Page images
PDF
EPUB

22. When we say, multiply 8 by 7, what do we mean? 23. In the statement, 9 times $12 are $108, name the multiplicand; the multiplier; the product; the factors; the abstract number; the concrete numbers; the like numbers. 24. Name the two factors of 25; of 27; of 35; of 63. 25. How many are 2 times 5 times 8 cents? Of what are 2, 5, and 8 factors?

26. Name three factors of 24; of 36; of 40.

27. At $8 a ton, what is the cost of 4 tons of coal?

Ans. $8+ $8+ $8+ $8, or 4 times $8 = $32.

28. What is the cost of 6 hats, at $5 a piece? At $7? 29. At 9 cents each, what will 6 melons cost? 8 melons? 30. How many are 7 times $5, minus $6? Plus $10 ? 31. How many are 10 times 6 bushels, plus 12 bushels? 32. How many are 6 times 12 miles, less 20 miles?

33. James gave 5 cents apiece for 6 oranges. How much change should he receive for 50 cents?

34. How much more than $35 will 5 barrels of flour cost, at $8 a barrel?

35. George had 10 cents, and James had 5 times as many. How many had both?

36. A man paid $4 a yard for 12 yards of cloth, and had $10 left? How much money had he at first?

37. What will be the cost of 6 cows at $26 each?

ANALYSIS.-Six cows will cost 6 times $26. 6 times 6 units are 36 units, or 3 tens and 6 units, and 6 times 2 tens are 12 tens, which, plus 3 tens and 6 units, are 15 tens and 6 units, or 156. Hence, 6 cows will cost $156.

38. If the cars run 25 miles an hour, how far will they run in 7 hours? In 6 hours?

39. If a house rent for $21 a month, what is the rent for 6 months? 8 months? 10 months?

40. When eggs are 18 cents a dozen, what is the cost of 5 dozen? Of 6 dozen? Of 10 dozen ?

41. How much less than $64 will 5 barrels of flour cost, at $9 a barrel? How much more is 6 × 12 +9 than 7 × 9-3 ? 42. What is the difference in cost of 8 cords of wood, at $3 a cord, and 6 tons of coal, at $5 a ton?

Find the required term in the following equations:

[blocks in formation]

55. When the multiplier consists of one figure. 1. Multiply 374 by 4.

EXPLANATION.-By this method, the result is obtained by addition. Since the units, tens, and hundreds in 374 are each to be taken 4 times, the result is obtained by writing 374 four times in a column, and finding the sum.

FIRST.

374

374

Equal parts.

374
374

1496 Sum.

Multiplicand,

SECOND.

374

4

1496

Multiplier,
Product,

EXPLANATION. - The preceding method is much shortened by multiplication. Write the multiplicand 374 but once; and since its parts, 3 hundreds, 7 tens, 4 units are each to be taken 4 times, write the multiplier 4 under the units, and multiply; thus, 4 times 4 units are 16 units, or 1 ten 6 units. Write the 6 units in units' place, and add the 1 ten to the product of the tens.

Next, 4 times 7 tens are 28 tens, and the 1 ten added make 29 tens, or

2 hundreds 9 tens. Write the 9 tens in tens' place, and add the 2 hundreds to the product of the hundreds.

Lastly, 4 times 3 hundreds are 12 hundreds, and the 2 hundreds added make 14 hundreds, or 1 thousand 4 hundreds, which write in the hun dreds' and thousands' places.

Hence, the product 1496 is the same as the sum of its equal parts.

[merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

12. What will be the cost of 231 tons of coal at $9 a ton ?

Although $9 is the true multiplicand, for convenience we may use it as the multiplier, and 231 as the multiplicand; but the product is dollars, because the true multiplicand is dollars.

This is obvious, since 231 tous at $1 a ton would cost $231, and at $9 a ton, 9 times $231.

13. What cost 2140 barrels of flour, at $8 a barrel?

14. What cost 1238 cords of wood, at $5 a cord?

15. What cost 752 pounds of nails, at 7 cents a pound? 5264 cents = $52.64.

SOLUTION.-7 cents × 752 =

When either factor contains cents, the product is cents, and may be changed to dollars and cents by putting the point (.) two places from the right, and prefixing the sign ($).

[blocks in formation]

20. At 6 cents a pound, what cost 675 pounds of rice?

21. At $4.37 a yard, what is the cost of 7 yards of cloth?

22. What cost 326 tons of coal, at $6 a ton?

23. What cost 379 pounds of nails, at 6 cents a pound? 24. At $6.75, what will 7 tons of coal cost?

56. When the multiplier consists of two or more figures.

[blocks in formation]

the multiplicand is to be taken 5 times plus 40 times, or 45 times. 5 times 736 is 3680, the first partial product; 4 tens or 40 times 736 is

29440, the second partial product.

The sum of the partial products is the entire product, 33120.

[blocks in formation]

RULE.-1. Write the multiplier under the multiplicand, placing units of the same order in the same column.

2. Beginning at the right, multiply each order of the multiplicand by each order of the multiplier, successively, and place the right-hand figure of each partial product under the order of the multiplier used.

3. The sum of the partial products is the required product. When there are ciphers in the multiplier, multiply by the significant figures only, since the product of any number by 0 is 0.

6. Multiply 6432 by 75; by 67; by 136; $36.45 by 34; by 37; by 126.

7. Multiply 23072 by 128; by 243; by 307; $142.50 by 63; by 234; by 325.

8. What will be the cost of building a line of telegraph 274 miles long, at $967 a mile? Of a brick wall 684 rods long, at $132 a rod ?

9. If 1049 pounds of seed cotton be raised from an acre of land, how many pounds will 386 acres produce?

10. If a cotton mill manufactures 628 yards of cloth in a day, how many yards can it make in 297 days?

What is the product
11. Of 2572 bushels by 94?
12. Of $403.06 by 127?
13. Of 86072 pounds by 208?
14. Of 316 times $487.46?
15. Of 507 times 30975 days?
16. Of 325 times 6408 cents?

Find the cost

17. Of 370607 by 4071 ?

18. Of 600326 by 2645 ? 19. Of 730096 by 5006? 20. Of 2407068 by 3406? 21. Of 408091 by 2407? 22. Of 73069 by 46035?

23. Of 386 railway coaches, at $7034.75 each.

24. Of 67 hogsheads of sugar, at $37.75 a hogshead? 25. Of 2347 acres of land, at $136 an acre?

57. The process of finding the product of several factors, by multiplying the first by the second, and the result by the third, and so on, is called Continued Multiplication. Thus, 126 × 72 9072, or, 126 × 3 × 4×6= 9072.

PRINCIPLE. The product of any number of factors in continued multiplication will be the same, in whatever order they are used.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]
« PreviousContinue »