28. How many are 9 × 12÷6? 9 × 12 ÷ 18? 9 X 1224?

29. How many are 10 × 12÷6? 10 × 12 ÷ 10? 10 X 12 20? 10 × 12 ÷ 6? 24?

30. How many are 10 × 16 ÷ 5? 8? 10 X 16 ÷ 20? 10 × 16 ÷ 32? 31. How many are 18 X 24 ÷ 9? 36? 18 X 248? 18 X 24 ÷ 6? 12? 18 X 24 ÷ 48?

10 × 12 ÷

10 × 16 ÷

18 × 24 ÷ 18 X 24 ÷

REVIEW.

SECTION XV.

1. BOUGHT coffee of four kinds; for Java I paid 12 cents a pound, for Mocha 13 cents, for Brazil 9 cents, and for St. Domingo 8 cents; what is the price paid for a package containing a pound of each kind?

2. How many are 100 64? 100 49? 100 36? 100 16? 100 9? 100 57?

3. How many are 5 + 4 + 8 +7 +6 +9? 4. How many are 5 +7 +5 +8+9+6? 5. How many are 4+8+6+9+11 + 12? 6. 4 tens and 9 tens and 7 tens and 8 tens are how many tens? are how many?

7. If sperm candles are worth 50 cents, and tallow candles 13 cents a pound, what is the difference in their value?

8. 36+ how many are 100? 49+ how many are 100? 64+ how many are 100?

9. From 6 times 8 subtract 2 times 8. ANS. 4 times 8, or 32.

10. From 7 times 9 subtract 4 times 9.

11. From 11 times 11 subtract 4 times 11.

12. A boy received 90 credit-marks during the week; 19 on Monday, 21 on Tuesday, 4 on Wednesday, 16 on Thursday, and 23 on Friday; how many did he receive on Saturday?

-70?

13. How many are 23+ 17+ 25+ 19 14. How many are 24+ 15 +32 +1260? 15. How many are 35+16+23+9

50?

16. Bought 14 yards of cotton cloth at 10 cents a yard, and 2 yards of linen at 75 cents a yard; for which did I pay the most, and how much?

17. From 7 times 12 take 6 times 9?

18. From 8 times 11 take 5 times 6?

19. 3 times 8+ how many are 6 times 7?

20. If fish is worth 5 cents a pound, and beef 10 cents, how many pounds of fish will be equal in value to 7 pounds of beef?

21. How many times may 5 be subtracted from 75 ? Then 75 are how many times 5? 5 times 15 are how many?

22. Two men are 45 miles apart, and are travelling in the same direction; the foremost man at the rate of 6 miles an hour, and the other 9 miles an hour; in how many hours will the one overtake the other? how far will each man have travelled in the time?

23. Two men are 60 miles apart, and travel towards each other; one at the rate of 4 miles an hour, and the other 6 miles an hour; in how many hours will they meet? how far will each have travelled? what number of miles does one travel more than the other?

24. Two men are fifteen miles apart, and travel in opposite directions; one at the rate of 3 miles an hour, and the other 2 miles an hour; how far apart will they be in 8 hours? If they then turn and travel towards each other, in what time will they meet? How many hours, and what distance, will each man have travelled from the time he set out?

25. 5 times 3 and 6 times 3 and 8 times 3 are how many times 3? are how many?

26. 6 times 4 and 7 times 4 and 5 times 4 are how many times 4? are how many?

27. A man selects 90 sheep from his flocks in different pastures, taking 15 sheep from each pasture; from how many flocks does he select?

28. 4 tens and 3 tens are how many times 5? 6? 7? 8? 9? 11? 12? 13?

29. A shop-keeper bought a piece of cloth, containing 12 yards, for 6 dollars a yard; he sold 7 yards at 8 dollars a yard, but the remainder being damaged, he was obliged to sell it at 4 dollars a yard; did he gain or lose, and how much?

30. If from cloth worth 72 dollars, a tailor makes 3 suits of clothing, how much must he receive for each suit, in order to gain 12 dollars?

31. 5 times 5 and 6 times 5 and 7 times 5 less 11 times 5 are how many times 5? are how many?

32. 3 times 6 and 4 times 6 and 11 times 6 less 7 times 6 are how many times 6? are how many?

33. What numbers multiplied together will produce 25? 49? 56? 72? 21? 34? 66? 84? 132? 144? 34. What two numbers added together will produce 17? 21? 48? 35? 18? 43?

35. What three numbers added together will produce 17? 24? 48? 35? 18? 43?

36. What four numbers added together will produce 17? 24? 48? 35? 18? 43?

37. 3 times 7 and 5 times 7 and 12 times 7 less 7 times 7 are how many times 7? are how many?

38. 4 times 8 and 6 times 8 and 13 times 8 less 9 times 8 are how many times 8? are how many?

39. What four numbers added together will produce 19? 25? 37? 41? 49? 55?

40. What five numbers added together will produce 19? 25? 37? 41? 49? 55 ?

PRIME AND COMPOSITE NUMBERS

SECTION XVI.

A NUMBER which cannot be formed by multiplying together two or more whole numbers greater than a unit is called a prime number; as 1, 2, 3, 5, 7.

A number that can be formed by multiplying together two or more whole numbers greater than a unit is called a composite number; as 4, 6, 9, 8.

When a composite number is analyzed into prime numbers, the prime numbers are called its prime factors. Thus the prime numbers 2 and 3 are prime factors of 6, because 3 X 2 = 6. The prime factors of 8 are 2, 2, 2; because 2 × 2 × 2: 8.

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The pupil will state which are prime and which composite numbers in the table, and analyze the composite numbers into their prime factors.

OBS. To find the prime factors of the composite numbers in the table, divide the even numbers by 2; the odd numbers by 3, 5, or 7. After the division has been performed once, the pupil will readily perceive what the other divisors must be, in order that all may be prime factors. Thus, the number 50 is an even number; 50225; the pupil will instantly perceive that the prime factors of 25 are 5, 5; therefore the prime factors of 50 are 2, 5, 5.

A NUMBER that will divide two or more numbers without a remainder is called a common factor of those numbers. The greatest number that will divide two or more numbers without a remainder is called the greatest common factor. Thus, 2, 3, and 6, are common factors of 12 and 18, but 6 is the greatest common factor of these numbers.

OBS. To find the greatest common factor of two numbers, divide the greater number by the smaller, and the smaller by the remainder, and thus continue dividing the last divisor by the last remainder, till nothing remains; the divisor used last of all is the greatest common factor. Thus, to find the greatest common factor of 12 and 18, divide the greater number (18) by the smaller number (12), and the smaller number (12) by the remainder (6), and, as there is no remainder, 6, the last divisor, is the greatest common factor.