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TAE Marine. REVIEW Change 5-6 to twelfths. Answer 10-12. To eighteenths. Answer 15-18. ; 8-12 are how many thirds? Answer 2-3. Divide both terms of 15-20 by 5 and show that the value of the fraction 1s not changed. The answer is %, which is equivalent to 15-20, since the fractional unit is 5 times as great. Change 18-36 to an equivalent fraction having a denomi- nator I half as great; 1 third as great. Answer 9-18; 6-12. Change 9-27 to a fraction having lower terms; 14-21; 25-30. Answer I-3; 2-3; 5-6. What is the lowest terms in which 12-24 can be expressed? ~ Answer 4. Change 9-36 to its lowest terms; 16-20; 32-40; 14-35}; 20-25. Answer 4; 4-5; 4-5; 2-53 4¢5. Name two common divisors of 18-36; 24-56. Answer 9 and 6;.8 and 4. Reduction of fractions is the process of changing their form without altering their value. A common factor of two or more numbers is a number that will divide each of them without remainder, The largest number that is a factor of two or more numbers is called the greatest common divisor. A fraction is reduced to higher terms when the numerator and denominator are expressed in larger numbers; thus, 34 = 6-8, or 9-12. A fraction is reduced to lower terms when the numerator and denominator are expressed in smaller numbers; or, a fraction is reduced to its lowest terms by dividing the nu- merator and denominator by their greatest common divisor. Thus, 8-12 = 4-6, or 2-3. A fraction is reduced to its lowest terms when its nu- merator and denominator are prime to each other; thus, 4-10 == 2-5: 12-16 ----. 14. Fractions are changed to higher terms by multiplication, and to lower terms by division. Multiplying or dividing toth terms of a fraction by the same number does not change the value of the fraction. Rule--To reduce a fraction to higher terms of a given denomination, divide the required denominator by the de- nominator of the given fraction, and multiply the terms of the given fraction by the quotient. Change 5-6 to a fraction whose denominator is 30. First divide 30, the required denominator, by 6, the denominator of the given fraction. The quotient 5 is the factor employed to produce the required denominator. Hence, multiply both terms of 5-6 by 5 and 25-30 is the required fraction. To reduce a fraction to its lowest terms. Divide the terms of the given fraction by their greatest common divisor. Reduce 12-16 to its lowest terms. The greatest common divisor of 12 and 16 is 4, which is contained in 12, 3 times and into 16, 4 times, or 34, their being no difference whatever in 12-16 and 34. Bear this in mind. Reduce to their lowest terms. . 288-360, 258-282, 288-so4. The answer to the first is 4-5} the second is 43-47, and the third 4-7. To reduce a whole number to an improper fraction. Rule--Multiply the whole number by the required de- nominator and under the result write the required denomi- nator. In 3. miles how many fourths of a mile? Since in I mile there are 4 fourths, in 3 miles there are 3 times 4 fourths ; Hence 3 = 12-4. Don't forget that 3 whole ones and 12-4 are the same. In 4 bushels how many eighths of a bushel? Answer 32-8. There is no difference between either of these. How many goths in 5? Answer 45-9. How many tenths of a dollar in $7. Answer 70-10. 70-10 are the same as 7 whole ones. .7 whole ones. 32. How many half dollars will pay for a ton of coal that cost $7? Answer 14. Bear in mind that 14 are the same ase = In the above cases we have no numerators to add, the whole numbers being multiplied by the required denominators. To reduce a mixed number to an improper fraction. Rule--Multiply the whole numbers by the denominator and add in the numerator of the fraction, and under the result write the denominator. ane In 536 how many eighths? Since 1 is equal to 8 eighths, 5 equals 5 times 8 eighths, or 40 eighths, and 34 added make 43-8. Hence, 534 = 43-8. ie In 634 cords of wood, how many fourths of 'a -cord? Answer 27-4. How many sixths in 8 5-6? Answer 53-6. Among how many boys can you distribute 534 'quarts of chestnuts, if you give %4 of a quart to each? Answer 23 boys. Among how many poor sailors can 4 5-6 tons of coal be distributed, if each sailor receives 1-6 of a ton? Answer 20. Remember that there is no difference whatever between 45-6 and 29-6. ae Examples for practice. Change 75 to the form of a frac- tion having 27 for its denominator. Answer 2025-27. : : Change 81 to a fraction having 24 for its denominator. Answer 1944-24. In 78 pounds how many sixteenths of a pound? Answer 1248-16. In 42 6-7 weeks, how many sevenths of a week? Answer ' 300-7. ae How many twentieths of a ton in 16 17-20 tons? Answer 337-40. Reduce 204 11-24 days to 24ths of a day? Answer 4907-24. To reduce an improper fraction to a whole or mixed number. Rule--Divide the numerator by the denominator. How many units are 18-4? Answer 4 2-4, and 2-4 reduced to its lowest terms is %4, or 4%. Since 4-4 equals 1, 18 fourths equals as many units as 4 fourths are contained in 18 fourths, which is 4 2-4 times. How many times 1 are 28-7? Answer 4 times. How many times I are 46-8? Answer 5 6-8 times. How many times I are 75-12? Answer 6 3-12. How many yards are 27-3 yds.? Answer 9 yds. How many dollars are $36-8? Answer $4 4-8, or $4%. In 90-12 feet how many feet? Answer 7 6-12, or 7%. In 108-9 of an acre, how many acres? Answer 12. In 180-20 of a ton, how many tons? Answer 9. How many rods in 525-40 of a rod? Answer 13%. To reduce fractions to equivalent fractions having a given. denominator. = Rule.--Divide the proposed denominator by the denomi-_ nator of the given fraction, and multiply both terms of the given fraction by the quotient. Thus, reduce 3-7 to four- teenths-- i4e 7 == 2. 3-7 X 2-2 = 6-14 Ans. How many 4ths in 1? Answer 4 fourths. How many 4ths in 4%? Answer 2 fourths. How many oths in 1? Answer 9-9. How many goths in 1-3? Answer 3-9. How many oths in 2-3? Answer 6-9. Express 2-3, 14, and 34, each as twelfths. Answer 2-3 = 8-12; % = 6-12, and % = 9-12. Change % and % to fractions of the same denominator. Answer 12-16 and 10-16. Do you thoroughly understand now that it takes two % to make a whole one, and 3-3, 4-4, 5-5; 6-6, 7-7, 8-8, 9-9, 10-10, 1-11, and so on, to make a whole one; that % of %, is % and ¥4 of % is 1-16, % of 1-16 is 1-32, ete? ee A. multiple of a number is a number exactly divisible by the given number. A number may have an unlimited num-