3. One gallon contains 4 quarts; how many quarts in 2

gallons ? -in 3 gallons ?

in 4 gallons?

4. Three men bought a horse; each man paid 23 dollars for his share; how many dollars did the horse cost them ? 5. A man has 4 farms worth 324 dollars each; how many dollars are they all worth?

6. In one dollar there are one hundred cents; how many cents in 5 dollars ?

7. How much will 4 pair of shoes cost at 2 dollars a pair ? 8. How much will two pounds of tea cost at 43 cents a

pound?

9. There are 24 hours in one day; how many hours in 2 days? in 7 days?

in 3 days?

in 4 days?

10. Six boys met a beggar, and gave him 15 cents each;

how many cents did the beggar receive ?

When questions occur, (as in the above examples,) where the same number is to be added to itself several times, the operation may be much facilitated by a rule, called Multiplication, in which the number to be repeated is called the multiplicand, and the number which shows how many times the multiplicand is to be repeated is called the multiplier. The multiplicand and multiplier, when spoken of collectively, are called the factors, (producers,) and the answer is called the product.

11. There is an orchard in which there are 5 rows of trees, and 27 trees in each row; how many trees in the orchard?

In this example, it is evident that the whole number of trees will be equal to the amount of five 27's added together.

In adding, we find that 7 taken five times amounts to 35. We write down the five units, and

reserve the 3 tens; the amount of 2 taken five times is 10, and the 3, which we reserved, makes 13, which, written to the left of units, makes the whole number of trees 135.

If we have learned that 7 taken 5 times amounts to 35, and that 2 taken 5 times amounts to 10, it is plain we need write the number 27 but once, and then, setting the multiplier under it, we may say, 5 times 7 are 35, writing down the 5, and reserving the 3 (tens) as in addition. Again, 5

times 2 (tens) are 10, (tens,) and 3, (tens,) which we

reserved, make 13,

(tens,) as before.

10. 12. There are on a board 3 rows of spots, and 4

spots in each row; how many spots on the board?

A slight inspection of the figure will

***

****

*

show, that the number of spots may be found either by taking 4 three times, (3 times 4 are 12,) or by taking 3 four times, (4 times 3 are 12;) for we may say there

are 3 rows of 4 spots each, or 4 rows of 3 spots each; therefore, we may use either of the given numbers for a multiplier, as best suits our convenience. We generally write the numbers as in subtraction, the larger uppermost, with units under units, tens under tens, &c. Thus,

Multiplicand, 4 spots.
Multiplier, 3 rows.

Product,

12 Ans.

Note. 4 and 3 are the factors, which produce the product 12.

Hence, Multiplication is a short way of performing many additions; in other words,-It is the method of repeating any number any given number of times.

SIGN. Two short lines, crossing each other in the form of the letter X, are the sign of multiplication. Thus, 3 × 4 = 12, signifies that 3 times 4 are equal to 12, or 4 times 3 are 12.

Note. Before any progress can be made in this rule, the following table must be committed perfectly to memory.

4 = 40 5 = 50 6 = 60 7 = 70 8 = 80

2×3= 6 5×007× 10 = 70 10 × 2X 48 5 × 1 5 7×11= 77 10 × 2 × 510 5 × 2=10 7×1284 10 × 9 = 90

2×6=12

2X 7-14

2 × 8=16

5×3=158× 0 = 0

5 X 420 8×1=

5×5=25 8× 2 =

2×9=185> 5×6=30 8× 3 = 2 × 10 =20 5×7=35 8× 4 = 2 × 11-22 5×8=40 8 × 5 =

2×12=24

5×9=458×6=

8 16

10 × 10 =100

10 × 11=110

10 × 12 =120

24 11 ×
32

40 11 ×

48 11 ×

0 =

0

11 x

1 = 11

2 = 22

3 = 33

3×12=366 × 9=54 9×6=

4×006×10=60 9 × 7 = 63 12 ×

4× 146×11=66 9 × 8 = 72 12 ×

4X2

4× 3 12 7× 0 = 0 9×10=90 12 × 4×4=167× 1 = 79×11= 99 12 ×

2

3

4

5

6

24

36

48

60

= 72

7 = 84

8 = 96

4×5=207×2=14 9×12=108 12×9=108

4×6=247×3=2110 × 0 =

012 × 10 = 120

45 12 ×

54 12 ×

86×12=72 9× 9 = 81 12 ×

10 12 × 11 = 132 20/12 × 12 =144

30|

9 × 2 = how many? 4×6= how many? 8×9=how many? 3×7=how many? 5 × 5 = how many?

4×3×2=24.

3×2×5=how many?
7×1×2=how many?
8×3×2=how many?
3×2×4×5 = how many?

13. What will 84 barrels of flour cost at 7 dollars a barrel? Ans. 588 dollars. 14. A merchant bought 273 hats at 8 dollars each; what did they cost? Ans. 2184 dollars. 15. How many inches are there in 253 feet, every foot being 12 inches?

OPERATION. 253 12

The product of 12, with each of the significant figures or digits, having been committed to memory from the multiplication table, it is just as easy to multiply by 12 as by a single figure. Thus, 12 times 3 are 36, &c 16. What will 476 barrels of fish cost at 11 dollars a bar rel? Ans. 5236 dollars.

Ans. 3036

17. A piece of valuable land, containing 33 acres, was sold for 246 dollars an acre; what did the whole come to ? As 12 is the largest number, the product of which, with the nine digits, is found in the multiplication table, therefore, when the multiplier exceeds 12, we multiply by each figure in the multiplier separately. Thus:

OPERATION.

246 dollars, the price of 1 acre.
33 number of acres.

738 dollars, the price of 3 acres.
738 dollars, the price of 30 acres.

The multiplier consists of 3 tens and 3 units. First, multiplying by the 3 units gives us 738 dollars, the price of 3 acres. the first figure of

Ans. 8118 dollars, the price of 33 acres. We then multiply by the 3 tens, writing the product (8) in ten's place, that is, directly under the figure by which we multiply. It now appears, that the product by the 3 tens consists of the same figures as the product by the three units; but there is this difference--the figures in the product by the 3 tens are all removed one place further toward the left hand, by which their value is increased tenfold, which is as it should be, because the price of 30 acres

is evidently ten times as much as the price of 3 acres, that is, 7380 dollars; and it is plain, that these two products, added together, give the price of 33 acres.

These examples will be sufficient to establish the fole lowing

RULE.

I. Write down the multiplicand, under which write the multiplier, placing units under units, tens under tens, &c., and draw a line underneath.

II. When the multiplier does not exceed 12, begin at the right hand of the multiplicand, and multiply each figure contained in it by the multiplier, setting down, and carrying, as in addition.

III. When the multiplier exceeds 12, multiply by each figure of the multiplier separately, first by the units, then by the tens, &c., remembering always to place the first figure of each product directly under the figure by which you multiply. Having gone through in this manner with each figure in the multiplier, add their several products together, and the sum of them will be the product required.

EXAMPLES FOR PRACTICE.

18. There are 320 rods in a mile; how many rods are here in 57 miles?

19. It is 436 miles from Boston to the city of Washington; how many rods is it?

20. What will 784 chests of tea cost, at 69 dollars a chest?

21. If 1851 men receive 758 dollars apiece, how man dollars will they all receive? Ans. 1403058 dollars.

22. There are 24 hours in a day; if a ship sail 7 miles in an hour, how many miles will she sail in 1 day, at that rate? how many miles in 36 days? how many miles in 1 year, or 365 days? Ans. 61320 miles in 1 year.

23. A merchant bought 13 pieces of cloth, each piece containing 28 yards, at 6 dollars a yard; how many yards were there, and what was the whole cost?

Ans. The whole cost was 2184 dollars.

24. Multiply 37864 by 235. Product,

8898040. 28399112. 817793024.