6. Add 361.04, .120, 78.0006, 101.54, 8.943, and .3 Ans. 549.9436.

together.

MULTIPLICATION OF DECIMALS.

Rule.

Set down the multiplier under the multiplicand, as in simple multiplication; and multiply without any regard to the decimal points.

When the operation of multiplying is completed, commence at the right-hand figure of the product, and count off as many figures towards the left as there are decimal figures in the multiplier and multiplicand, and there place the decimal point.

Note. If the number of figures in the product is not so great as the number of decimal figures in both the multiplier and multiplicand, a sufficient number of ciphers must be placed to the left of the product, to make the figures in the product equal to the decimals in both factors, and the decimal point must then be placed to the left of the ciphers.

Questions.

How do you place the multiplier and multiplicand in multiplication of decimals?

When the operation of multiplying is completed, how do you proceed to find where the decimal point is to be placed?

What is to be noted, when the number of figures in the product is not equal to the number of figures in both factors?

Examples.

1. Multiply .322 by 6.12

6.12

644

322

1932

1.97064 Ans.

Place the less number under the greater, as in simple subtraction; observing that the decimal points stand exactly under each other: then subtract as in simple subtraction; taking care to place the decimal point in the remainder exactly under those in the example.

Questions.

How do you place the numbers in subtraction of decimals?

What is to be observed with respect to placing the decimal point in the remainder?

1. Set down the divisor and dividend, as in whole numbers, and divide without any regard to the decimal points. 2. When the operation of dividing is completed, point off from the right of the quotients as many figures as the decimal figures in the dividend exceed those in the divisor, and there fix the decimal point.

Note. If there should not be as many figures in the quotient, as the decimal figures in the dividend exceed those in the divisor,

M 2

place as many ciphers to the left of the quotient as will make up the number, and place the decimal point to the left.

Note 2.-If the dividend should be less than the divisor, annex ciphers until it will contain the divisor, and fix the decimal point in the quotient accordingly.

Note 3.-If there be a remainder, annex ciphers to it, and proceed in the same manner as though the ciphers had been placed to the right of the dividend before commencing the operation.

Questions.

What is first to be done, when you commence an operation in division of decimals?

When the operation of dividing is completed, how do you find where the decimal point ought to be placed?

If there should not be as many figures in the quotient as the decimal figures exceed those in the divisor, what is to be done?

If the dividend be less than the divisor, what is to be done?

If there be a remainder, how do you proceed with it?

REDUCTION OF DECIMALS.

Case 1.

To reduce a vulgar fraction to a decimal.

Rule.

Place ciphers to the right of the numerator, until you can divide it by the denominator, and continue to divide until there is no remainder left; or if it be a number which will never come out without a remainder, until it is carried out to a convenient number of decimal places,

Note.-There must be as many places in the quotient as there have been ciphers annexed to the dividend.

Case 2.

To reduce any given sum or quantity to the decimal of any higher given denomination.

Rule.

1. Reduce the given sum or quantity to the lowest denomination mentioned in it.

2. Reduce one of that denomination of which you wish to make it a decimal, to the same denomination with the given sum.

3. Divide the given quantity so reduced by one of the denomination of which you wish to make it a decimal; the quotient will be the decimal required.

Case 3.

To reduce a decimal fraction to its proper value.

Rule.

Multiply the given fraction continually by the denomination next lower than that of which it is a decimal, for the proper value.

Questions.

How do you reduce a vulgar fraction to a decimal?

What is to be noticed, respecting the number of decimal places in the quotient?

How do you reduce any given sum or quantity to the decimal of any given denomination?

How do you reduce a decimal fraction to its proper value?

1. Reduce 3s. 6d. to the decimal of a pound.

240)42.000(.175 decimals. A

240

1800

1680

1200

1200

2. Reduce 2R. 4P. to the decimal of an acre.

Ans. .525.

3. Reduce 2 qr. 2 nails to the-decimal of a yard.

Ans. .625.

4. Reduce 5 minutes to the decimal of an hour.

Ans. .08333.

5. Reduce 10 grains to the decimal of an ounce, apothe caries' weight. Ans. .02083.+ 6. Reduce 2 quarts 1 pint to the decimal of a hogshead. Ans. .00992.

Case 3.

1. What is the value of .375 of a dollar? Ans. 37els.