Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση
[blocks in formation]

How does the number of decimal places in the product (.00025) compare with the number of decimal places in both the multiplier (.05) and the multiplicand (.005)?

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

510.00

625 in the decimal form =5.625

How does the number of decimal places in the product (5.625) compare with the number of decimal places in both the multiplier (3.75) and the multiplicand (1.5)?

In the above examples we see the following1:

PRINCIPLE: In multiplying decimals, the number of decimal places in the product is equal to the sum of the decimal places in both the multiplicand and the multiplier1.

In multiplication of decimals it is not necessary to place units under units, tenths under tenths, etc.

4. Multiply .025 by 1.5

.025

1.5

125

25

.0375

Multiply as if the numbers were whole numbers.

There are

3 decimal places in the multiplicand and one decimal place
in the multiplier. Therefore, there must be 3+1, or 4 decimal
places in the product. We must prefix a zero before the 3
and place the decimal point in front of this zero.
.025 X 1.5= .0375

Then

1To the teacher: All new principles should be developed inductively as shown above. If the pupils are not able to see the principle from the three illustrations that are given, additional examples can readily be supplied by the teacher until the pupils are able to see the principle involved.

[blocks in formation]

41. An owner of a factory employs 21 men at $2.50 per day, 14 men at $3.25 per day and 8 men at $3.75 per day. Find the total amount of wages paid per day.

42. A farm of 83.5 acres was sold for $122.75 per acre. Find the amount received for the farm.

43. Mr. Adams bought 8 tons of hard coal at $10.75 per ton. What was the cost of that amount of coal?

44. Philip went to visit his grandparents who lived 85 miles away. He traveled .3 of the distance by boat and the rest by train. How many miles did he travel each way?

45. A farmer had a drove of 64 hogs and sold .75 of them. How many did he sell?

46. A gardener sold a grocer 16 bushels of rutabagas at 85 cents a bushel. He received in exchange 125 pounds of sugar at 11 cents per pound, and the balance in cash. How much cash did he receive?

47. Find the cost of 1.75 cwt. of freight at $.24 per cwt. (Cwt. is an abbreviation of hundred weight.)

Exercise 7. Multiplying by 10, 100, 1000, Etc.

1. Multiply .5 by 10; 3.5 by 10; .08 by 10; 6.005 by 10; 12.35 by 10.

2. Compare the positions of the decimal points in the products with the positions of the decimal point in the multiplicands.

If you have multiplied correctly, your results should show that: Multiplying a decimal by 10 moves the decimal point one place to the right.

3. Multiply .5 by 100; 3.5 by 100; .08 by 100; 6.005 by 100; 12.35 by 100.

4. Compare the positions of the decimal points in the products with the positions of the decimal points in the multiplicands.

5. Multiplying a decimal by 100 moves the decimal point how many places to the right?

6. Multiply each of the multiplicands in the first problem by 1000 and determine how many places the decimal point is moved to the right in pointing off the products.

From these examples we see that in multiplying by ten or any number which is a product of tens (as 100, 1000, etc.), we move the decimal point as many places to the right as there are zeros in the multiplier.

Multiply each of the following numbers by 10, by 100, by 1000, without using a pencil:

[blocks in formation]

Exercise 8. Division of a Decimal by a Whole Number.

1. Divide .8 by 4

8

Express .8 as the common fraction 10

8
10÷4= 10 expressed as a decimal=.2

[blocks in formation]

12

.12=100 100÷4-180 180 as a decimal=.03

4. Divide .025 by 5

.025-1850

=

[blocks in formation]

We may now put these examples in the regular division form, pointing off the quotients by the answers obtained by using common fractions:

[blocks in formation]

PRINCIPLE: In dividing a decimal by a whole number the
decimal point is placed in the quotient directly above the
decimal point in the dividend.

[blocks in formation]
[merged small][merged small][merged small][merged small][merged small][subsumed][merged small][subsumed][subsumed][subsumed][ocr errors][subsumed][merged small][merged small][merged small][subsumed][ocr errors][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][subsumed][subsumed][subsumed][merged small][ocr errors][subsumed]

180.03. Therefore .375÷12.5=.03.

Let us next put these examples in a long division form so that the principle of division of decimals may be more clearly The quotients are pointed off as shown above:

seen.

[blocks in formation]

5. Answer the following questions for each of the above problems:

(a) How many decimal places are there in the divisor? (b) The decimal point in the quotient is how many places to the right of the decimal point in the dividend?

« ΠροηγούμενηΣυνέχεια »