Find the greatest common divisor of:

10. 672 and 960.

11. 616 and 1012.

12. 272 and 428.

13. 1650 and 1920.

14. 696, 1218, and 1160. 15. 450, 720, and 810.

16. What is the greatest prime factor common to 4242 and 2626?

17. A grocer had 84 bananas and 126 lemons, which he wished to put into bags, each bag containing the largest number possible, and each containing the same number. How many could be put into each bag?

18. A man has three fields containing respectively 14, 18, and 22 acres. He wishes to cut them into the largest possible lots of equal size. How much land will each lot contain? How many lots will each field contain?

19. What is a multiple of a number? A common multiple? The least common multiple?

Find the least common multiple of: 20. 96, 196, 42, and 54.

21. 45, 36, 70, and 90.

22. 36, 40, 42, and 48.

23.

252, 462, and 1092.

24. 120, 280, and 308.

25. 36, 110, 98, and 66.

26. Find the least common multiple of the even numbers to and including 20.

27. What is the least sum with which I can buy an exact number of chairs at $6, $ 8, or $5 each?

28. What is the smallest sum of money that may be expended by using an exact number of nickels, dimes, quarters, or 3-cent pieces?

How many pieces of each kind will the sum contain?

29. John can run around a block in 6 minutes, James in 8 minutes, and Henry in 9 minutes. If they start together, how long before they will all be together again at the starting-point?

30. What is the shortest piece of rope that can be cut into pieces 32, 36, and 44 feet long?

39. 240 × 48 × 70 × 18 ÷ 42 × 15 × 54 × 7 = ?

40. Divide the product of 25, 14, and 11 by the product of 15, 7, and 22.

41. How many bushels of wheat at $1.10 a bushel must be given for 6 pieces of cloth each containing 33 yards at 50 cents a yard?

42. How many cords of wood at $3 a cord will pay for 30 lb. of sugar at 5 cents a pound?

43. If 8 men can do a piece of work in 6 days, in how many days can 12 men do it?

44. How many pounds of sugar can be bought for $7 if 21 lb. cost $1.05?

45. How many pounds of maple sugar at 12 cents a pound must a farmer exchange for 15 pounds of coffee at 24 cents a pound?

46. A milkman exchanges 8 cans of milk, 30 quarts in a can, at 4 cents a quart, for 3 pieces of sheeting, 40 yards in a piece. What is the price of the sheeting per yard?

COMMON FRACTIONS.

116. 1. When any whole thing, as an apple, is divided into two equal pieces, what part of the whole will each piece be?

2. If anything is divided into 3 equal parts, what is each part called? Into 4 equal parts? Into 5 equal parts? Into 8 equal parts?

3. One of the two equal parts of an apple is one half of it. One half is written.

4. One of the two equal parts of a number is of the number.

5. How many are of 4 oranges?of 20 cents? of 10?

6. One of the three equal parts of anything is one-third of it. One-third is written. How many are of 6 men? of 12 dollars? of 18 days? of 24?

117. One or more of the equal parts of a unit is called a Fraction.

The unit of which the fraction is a part is called the Unit of the Fraction.

One of the equal parts is called a Fractional Unit.

Two or more fractions having the same fractional unit are Like Fractions.

118. A Fraction is written with two numbers, one above the other, with a line between them; as .

The number below the line is the Denominator, and it shows into how many equal parts the unit is divided. Thus, in the fraction, 8 is the denominator.

The number above the line is the Numerator, and it shows how many of the parts are taken.

Thus, in the fraction ğ, 5 is the numerator.

The numerator and denominator are called the Terms of a Fraction.

Thus, 3 and 4 are the terms of 4.

119. A Common Fraction is a fraction written with its numerator above its denominator with a line between.

120. A Proper Fraction is a fraction whose value is less than 1. Its numerator is less than its denominator; as 4, 4, 7.

3

121. An Improper Fraction is a fraction whose value is 1 or more than 1. Its numerator is equal to or greater than its denominator; as 4, 4, . 5 11.

122. An integer may be written in fractional form by giving it 1 for a denominator, when it becomes an improper fraction.

Thus, 5, 4 = 4.

123. A number composed of an integer and a fraction is a Mixed Number.

Thus, 31, 127.

124. A fraction is indicated division, the numerator being the dividend, and the denominator the divisor.

Thus, means 34. 12 means 12÷3.

125. The Value of a Fraction is the quotient of the numerator divided by the denominator.

1. In one apple there are how many halves? many fourths? How many eighths?

2. In of an apple, how many fourths? eighths?

3. How many eighths in & of an apple?

How

How many

4. In one apple there are how many thirds? How many sixths?

5. In there are how many sixths? How many ninths? In how many sixths? How many ninths?

6. Name a fraction that is equal to . Name a fraction equal to

To

7. Change to halves. Change to thirds.

8. Change to fourths. To eighths.