7 How do you divide when the divisor is a composite number?

8 When there are remainders after division, how do you find the true remainder?

9 Divide the following numbers by the factors and find the remainders:

416,705 by 315 7 X 9 X 5

804,106 by 4623 X 2 X 7 X 11

756,807 by 34564 X 8 X 9 X 12

10 How do you divide with cyphers annexed to the divisor?

11 How do you find the true remainder when cyphers are annexed to the divisor?

12 How do you divide when the divisor contains a fraction?

13 What does the analysis of a practical question require?

14 How do you find the cost of any number of things?

15 How do you find the cost of any number of things, when the price is an aliquot part of a dollar?

16 How do you find the cost of articles sold by the hundred or thousand?

17 How do you find the cost of articles sold by the ton?

18 What will be the cost of 45 bushels of apples at 25 cents a bushel?

19 What will be the cost of 3,742 feet of timber at $3.25 per 100?

20 What will be the cost of 1,575 lbs of plaster at $3.84 per ton? Art. 76, Ex. 1.

PRACTICE.

1 What is practice? P. 84.

2 What is an aliquot part of a number? 3 What is the cost of 376 yards of cloth at $1.75 per yard?

4 What is the cost of 354 yards of cord at 11d. per yard?

5 If linen is 2s. 6d. a yard, what will be the cost of 660 yards?

LONGITUDE AND TIME.

1 How is the equator of the earth supposed to be divided? P. 84.

2 How does the sun appear to move?

3 What is a day?

4 How far does the sun appear to move in an hour?

5 How do you reduce degrees of longitude to time?

6 What is the hour when the sun is on the meridian?

7 When the sun is on the meridian of any place, how will the time be for all places east? west?

8 If you have difference of time, how do you find the time?

9 How do you reduce time to degrees and minutes of longitude?

10 The difference of longitude between St. Louis and New York is 15° 35'. In traveling from New York to St. Louis, will a watch, keeping accurate

time, be fast or slow at St. Louis, and how much? Art. 82, Ex. 10.

11 If the difference of time between London and Oregon City is 8 hours, what is the difference in longitude? Art. 82, Ex. 9.

12 When it is 12 m. at New York it is 11 o'clock 6 minutes and 28 seconds at Cincinnati: what is their difference of longitude? Art. 82, Ex. 3.

PROPERTIES OF NUMBERS.

1 What is an integral number? P. 95.
2 When is one number divisible by another?
3 What is a composite number?

4 By what is a composite number always divisible?

5 When are two numbers prime to each other? 6 What numbers are not reckoned among the divisors of prime or composite numbers?

7 To what product is every number equal? 8 How do you find the prime factors of any number?

9 What are the prime factors of 105?

10 How do you find the prime factors common to several numbers?

11 What are the prime factors common to 420, 630, 1050, and 2,100?

DIVISIBILITY OF NUMBERS.

1 How many even numbers are prime? P. 97. 2 What numbers will 2 divide?

8 When will the divisor exactly divide the dividend?

9 When will any number divide a product?

11 When will a number divide either of them separately?

12 When will a number divide exactly the difference of two numbers?

13 If a number divide the dividend and divisor, what other number will it also divide ?

GREATEST COMMON DIVISOR.

1 What is a common divisor of two or more numbers? P. 99.

2 What is the greatest common divisor of two or more numbers ?

3 How do you find the greatest common divisor of two or more numbers?

4 What is the greatest cominon divisor of 84, 154, 210?

5 What is the rule when the numbers are large?

6 What is the greatest common divisor of 3328, and 4592?

7 What is the greatest common divisor of 5270, 5952, 5394, and 3038? Art. 94, Ex. 5.

LEAST COMMON MULTIPLE.

1 What is a multiple of a number? P. 102. 2 What is a common multiple of two or more numbers?

3 What is the least common multiple of two or more numbers?

4 How do you find the least common multiple of several numbers?

5 What is the least common multiple of 4, 9, 10, 15, 18, 20, 21?

6 What is the least common multiple of 49, 14, 84, 168, 98 ?

CANCELLATION.

1 What is cancellation?

2 On what principles do the operations of cancellation depend?

3 How do you perform the operations of cancellation?

4 What is the quotient of (240×441×16) (175×56×27) ?

COMMON FRACTIONS.

1 What is a unit? P. 108.

2 What is each part called when the unit is divided into two equal parts? Into three? Into four Into twelve?

3 How may the be regarded? The The 1, etc.?

4 What is each part called?