DIVISION.

66. 1. 4 is one factor of 8; what is the other?

2. 3 is one factor of 9; what is the other?

3.

2 is one factor of 12; what is the other? 4. 4 is one factor of 16; what is the other?

9.

10.

10 is one factor of 40; what is the other?

9 is one factor of 72; what is the other?

11. 12 is one factor of 108; what is the other?

12. 11 is one factor of 132; what is the other?

When the factors are given to find the product, what is the work called?

When the product and one factor are given to find the other factor, the work is called Division.

The Dividend is the number to be divided (or the Product).

The Divisor is the given factor.

The Quotient is the required factor.

The sign of division is. It is read divided by.

Thus, 54÷6-9 is read: 54 divided by 6 equal 9. Division demands a knowledge of the multiplication table quite as much as multiplication itself; for every step in dividing requires that we find the other factor which, taken with the divisor, will produce the largest multiple in that part of the dividend with which we are dealing. Division is just as impossible without using the remembered results of the multiplication table as is multiplication.

68. The divisor for each line of dividends in the following exercises is written at the left.

Name the

9 15 36 27

12

36

24

48

21

8. 12)36 60 108 48 120 84 144 96 132

In the following exercises name the quotients and the remainders:

9. 3)10 22 16 13 25 32 37

1. A boy averages 6 miles an hour on his bicycle. How many hours will it take him to go 48 miles?

2. Henry paid 63 cents for berries at 9 cents a quart. How many quarts did he buy?

3. An orchard has 72 trees, and there are 8 trees in a row. How many rows are there?

4. A boy goes 48 miles in 8 hours on his bicycle. How many miles does he average per hour?

5. Henry paid 63 cents for 7 quarts of berries. How many cents a quart did he pay?

6. In an orchard are 72 trees in 9 equal rows. How many trees are there in a row?

From these problems it will be seen that either factor may be the given one. In the first three the given factor corresponds to the multiplicand in the

opposite process of multiplication; it is of the same kind as the dividend. The quotient is an "abstract" number showing how many "times" the dividend contains the divisor. In the last three problems the given factor corresponds to the multiplier; it is an "abstract" number, showing what part of the dividend is to be found. The quotient is of the same kind as the dividend of which it is a part. Hence, there are two distinct cases in division when the dividend is a concrete number. The first is division proper, or, Division is finding how many times one number is contained in another. The second case is sometimes called Partition.

Partition is finding one of the parts when a given number is separated into a given number of equal parts.

If both given numbers are abstract, the problem may be considered as one of division proper, or of partition, indifferently; but an explanation of the process should correspond to one or the other supposition.

The remainder is always of the same kind as the dividend.

ORAL EXERCISES.

70. Tell whether the following problems are division proper or partition:

1. At 6 cents a quart, how many quarts of milk will 42 cents buy?

SOLUTION: At 6 cents a quart, 42 cents will buy as many quarts of milk as there are times 6 cents in 42 cents, which is 7 times; hence, 7 quarts can be bought.

2. Hugh paid 35 cents for 5 cakes of maple sugar. What was the price per cake?

SOLUTION: If 5 cakes cost 35 cents, 1 cake costs one fifth of 35 cents, or 7 cents.