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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 di. visor, and not the fraction itself, as in the division of frac. tions.
2 3 4
3)+3=18 Answer. In the above process, both terms of the fraction in are divided by 3; the answer is divided by 2; and this answer again is divided by 3.
The last answer is in 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 il 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 ite lowest terms, viz. .
RULE FOR FINDING THE GREATEST COMMON MEASURE OF Á 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 terms.
Reduce the following Fractions to their lowest terms. 438; 14; 14; 13; ; 101799 iniz; 1163; .
Ans. Vi hai t; } it ; Tézifis.
Reduce the following; 4; 4434 ; 428344 i 49877; Win; ; Ti
15 8 2 12811
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 L2 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 to of a £ to a fraction of the shilling order, we multiply it by 20, making it for For Loo of a shilling is the same as zoo of a pound.
If we wish to change too of a shilling, to the same value in a fraction of the pound order, we divide % by 20, making it too. (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 à 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 denomi. nator by 12, making it go 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 num. ber of shillings which make a pound, making it tozo of a pound. It must be remembered that multiplying the deno. minator 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 it 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 ijt of a penny in 1ša of a shilling.
RULE FOR REDUCING FRACTIONS OF ONE ORDER TO AN
To reduce a fraction of a higher order to one of 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 frac. tion is reduced to the order required.
What is the rule for reducing fractions of one order to another order ?
EXAMPLES. Reduce 12km of a guinea, (or of 28 shillings,) to the fraction of a penny.
Reduce of a guinea to the fraction of a pound. Reduce of a pound Troy, to the fraction of an
Reduce of an ounce to the fraction of a pound Troy. Reduce o of a pound avoirdupoise to the fraction of an A man has zit of a hogshead of wine, what part of a pint is it?
A vine grew too of a mile, what part of a foot was it ? Reduce of of a pound to the fraction of a shilling. Reduce že of į 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 13} shillings. This } of a shilling may be reduced to pence in the same way, of a shilling is 1 shilling divided by 3. This 1 shilling can be changed to pence, and then divided by 3, the an. swer 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.
1. How many ounces in of a lb. Avoirdupoise ? 2. How many days, hours and minutes, in of a month ? 3. What is the value of, of a yard ? 4. What is the value of is of a ton ? 5. How many pence in of a lb. ? 6. How many drams in of a lb. Avoirdupoise ? 7. How many grains in of a lb. Troy weight ?
8. How many scruples in of a lb. Apothecaries weight !
9. How many pints in of a bushel ?
REDUCTION OF UNITS OF ONE ORDER TO
FRACTIONS OF ANOTIIER ORDER.
It is necessary often to reverse the preceding process, and change units to fractions of another order. For ex. ample, to change 13s. 4d. to a fraction of the pound or. der.
To do this we change the 13s. 4d. to units of the lowest order mentioned, viz. 160 pence. This is to be the nume. rator 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 10% 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.