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N. B. The brackets at the right of the fractions show that both terms of the fraction are to be divided by the divisor, and not the fraction itself, as in the division of frac tions.

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In the above process, both terms of the fraction 234 are divided by 3; the answer is divided by 2; and this answer again is divided by 3.

The last answer is

which cannot have both terms divided by any number without a remainder.

The other method of reducing a fraction to its lowest terms, is first to find the number which is the greatest common measure, and then to divide the fraction by this number.

The following is the method of finding the greatest common measure, and reducing to the lowest terms. Reduce to its lowest terms.

The denominator is first placed as a dividend, and the numerator, as a divisor; (below.) After subtracting, the remainder (14) is used for the divisor, and the first divisor (21) is used for the dividend. This process of dividing the last divisor by the last remainder is continued till nothing remains. The last divisor (7) is the greatest

common measure.

We then take the fraction and divide both terms by 7, the greatest common measure, and it is reduced to its lowest terms, viz. 3.

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RULE FOR FINDING THE GREATEST COMMON MEASURE OF A FRACTION AND REDUCING IT TO ITS LOWEST TERMS.

Divide the greater number by the less. Divide the divisor by the remainder, and continue to divide the last divisor by the last remainder, till nothing remains. The last divisor is the greatest common measure, by which both terms of the fraction are to be divided, and it is reduced to its lowest

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; 12811

Reduce the following; 88; 4932; MANS: 24997;

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948 8764

103284 7328472'

342954

REDUCTION OF FRACTIONS FROM ONE ORDER TO ANOTHER ORDER.

It will be recollected that in changing whole numbers from one order to another, it was done by multiplication and division.

Thus, if 40 shillings were to be changed to pounds, we divided them by the number of shillings in a pound, and if £2 were to be reduced to shillings, we multiplied them by the number of shillings in a pound.

The same process is used in changing fractions of one order to fractions of another order.

Thus, if we wish to change of a £ to a fraction of the shilling order, we multiply it by 20, making it 20 For 20% of a shilling is the same as of a pound.

40

200

If we wish to change of a shilling, to the same value in a fraction of the pound order, we divide by 20, making it. (This could also be divided by multiplying its denominator by 20.)

If then we wish to change a fraction of a lower order to the same value in a higher order, we must divide the frac tion, by multiplying the denominator, by that number of units

What is the rule for finding the greatest common measure of a fraction?

(of the order to which the fraction belongs) which make a unit of the order to which it is to be changed.

Thus if we wish to change of a penny to the same value in the fraction of a shilling, we multiply its denominator by 12, making it of a shilling. If we wish to change this to the same value in a fraction of the pound order, we must now multiply its denominator by the number of shillings which make a pound, making it of a pound. It must be remembered that multiplying the denominator of a fraction, is dividing the fraction.

If, on the contrary, we wish to change a fraction of a higher order to one of the same value in a lower order, we must multiply.

Thus, to change of a shilling to the penny order, we must multiply it by 12. This we do by multiplying its numerator by 12, and the answer is 24. For as there are 12 times as many whole pence in a whole shilling, so there are 12 times as many of a penny in of a shilling.

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To reduce a fraction of a higher order to one of a lower order.

Multiply the fraction by that number of units of the next lower order, which are required to make one unit of the order to which the fraction belongs. Continue this process till the fraction is reduced to the order required.

To reduce a fraction of a lower to one of a higher order.

Divide the fraction (by multiplying the denominator) by the number of units which are required to make one unit of the next higher order. Continue this process till the fraction is reduced to the order required.

What is the rule for reducing fractions of one order to another order?

EXAMPLES.

Reduce of a guinea, (or of 28 shillings,) to the fraction of a penny.

Reduce of a guinea to the fraction of a pound. $

Reduce

ounce.

of a pound Troy, to the fraction of an

Reduce of an ounce to the fraction of a pound Troy. Reduce of a pound avoirdupoise to the fraction of an

ounce.

A man has

pint is it?

A vine grew
Reduce of
Reduce of

of a hogshead of wine, what part of a

of a mile, what part of a foot was it? of a pound to the fraction of a shilling. of 3 shillings, to the fraction of a pound.

REDUCTION OF FRACTIONS OF ONE ORDER, TO UNITS OF A LOWER ORDER.

It is often necessary to change a fraction of one order, to units of a lower order. For example, we may wish to change of a unit of the pound order, to units of the shilling order.

This of a £ is 2 pounds divided by 3. These 2 pounds are changed to shillings, by multiplying by 20, and then divided by 3, and the answer is 133 shillings. This of a shilling may be reduced to pence in the same way, for of a shilling is 1 shilling divided by 3. This 1 shilling can be changed to pence, and then divided by 3, the answer is 4 pence.

RULE FOR FINDING THE VALUE OF A FRACTION IN UNITS OF A LOWER ORDER.

Consider the numerator as so many units of the order in which it stands, and then change it to units of the order in

What is the rule for finding the value of a fraction in units of a lower order?

which you wish to find the value of the fraction. Divide by the denominator, and the quotient is the answer, and is of the same order as the dividend.

EXAMPLES.

1. How many ounces in 2. How many days, hours 3. What is the value of 4. What is the value of 5. How many pence in 6. How many drams in 3 7. How many grains in 8. How many scruples weight?

of a lb. Avoirdupoise?
and minutes, in 4 of a month?
of a yard?
of a ton?
of a lb. ?

of a lb. Avoirdupoise?
of a lb. Troy weight?
in

of a' lb. Apothecaries

9. How many pints in of a bushel?

REDUCTION OF UNITS OF ONE ORDER TO FRACTIONS OF ANOTHER ORDER.

It is necessary often to reverse the preceding process, and change units to fractions of another order. For example, to change 13s. 4d, to a fraction of the pound order.

To do this we change the 13s. 4d. to units of the lowest order mentioned, viz. 160 pence. This is to be the numerator of the fraction. We then change a unit of the pound order to pence (240) and this is the denominator of the fraction. The answer is 8 of a pound.

For if 13s. 4d. is 160 pence, and a £ is 240 pence, then 13s. 4d. is 10 of a pound.

RULE FOR REDUCING UNITS OF ONE ORDER TO FRACTIONS OF ANOTHER ORDER.

Change the given sum to units of the lowest order mentioned, and make them the numerator.

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