REM,—When we consider that the numerator of a fraction represents a dividend, and the denominator a divisor, a complex fraction is readily reduced to a simple fraction. 1. to a simple fraction. = 15 3 = 371 4. Reduce 621 to a simple fraction. 371 one X 621 Its 1001 401 201 131 5. Multiply Х Х 1001 603 481^ 131 1 X= 141.. 6. Divide by Х *x*XXX$=. # X4 X =. In changing the division to multiplication, the whole divisor must be inverted ; that is, becomes the numerator and becomes the denominator, with the sign of multiplication; then again the two denominators must be inverted ; then they are all in the form of multiplication. PROBLEMS. 1. Reduce 1. Reduce to a simple fraction. x= simple fraction. REM.-It is evident that the above expression indicates that d to be divided by s. X X X= 38. REM.-By inverting the whole divisor, problem 3d is changed from division to multiplication. EXAMPLES. 31 1. Reduce to a simple fraction. 3 2. Reduce 2 3 x = = 75. 621 3. Reduce 87} 4 x sto = 4 simple-fraction. 1. A man spends of his income for board, 1 for clothing, and has 50 dollars left, what is his income? Ans. 600 dollars. 2. What number divided by 5 will give for a quotient ? Ans. 4. Ans. 3. What number multiplied by } will give a product of 4 ? 4. In an orchard 1 of the trees bear apples, 1 peaches, + plums, and 20 trees bear pears. How many trees in the orchard ? Ans. 80 trees. 5. What are the numbers between 15 and 450 which have the former for their greatest common divisor, and the latter for their least common multiple ? Ans. 30, 45, 75, 90, 150, 225. 6. What six numbers between 35 and 840 have the former for their greatest common divisor, and the latter for their least common multiple? Ans. 70, 105, 140, 210, 280, 420. 7. A father bequeathed of his estate to one son, and the rest of his estate to another; the difference of their legacies were 1560 dollars. How much did each receive ? Ans. The one 7800 dollars, and the other 6240 dollars. 8. A cargo is worth five times the value of the ship. What part of the cargo is of the ship and cargo? Ans. 1. REM.—2 is what part of 3? Ans. j. 3 is what part of 4? 9. If A can do a piece of work in 4 days, and B can do it in 5 days, what part can each do in a day? What part of it can both do in a day? How many days will it take both to do it? Ans. A can do 4 in a day, B }, both , and both can do it in 2 days. 10. A and B bought a barrel of flour, for which A paid 5 dollars, and B paid 6 dollars. What part of the flour should each have? Ans. A and B 1. 11. Three men, A, B, and C, bought 640 acres of land. A paid 4000 dollars, B paid 5000 dollars, and C 7000 dollars. How many acres should each receive? Ans. A 160 acres, B 200 acres, and.C 280 acres. 12. A man left } of his property to his wife, } to each of his two daughters, 1 to his son, and the remainder, which was 500 dollars, to his servant. What was the value of his whole estate ? Ans. 6000 dollars. 13. If 3650 is Dg of some number, what is of the same number? Ans. 5256. 14. A sold of a ship for 3650 dollars, and B owns Po of the ship. What is it worth at the same rate ? Ans. 5256. DECIMAL FRACTIONS. Fractions whose denominators are 10, 100, 1000, etc., are rendered decimals of the same name by a little change in form; thus, a decimal point is placed on the left of the decimals, or on the right of the units, and the same relation exists between the successive orders, as in abstract numbers, but the orders themselves are reversed. It = .1, ito = .01, Totoo = .001, and are read alike; thus, one tenth, one thousandth, Also, * = .3, read three tenths; To = .07, seven hundredths; .36, thirty-six hundredths; M = .456, four hundred and fifty-six thousandths. Hence, to enumerate a decimal fraction, read it as you would an integral number, adding to this the name of the denominator, when a common fraction, which will be expressed by 1 with as many zeros attached to it as there are numbers of decimal figures. |