St CHAP. IV. SUBTRACTION OF FRACTIONS. UBTRACTION 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 fraction the difference of the given fractions. II. When they have not a common Denominator. Reduce them to a common denominator, and then work as last. [8] [9] [10] [11] [12] [13] Answ. 14 [14] 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. From 29 Take 0 Let it be required to take from 2; I take 1 the numerator of from the denominator 4, and 3 the remainder 1 put, for a numerator over the denominator, viz. 3, the fraction remaining; then I take 1 from the given whole number 2 and 1 remains; so is the remainder found 13, 2. E. I. Rem. 1 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 1; the sum take from the greater whole number. IV. A Fraction or a mixt Number from a mixt 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. V. A Fraction or a mixt Number from a mixt Number when the Fraction to be subtracted is the greater. Rule. 1. Reduce the given fractions to one common denomi nator. 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 to the lesser whole number, and subtract the sum from the greater. Application. Let it be required to take 23 from 5? The given fractions being brought to one common denominator will be and; I take the greater numerator 3 from the common denominator 4 and 1 remains, which added to 2 the lesser numerator, makes 3 for the numerator 54...2 2...3 Rem. 22 3 of the remaining fraction ; then I carry 1 to 2 the lesser whole number, makes 3 from 5 and 2 remains; whence the remainder sought is found 23. Quest. 1. What is the difference of, and 41 P Answ. &. 5. Bought a piece of cloth containing 47 yards, of which I cut 241 yards; I demand how much I have by me? Ansu. 22 yards. 6. A man had 4 bags of money, containing in all 5001. in the first was 1303; in the second 971; in the third 110: I want to know what was in the fourth? Answ. 161. CHAP. V. MULTIPLICATION OF FRACTIONS. Rule. Multiply the Numerators into each other for the Numerator; and the given Denominators for the Denomina tor of the Product. Application. 2-3 c 36 12 e f g 24 h 36 Application. Let the fractions M N be given to be multiplied, the numerators 2 and 3 being multiplied into each other make 6 d for the numerator of the product O, and 3 multiplied into 4 makes 12 for the denominator; so or is the product found by the Rule. 6 ΤΣ 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.. 4.1 by 5. by 3 Answ, 1 6.1 by 32. 7. 2 4 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. |