UNIT FRACTIONS
PROBLEMS
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| 11. Let | 1 4 |
be the unit, and count up to 3 | 1 4 |
| " | 1 4 |
, | 2 4 |
, | 3 4 |
, | 4 4 |
or 1; | 1 | 1 4 |
, 1 | 2 4 |
, 1 | 3 4 |
, 2; | 2 | 1 4 |
, 2 | 2 4 |
, 2 | 3 4 |
, 3; | 3 | 1 4 |
. | " |
| 12. Let | 1 6 |
be the unit, and count up to 2 | 1 6 |
| " | 1 6 |
, | 2 6 |
, | 3 6 |
, | 4 6 |
, | 5 6 |
, 1; | 1 | 1 6 |
, 1 | 2 6 |
, 1 | 3 6 |
, 1 | 4 6 |
, 1 | 5 6 |
, 2; | 2 | 1 6 |
" | . |
| 13. a) In the fraction | 7 8 |
, what number is the unit? | 1 8 |
13. b) How many of them are there? 7
14. Every fraction is a sum of unit fractions. Write the following as a
14. sum of unit fractions.
| 14. a) | 3 8 |
= | 1 8 |
+ | 1 8 |
+ | 1 8 |
| 14. b) | 4 5 |
= | 1 5 |
+ | 1 5 |
+ | 1 5 |
+ | 1 5 |
| 14. c) | 5 3 |
= | 1 3 |
+ | 1 3 |
+ | 1 3 |
+ | 1 3 |
+ | 1 3 |
15. Add.
| 15. a) | 2 7 |
+ | 3 7 |
= | 5 7 |
b) | 1 5 |
+ | 3 5 |
= | 4 5 |
c) | 5 8 |
+ | 6 8 |
= | 11 8 |
= 1 | 3 8 |
16. Write the missing numerator. 1 is equal to
| 16. a) | 3 3 |
b) | 4 4 |
c) | 5 5 |
d) | 10 10 |
e) | 16 16 |
f) | 100 100 |
17. Calculate mentally.
| 17. a) 3 | 5 8 |
+ | 2 8 |
= 3 | 7 8 |
b) 3 | 5 8 |
 |
2 8 |
= 3 | 3 8 |
c) 3 | 5 8 |
+ | 3 8 |
= 4 | |||
| 18. d) 1 | 3 5 |
+ | 2 5 |
= 2 | e) 7 | 1 4 |
+ | 3 4 |
= 8 | f) 9 | 5 6 |
+ | 1 6 |
= 10 | |||||
18. How many times is each of these contained in 1?
| a) | 1 2 |
2 | b) | 1 4 |
4 | c) | 1 8 |
8 | d) | 1 16 |
16 |
| 19. a) How many times is | 1 3 |
contained in 2? That is, 2 = | 6 3 |
| 18. b) How many times is | 1 4 |
contained in 5? 20 | |
| 19. c) How many times is | 1 6 |
contained in 8? 48 | |
| 19. d) How many times is | 1 8 |
contained in 10? 80 | |
| 19. e) How many times is | 1 16 |
contained in 20? 320 | |
10. The complement to 1. Calculate mentally.
| 10. a) 1 − | 2 3 |
= | 1 3 |
b) 1 − | 5 12 |
= | 7 12 |
c) 1 − | 1 10 |
= | 9 10 |
| 10. d) 1 − | 7 20 |
= | 13 20 |
e) 1 − | 49 100 |
= | 51 100 |
11. Calculate mentally.
| 11. a) 8 | 5 5 |
− | 1 5 |
= 8 | 4 5 |
b) 9 − | 1 5 |
= 8 | 4 5 |
. | Compare part a). |
| 11. c) 7 | 4 4 |
− | 3 4 |
= 7 | 1 4 |
d) 8 − | 3 4 |
= 7 | 1 4 |
. | Compare part c). |
12. Calculate mentally.
| 12. a) 6 − | 1 2 |
= 5 | 1 2 |
b) 8 − | 1 3 |
= 7 | 2 3 |
c) 7 − | 3 4 |
= 6 | 1 4 |
||
| 12. d) 3 − | 5 8 |
= 2 | 3 8 |
e) 4 − | 2 5 |
= 3 | 3 5 |
f) 2 − | 2 7 |
= 1 | 5 7 |
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