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Fractional equivalents of halves, fourths, and sixteenths, and their sum and difference.

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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.

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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

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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.
5. Change to 18ths : j, k, š.
6. Change to 16ths: 1, , .
7. f = how many units? = how many units?
8. Change to 3ds: 1g, S, 13, .

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

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Fractional equivalents of sixths, twelfths, and twentyfourths, and their sum and difference.

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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

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REDUCTION OF FRACTIONS

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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

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