Fractional equivalents of halves, fourths, and sixteenths, and their sum and difference. 1. How do these three units compare in size? 2. Into how many parts is the first square divided ?. the second square? the third square ? 3. 1 of the first square fourths of the second square sixteenths of the third square. 4. j =-units ; 4 =-units; f = -units; 18 -units; 16=- units. 5. } = = =1 6. 1 =j=1&; } = 1a. 7. f =j=1&; f = ☆ = 1a. 8. g = 16 = ; f = 16 = ; f = 1a = 4. 9. } +} + { = ģ ; 1 + $ + 16 = id; 17-1=1&: Add : . 10. 3] ft. 11. 161 ft. 12. 121 13. 103 204 ft. 52 17} ft. 10% 83 14] 52 ft. 21 ft. 3] ft. 102. ft. 121 Subtract: 14. $ 127 81 15. 234 yd. 1816 yd. 16. 131 mi. 17. 681 9-3. mi. 52-16 16 18. A flower bed is 4 ft. 6 in. long and 3 ft. 4 in. wide. Find the distance around it. 19. The school ground is in the form of a square, 131 rd. on a side. Find the distance in rods around it. Fractional equivalents of sixths, twelfths, and eighteenths, and their sum and difference. 1 unit = {= 12 = 15 1. Into how many thirds can the oblong be divided ? into how many twelfths ? into how many eighteenths? 2. f = 1a = id; = 12= 18. 3. of a day = how many 9ths of a day? how many 18ths of a day? 4. 1 hour = iz of an hour; is of an hour. 9. Draw oblongs and show that ž= ; f = 1; 1: = }; 13 = 3; 1'2 = . 10. 18 = how many units? 48 = how many units and remaining ? 11. Change to units and parts of units: 3, 2, 1, 1.2, 18, 5, 18, 18, 18 2 18 Fractional equivalents of sixths, twelfths, and twentyfourths, and their sum and difference. 1. What part of the oblong = 8 of it? is of it? It of it? 2. á of the oblong = 1 of the oblong; equals 14 of it. 3. of the oblong = { of the oblòng ; equals 1 of it. 4. & +&+*+&=; equals how many units ? 5. Any unit can be divided into how many halves ? 3ds ? 4ths ? 5ths? 6ths? 7ths? 8ths? 16ths? 24ths, etc.? 6. Add 1 and 12 ; ia and 24. From A take ik. 7. From subtract & ; 1 ; ; . 8. & means that a unit () and a part of a unit (!) have been added. What does mean? g? Add: 9. 18j in. 10. 15. bu. 11. 191 12. 4033 2011 in. 2724 bu. 3262 3011 39 411. bu. 20% 39,4 in. 181 REDUCTION OF FRACTIONS and 1. Notice in the diagrain on p. 30 that * = 4 By what number are both numerator and denominator of à multiplied to change it to ? Is there any difference in value between 4 ? Notice that the terms in iare larger or higher than in. The change of į to the equal fraction 4 is called changing or reducing į to higher terms. 2. By what number must both terms of be divided to change a to ž? Is there any difference in value between 24 and 1 ? Which fraction has the lower terms ? ? The change of 4 to d is called reducing a to lower terms. 3. Notice in the diagram that 24 = = . When 24 is changed to try it is reduced to lower terms but not to its lowest terms, since 1 can be changed to still lower terms, & Can į be reduced to still lower terms? The change of 44 to is called reducing 24 to its lowest terms. 4. By what number must both terms of 1 be multiplied to change it to the equal fraction ? By what number must both terms of % be divided to change it to the equal fraction #? Is in its lowest terms ? Multiplying or dividing both terms of a fraction by the same number does not alter its value. 5. Reduce to higher terms : ; ; ; ; ; } ; ģ; to 6. Reduce to lowest terms : 4; ; 4; $; * Fractions like }, }, and , which have the same denominator, are said to have a common denominator. Similar fractions are fractions that have a common denominator. 7. Change to similar fractions, and f; } and ; ; ; and i; g. }, }, and |