DIVISION

50. 1. What number multiplied by 4 gives $20 as a product? 4 × ($) = $20.

2. If 4 times $5 is $20, then how many times is $5 contained in $20? $20÷$5=

3. How many times is $2 contained in $10? In $16? In $17, with what remainder?

4. If a man earns $15 in 3 days, how much does he earn a day?

5. If the product of two numbers is 35, and one of the factors is 7, what is the other? If one of the factors is 5, what is the other?

51. The process of finding either factor when the other factor and their product are given is called Division.

52. The given product is called the Dividend, the given factor is called the Divisor, and the factor to be found is called the Quotient.

53. Division is seen to be the inverse of multiplication. In the latter, multiplicand and multiplier are given, while the product is required. In the former, dividend corresponds to product, divisor to one factor, and quotient to the other.

Point out the factors in these examples; the product; the dividends; the divisors; the quotients. Observe that

to find a quotient we need recall only how many of the given divisors equal the dividend.

54. Division includes

(a) Finding one of the equal parts of a number; as, of $10 $5. $10 ÷ 2 = $5.

=

(b) Finding how many times one number contains another of the same kind; as, $20÷$5=4; 15 ft.÷5 ft.=3.

1. What is one of the 3 equal parts of $21?

of $21 = $7, or $21 ÷ 3 = $7.

In this case the dividend is concrete and the divisor abstract. tient is concrete, since it must correspond to the multiplicand.

2. How many times is $3 contained in $21?

$21 $37.

The quo

In this case the dividend and divisor are concrete. The quotient is abstract, since it must correspond to the multiplier.

3. When 60 ft. is the dividend and 12 the divisor, what is the quotient?

4. When 50% is the dividend and 10 the divisor, what is the quotient?

5. Find by trial whether the product of the quotient and divisor is equal to the dividend.

6. When $48 is the dividend and $6 the quotient, what is the divisor?

7. When $9 is the divisor and 3 the quotient, what is the dividend?

8. When 9 is the divisor and 72 the dividend, what is the quotient?

9. If you have a dozen apples and wish to give me of them, you must give me one of the 4 equal parts of 12 apples. That is, you must divide 12 apples by 4.

10. What is of 45 feet? ? ?

55. 1. When books are $2 each, how many can you buy for $7? How much money will you have left?

2. How many 3's in 6? How many in 10? How many ones are left over?

3. When you take 5 cents from 18 cents three times, how many cents remain? Is the remainder a part of the 18 cents? Is it greater or less than the 5 cents?

56. The number remaining when the division is not exact is called the Remainder. It is a part of the dividend, and always less than the divisor.

The product of divisor and quotient, plus the remainder, if any, is equal to the dividend. Verify this by trial.

57. Show that 5 tens and 6 ones are equal to 4 tens and 16 ones.

59. 1. Mr. B divided $9 equally among 3 boys. How much did each boy receive?

Since 3 boys received $9, each boy received of $9, or $3. $9÷3=$3.

2. When chestnuts are $3 a bushel, how many bushels can be bought for $24?

At $3 a bushel as many bushels can be bought for $24 as $3 is contained times in $24. There are 8 times $3 in $24. Hence 8 bushels can be bought.

It will be observed that in the division the quotient 8 is not 8 bushels, but an abstract number, which is interpreted in the conclusion.

3. There are 4 pecks in a bushel. How many bushels are there in 36 pecks?

4. If 4 bags of the same size contain 32 bushels of beans, how many bushels are in each bag?

5. A jeweler paid $84 for 7 watches. average price paid?

What was the

6. A gardener tied 54 radishes in bunches of 6 each, How many bunches did he have?