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SoN of Fractions is the taking of a lesser Fraction from a greater; likewise, a mixt Number or Fraction from a greater mixt number or a whole Number.

I. Fractions which have a common Denominator.

Subtract the numerator of the less from the numerator of the greater, and to their difference subscribe the common denominator; so is this new fraetion the difference of the given fractions.

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II. When they have not a common Denominator.

Reduce them to a common denominator, and then work as {f' last.

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1. II I. .4

III. A Fraction from a whole Number.

Subtract the numerator of the fraction from its denominator, and place the remainder over the denominator, for the fractional part of the difference sought; then subtract 1 from the given whole number, for the integral part of the remainder ; so is a fraction or mixt number found which shall be the remainder or difference required.

Application and Reason.

Let it be required to take ; from 2; I take 1 the nume. rator of from the denominator 4, and 3

the remainder I put, for a numerator over From 23 the denominator, viz. 3, the fraction re- Take of maining; then I take 1 from the given

whole number 2 and 1 remains; so is the Rem. # remainder found 13, 2. E. I.

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In like manner to subtract a mixt number from a whole number, subtract the fractional part as above, and to the lesser whole number add l ; the sum take from the greater whole number.

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IV. A Fraction or a mixt Number from a mirt Number when the Fraction to be subtracted is the less.

Subtract the less fraction from the greater fraction, and the less whole number from the greater,

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V. A Fraction or a mirt Number from a not Number when the Fruction to be subtracted is the greater.

Rule.

1. Reduce the given fractions to one common denomiloatOr.

2. Then subtract the numerator of the greater fraction from the common denominator, and to the remainder add the numerator of the lesser, the sum is the numerator to the common denominator, for the fractional part of the remainder.

3. Carry 1 to the lesser whole number, and subtract the sum from the greater.

Application.

Let it be required to take 23 from 54
The given fractions being brought

to one common denominator will be # 5#...2 and #; I take the greater numerator 3 2#... 3 from the common denominator 4 and 1

remains, which added to 2 the lesser Rem. 23 3

numerator, makes 3 for the numerator of the remaining fraction #; then I carry I to 2 the lesser whole' number, makes 3 from 5 and 2 remains; whence the remainder sought is found 23. - 2 Examples,

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Eramples. [36] [37] [38] [39] [40] From 2: 9} 191°r 13; 123 Take of 6; 0.7; 94; 9: QUESTIONS, wuest. 1, What is the difference of , and ; ; ; Answ. },

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3. What is the difference between 10; and 12; Answ. 1 #.

4. What differs 33 from 48 Answ 47%.

5. Bought a piece of cloth containing 473 yards, of which I cut 243 yards; I demand how much I have by me? Answ. 22; 3 yards.

6. A man had 4 bags of money, containing in all 500l. in the first was 1303; in the second 974; ; in the third 1 1017; : I want to know what was in the fourth Answ. 1614l.

CHAP. W.

MULTIPLICATION OF FRACTIONS.

- Rule.

Multiply the Numerators into each other for the Nu

merator; and the given Denominators for the Denominator of the Product.

Application, Application.

M N Let the fractions M N be given to be a 2–3 c multiplied, the numerators 2 and 3 be- ing multiplied into each other make 6 b 3–4 d for the numerator of the product O,

6 e and 3 multiplied into 4 makes 12 for the - - denominator; so #: or # is the proule.

12 f duct found by the
O

g 24 h 36 -

If whole numbers or mixt numbers be given to be multiplied, reduce them to improper fractions, and multiply them by the Rule, and, if the product be an improper frac-tion, it may be brought back to a mixt or whole number.

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Note. Where several fractions are to be multiplied, if the numerator of one fraction be equal to the denominator of another, these equal numerators and denominators may be omitted.

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