infer from the nature of causes and effects? Art. 202.

4. When are two numbers directly proportional? Art. 205. 5. When are two numbers inversely proportional? Art. 205. 6. If two numbers are inversely proportional, what is either equal to? Why? Art. 207.

7. If 72 horses eat a certain quantity of hay in 76 weeks, how many horses will consume the same in 90 weeks? Art. 208. Ex. 28.

COMPOUND PROPORTION.

1. Define Compound Proportion, and tell what it embraces. Art. 209.

2. What is always required? Art. 209.

3. Give the rule and reason for compound proportion. Art. 210.

4. If 5 compositors in 16 days, working 14 hours a day, can compose 20 sheets of 24 pages each, 50 lines in a page, and 40 letters in a line, in how many days, working 7 hours a day, can 10 compositors compose 40 sheets of 16 pages in a sheet, 60 lines in a page, and 50 letters in a line? Art. 210. Ex. 19.

PARTNERSHIP.

1. Define Partnership. Partners. Capital or Stock. Art.

211.

2. What is dividend? Loss? Art. 211.

3. Give rule and reason for Partnership. Art. 212.

COMPOUND PARTNERSHIP.

1. Define Compound Partnership. Art. 218.

2. Give the REASON, and not the rule, for compound partnership.

3. Where men take an interest in a mining company, A puts in $480 for 6 months, B a sum not named for 12 months, and C $320 for a time not mentioned; when the accounts were settled A received $600 for his stock and profit, B $1200 for his, and C $520 for his; what was B's stock and C's time? Art. 213. 10.

Ex.

PER CENTAGE.

1. Define per centage. What is the base? Art. 214.

2. Define per cent.

Rate per cent.

Art. 215.

3. How do you find the per centage of any number? Art. 216. 4. How do you find the per cent, which one number is of another? Art. 217.

5. How do you find the base when the per centage is added to or subtracted from the base? Art. 218.

6. What per cent. of 800 is eleven?

Art. 217. Ex. 9.

7. A grocer purchased a lot of teas and sugar, on which he lost 16 per cent. for selling them for $4200; what did he pay for the goods? Art. 218. Ex. 4.