What is a bill? An account? A debtor? A creditor? How is a bill receipted? What is a footing? What is debit? Write the abbreviations of at, account, amount, balance, company, creditor, debtor, paid, and received. How do you find the footing of a bill? How the balance? What is reduction? Define reduction descend

sure.

ing. Define reduction ascending. Recite the table of troy weight. What is its primary unit? Recite the table of avoirdupois weight. Recite the table of long measure. What is its unit of measure? What is magnitude? What is a line? A curved line? A straight line? What are parallel lines? Recite the table of surveyor's measure. For what is it used? What is a surface? An angle? Illustrate an angle, and name its parts. Define a square. A square foot. A square yard. What is the primary unit of the measure of surface? What is an area? How is the area of a square or rectangle found? Recite the table of square measure. Recite the table of fluid measure. For what used? What is its primary unit? Recite the table of dry measure. For what used? What is the primary unit? Describe the bushel. What is a circle? What the circumference? Diameter? Radius? Recite the table of angular meaWhat is its primary unit? What is longitude? Recite the table of longitude. What is a volume? A cube? Faces of a cube? Edges? Recite the table of cubic measure. What is a cubic foot? A cord foot? A cord of wood? How do you reduce pounds sterling to shillings? How farthings to pounds? What fundamental rule is used in reduction descending? In reduction ascending? Tell the number of days in each month of the civil year. How can you tell when a year is a common year? How, when it is leap year? How many days in each? Is 1878 a leap year? Will the year 2000 be common, or leap year? How many days were there in the year 1800? When will the next leap year occur? What is compound addition? What compound numbers can be added? Give the rule for addition of compound numbers? What is subtraction of compound numbers? Give the rule. How do you find the interval between two dates? What is multiplication of compound numbers? Give the rule. What is division of compound numbers? How many cases are there? Give the rule when the divisor is abstract. the rule when the divisor is similar to the dividend.

Give

NOTE.--For a more extended treatment of Denominate Num

bers, see Davies & Peck's Complete Arithmetic.

PERCENTAGE AND ITS APPLICATIONS.

224. Per cent means by the hundred, or hundredths. Thus, 3 per cent of $100 is 8 of $100, or $3. 1. What is 2 per cent of 100? Of 300? Of 60 ?

2. How many dollars is 5 per cent of $100? Of $50 ? 3. How many yds. is 7 per cent of 100 yds? Of 500 yds.?

225. The sign of per cent is %. Thus, 3% of 20 is read 3 per cent of 20.

Read the following examples:

4. 4% of 20; 5% of 100; 6% of 30; 7% of $200.

5. 1% of $100; 9% of 27; 10% of 33 feet; 11% of 50. 6. 12% of 17 bushels; 20% of 450 ships; 30% of 72. 226. The rate per cent, or simply rate, is the number of hundredths taken; thus, in the expression 7% of 245, the rate is 7 hundredths.

1. How many per cent is .04? .06? .08? .07? .12? .17? 2. How many hundredths is 6%? 3%? 5%? 7%? 11%? 3. How many hundredths is 18%? 17%? 21%? 25%? 4. How many per cent is .25? .31? .15? .18? .09? 5. What is the decimal expression for 14% ?

Per cent expressed by means of a common fraction may be expressed decimally by annexing two ciphers to the denominator, and reducing the result to a decimal.

9. Express % decimally. 10. What decimal fraction is 3%?

11. How many hundredths is 100%? 200%?

12. How many hundredths is 125%? Express it decimally.

SOLUTION. 125% 185 1.25, Ans.

=

13. Express 250% decimally.

227. Percentage is some per cent of a given number. Thus, $6 is the percentage on $100, when the rate is 6 per cent.

1. What is the percentage on $200 at 5 per cent? 2. What is the percentage on $3528 at 2 per cent ? 3. What is the percentage on $230 at 7 per cent? 4. What is the percentage on 350 yards, at rate of 3%? 5. Find the percentage on $15 at 50 per cent.

228. Base is the number on which percentage is reckoned. In the expression 7% of $100, the base is $100.

229. Amount is the base increased by the percentage. The amount of $100 at 8 per cent, is $100 + $8 = $108.

1. What is the amount of $200 at 3 per cent ?

2. If 500 is the base, and 6 the rate, what is the amount? What, if 600 is the base, and 7 the rate? 3. If $648 is the base, and $16 the percentage, what is the amount?

4. Find the amount when the base is $4000, at 2%. 5. Find the amount when the rate is 6, and the base is $456.

230. The Difference is the base diminished by the percentage. Thus, the difference of $100 diminished by 8 per cent, is $100 – $8 = $92.

1. What is $600 diminished by 3 per cent?

2. Find the difference when the base is $875 and the percentage $26.25.

3. Find the difference when the base is $10,000 and the rate is 6%.

4. What is the difference when the base is $275 and the rate is 4% ?

5. What is the difference when the base is $72 and the rate is 30% ?

EXERCISES For Oral Work.

1. What is 5 per cent of 40 lbs. ?

2. If $80 is increased by 5% of itself, what is the amount? 3. What is the difference of 80 yards diminished by 3 per cent of itself?

4. What per cent of $100 is $7? 8? 18? 20?

5. The base is $200 and the rate 7%; what is the amount? What is the difference?

6. A man had 30 chickens, 20 per cent of them were destroyed by foxes; how many were destroyed? How many were left ?

7. How many marbles are 7% of 500 marbles?

8. A boy answered 25 questions in arithmetic, his brother answered 60% of that number; how many questions did the brother answer?

9. A man who held $10,000 worth of United States bonds, sold 10% of them; what value of bonds did he sell? What value of bonds had he left?

10. Let the base be $20,000 and the rate 6%; what is the percentage? What the amount? What the difference?

PRINCIPLES.

231. From what precedes we have the following principles:

1. The percentage is equal to the base multiplied by the rate expressed decimally.

2. The amount is equal to the base multiplied by 1 plus the rate expressed decimally.

3. The difference is equal to the base multiplied by 1 minus the rate expressed decimally.

Since either of two factors is equal to their product divided by the other, we have the following principles:

4. The rate is equal to the percentage, divided by the base.

5. The base is equal to the percentage divided by the rate expressed decimally; to the amount divided by 1 plus the rate; or to the difference divided by 1 minus the rate expressed decimally.

232. To find the Percentage, when the base and rate are given.

See Principle 1, Art. 231.

EXAMPLES.

1. What is 5% of 75 lbs. ?

SOLUTION. 75 lbs. x .05 = Ans. 3.75 lbs.

2. What is 7% of 115 lbs.?

Of 25 lbs.?

Of 50 lbs.?

Of $248?

Of $600 ?

3. What is 11% of $315? 4. What is 16% of 52 wks.?

Of 20 wks.? Of 50 wks.?

5. What is 25% of 4,120 yds.? Of 5640 yds.? 6. What is 40% of 72 bu.? Of 300 bu.?