1. What will 40 tons of hay cost at $20 a ton? 4X2=8, and 8 with the two ciphers=$800. 2. What is the product of 30 multiplied by 60? 3. What is the product of 80 multiplied by 60? 4. What is the product of 50 multiplied by 70 ? 5. What is the product of 90 multiplied by 40? 6. What is the product of 700 multiplied by 20? 7. What is the product of 80 multiplied by 30? 8. What is the product of 50 multiplied by 30? 9. What is the product of 20 multiplied by 90? 10. What is the product of 70 multiplied by 30? 11. What is the product of 80 multiplied by 70?

§ 61. If one of the numbers is composed of units and tens, they can be multiplied mentally, by multiplying the units and tens separately and then adding the products together.

1. A farmer bought 23 sheep at 3 dollars each, how much did he pay for the whole number?

OPERATION. 23=20+3, or 2 tens and 3 units. Then 20 sheep at $3=$60; and 3 sheep at $3-$9. Then $60+$9=$69, Ans.

2. What will 32 loads of hay cost at $9 a load? at $10 a load?

3. If one acre of land cost $37, what will 7 acres cost? 9 -acres? 8 acres?

4. What will 7 rolls of broadcloth cost at $31 a roll? at $28? at $36 ?

5. What will 9 loads of wood cost at $17 a load? $15 a load? $12 a load?

6. In 1 gallon there are 4 quarts. How many quarts in 26 gallons? in 33 gallons?

7. In 1 pound there are 16 ounces. How many ounces in 8 pounds? in 11 pounds?

8. In 1 quarter of a hundredweight there are 25 pounds. How many pounds in six quarters of a hundredweight? in 7 quarters? in 9 quarters ?

9. In 1 pistole there are 22 shillings. How many shillings in 6 pistoles? in 8 pistoles? in 4 pistoles? in 7 pistoles ?

10. In 1 guinea there are 28 shillings. How many shillings in 4 guineas? in 7 guineas? in 5 guineas? in 8 guineas?

SIMPLE MULTIPLICATION, written.

§ 62.-1. In multiplication we repeat one number as many times as there are units in another. (§ 57.) Suppose it is required to find the amount of 4 times 17. This is determined by multiplication. Thus we say, 4 times 7 is 28, and write down the 8 only; we then say 4 times 1 are 4 and 2 to carry are 6; we then write the 6 on the left of the 8, and thus obtain the true product, 68. The same result is obtained by writing 17 down 4 times and adding; that is four 17s added together give the same result as one 17 multiplied by 4; for 17X4-68, and 17+17+17+17=68.

2. Two numbers are always required for the performance of any operation in multiplication. These numbers are called, the one the multiplicand, the other the multiplier. The number which results from multiplying two numbers together is called the product. Thus in the operation above, 17 is the multiplicand, 4 the multiplier, and 68 the product.

3. The multiplier and multiplicand together are called factors. By this we mean that they are the makers or producers of the number obtained, that is the product.

4. The product is obtained by repeating the multiplicand; it must therefore agree with it in denomination.

5. The multiplier is to be considered merely as an abstract number, expressing simply the number of repetitions to which the multiplicand is subjected.

6. It is usual in multiplication to make the larger number the multiplicand, and the smaller one the multiplier.

62. How often is one number repeated in multiplication? How else may the same result be obtained? How many numbers are employed? What called? What is the resulting number called? What are the multiplicand and multiplier together called? What do we mean by that? How is the product obtained? With what must it agree? How consider the multiplier? Expressing what?

The truth or accuracy of the result does not however depend on this order of multiplication; for 12×4=4X12; that is we obtain the same product, viz. 48, whether we multiply 12 by 4, or 4 by 12. Convenience is however promoted by

multiplying the larger by the smaller number.

7. The sign or character by which the multiplication of one number by another is indicated, consists of an oblique cross, (X).

§ 63. TO MULTIPLY BY ANY NUMBER NOT GREATER THAN 12.

RULE.

Write the multiplier under the multiplicand; and, beginning with the right-hand figure of the multiplicand, multiply each figure by the multiplier, and place the number produced under the figure multiplied, in all cases whenever that number is less than 10. If, however, the number produced be more than 10, write down only the right-hand figure of that number, and add the 10s to the product of the next figure of the multiplicand.

(a) The entire product of the left-hand figure of the multiplicand must in all cases be written down.

(b) Whenever the multiplier consists of units only, the denomination of each figure of the product will be the same as that of the figure multiplied.

1. What is the product of 456 multiplied by 8?

PERFORMED. 4 5 6 multiplicand.

8=multiplier.

36 48

EXPLANATION. I here

product.

say 8 times 6 are 48, and writing down the 8, add the 4 to the product of 5 multiplied by 8.

What is usual! Is this necessary? Illustrate. What is the sign of multiplication!

63. How write the numbers! Begin with what figure? How proceed? If the number produced be more than 10, how proceed? What must be done relative to the product of the left-hand figure? Whenever the multiplier consists of units, what is the denomination of each figure of the product!

That is, I say 8 times 5 are 40 and 4 added make 44, and writing down the right-hand 4, I add the left-hand one to the product of 4 multiplied by 8, and obtain 36; the whole " of which is written down, it being the product of the left hand figure of the multiplicand.

2. Multiply 7246 by 7.

PERFORMED. 7 2 4 6 multiplicand.

7=multiplier.

50722 product.

EXPLANATION. 6x7=42; write down 2 and carry 4. 4x7=28, and 28+4=32; write down 2 and carry 3. And again, 7×2=14, and 14+3=17; write down 7 and carry 1; and finally, 7×7=49, and 49+1=50, all of which is written down, thus producing the entire product 50722.

11. What is the value of 376 yards of broadcloth at $7 per yard?

Ans. $2632. 12. How much can a man earn by 378 days' labor, if he receive $3 per day?

Ans. $1134.

13. What will 493 barrels of flour cost at $7 a barrel ? Ans. $3451. 14. A hatter has in store 539 hats, of an average value of $4. What is the total value? Ans. $2156. 15. How much will 163 loads of hay come to, at $12 a load? Ans. $1956. 16. How far can a man travel in 276 hours if he travel 9 miles an hour? Ans. 2484 miles.

17. A man bought a farm containing 789 acres and paid $8 an acre. How much did the whole cost? Ans. $6312. 18. What will 3785 pounds of beef cost at 11 cents a pound? Ans. 41635 cents.

19. If a pound of sugar cost 7 cents, what will 8958 pounds cost? Ans. 62706 cents.

20. If the value of a load of straw be $6, what are

989 loads worth?

Ans. $5934. 21. In 1 foot there are 12 inches. How many inches in 678 feet?

22. In 1 mile there are 8 furlongs. in 1272 miles?

Ans. 8136 in. How many furlongs Ans. 10176 fur. Ans. 10952 fur

23. How many furlongs in 1369 miles. longs. How many in 667 miles? Ans. 5336 furlongs. How many in 2981 miles? Ans. 23848. Ans. 141480.

24. In 1 furlong there are 40 rods. 976 furlongs? (§ 56.)

25. How many rods are there in 897

In 17685 miles?

How many rods in
Ans. 39040 rods.

furlongs?

Ans. 35880 rods.

26. In 1 pound sterling there are 20 shillings. How many shillings in 886 pounds? Ans. 17720s.

27. How many shillings in 1789 pounds? Ans. 35780s. In 5683 pounds? Ans. 113660s. In 3587 pounds? Ans. 71740s. In 1859 pounds? Ans. 37180s.

28. In 1 shilling there are 12 pence. How many pence in 653 shillings? Ans. 7836 pence. In 859 shillings? Ans. 10308 pence. In 8764 shillings? Ans. 105168 pence. In 6853 shillings? Ans. 82236 pence.

29. In 653 pounds how many pence? (Multiply first by 20, and then by 12. See sums 26 and 28.)

Ans. 156720 pence. 30. In 1875 pounds how many pence? Ans. 450000 pence. In 2163 pounds? Ans. 519120 pence.

31. In 1 penny there are four farthings. How many farthings in 1684 pence? Ans. 6736 farthings. 32. In 2856 pence how many farthings? Ans. 11424. How many in 2196 pence? Ans. 8784.

33. In 1728 pence how many farthings? Ans. 6912. In 3756 pence? Ans. 15024.

34. In 576 pounds how many farthings? (See sums 26, 28, and 31.) Ans. 552960 farthings.

35. In 358 pounds how many farthings? Ans. 343680. In 297 pounds? Ans. 285120.