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? 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, 13 rd. on a side. Find the distance in rods around it. Fractional equivalents of sixths, twelfths, and eighteenths, and their sum and difference. 1. Into how many thirds can the oblong be divided? into how many twelfths? into how many eighteenths? 2. 3. of a day how many 9ths of a day? how many 18ths of a day? = 4. hour of an hour; of an hour. = = 18 } = 1 9. Draw oblongs and show that ; ; 8 = 1; = = = 10. 18 how many units? 28= how many units and remaining? 11. Change to units and parts of units:,, 12, 12, 18, 8, 18, 18, 28. Fractional equivalents of sixths, twelfths, and twentyfourths, and their sum and difference. 1. What part of the oblong = % of it? of it? 1 of it? 2. of the oblong of the oblong; equals of it. = 12 = ; equals how many units? 4. 8 + 8 + 8 + 8 = 8+8+8+8 of the oblông; equals 24 of it. 5. Any unit can be divided into how many halves? 3ds? 4ths? 5ths? 6ths? 7ths? 8ths? 16ths? 24ths, etc.? 6. Add and; and 4. From take. 12 7. From subtract ; ; 5; 12. 24 8. § means that a unit (§) and a part of a unit (g) have been added. What does mean? ? REDUCTION OF FRACTIONS = 1. Notice in the diagram on p. 30 that 4. By what number are both numerator and denominator of multiplied to change it to? Is there any difference in value between and? Notice that the terms in are larger or higher than in The change of to the equal fraction is called changing or reducing to higher terms. 24 2. By what number must both terms of be divided to change to? Is there any difference in value between and ? Which fraction has the lower terms? The change of 4to is called reducing to lower terms. = = 3. Notice in the diagram that 4-2. When is changed to it is reduced to lower terms but not to its lowest terms, since can be changed to still lower terms, Can be reduced to still lower terms? The change of 4 to is called reducing to its lowest terms. 4. By what number must both terms of 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: ; ; q; t ; ; ; ; 16. 6. Reduce to lowest terms: ; ; ; ; ; 10. Fractions like, f, and 4, 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 4; } and }; } and 12; §, and §. |