At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Alright, let's tackle this exercise step-by-step.
### Part (a) Count in thirds from [tex]\(\frac{1}{3}\)[/tex] to [tex]\(3 \frac{2}{3}\)[/tex]:
We start at [tex]\(\frac{1}{3}\)[/tex] and add [tex]\(\frac{1}{3}\)[/tex] incrementally until we reach [tex]\(3 \frac{2}{3}\)[/tex].
1. [tex]\(\frac{1}{3}\)[/tex]
2. [tex]\(\frac{1}{3} + \frac{1}{3} = \frac{2}{3}\)[/tex]
3. [tex]\(\frac{2}{3} + \frac{1}{3} = 1\)[/tex]
4. [tex]\(1 + \frac{1}{3} = 1 \frac{1}{3}\)[/tex]
5. [tex]\(1 \frac{1}{3} + \frac{1}{3} = 1 \frac{2}{3}\)[/tex]
6. [tex]\(1 \frac{2}{3} + \frac{1}{3} = 2\)[/tex]
7. [tex]\(2 + \frac{1}{3} = 2 \frac{1}{3}\)[/tex]
8. [tex]\(2 \frac{1}{3} + \frac{1}{3} = 2 \frac{2}{3}\)[/tex]
9. [tex]\(2 \frac{2}{3} + \frac{1}{3} = 3\)[/tex]
10. [tex]\(3 + \frac{1}{3} = 3 \frac{1}{3}\)[/tex]
11. [tex]\(3 \frac{1}{3} + \frac{1}{3} = 3 \frac{2}{3}\)[/tex]
So the sequence in decimals is:
[tex]\[ [0.3333333333333333, 0.6666666666666666, 1.0, 1.3333333333333333, 1.6666666666666665, 1.9999999999999998, 2.333333333333333, 2.6666666666666665, 3.0, 3.3333333333333335 ] \][/tex]
### Part (b) Count in quarters from [tex]\(\frac{1}{4}\)[/tex] to [tex]\(4 \frac{3}{4}\)[/tex]:
We start at [tex]\(\frac{1}{4}\)[/tex] and add [tex]\(\frac{1}{4}\)[/tex] incrementally until we reach [tex]\(4 \frac{3}{4}\)[/tex].
1. [tex]\(\frac{1}{4}\)[/tex]
2. [tex]\(\frac{1}{4} + \(\frac{1}{4}\)[/tex] = [tex]\(\frac{1}{2}\)[/tex]\)
3. [tex]\(\(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = [tex]\(\frac{3}{4}\)[/tex]\)
4. [tex]\(\(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1\)
5. [tex]\(1 + \(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{1}{4}\)[/tex]\)
6. [tex]\(1 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{1}{2}\)[/tex]\)
7. [tex]\(1 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{3}{4}\)[/tex]\)
8. [tex]\(1 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2\)
9. [tex]\(2 + \(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{1}{4}\)[/tex]\)
10. [tex]\(2 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{1}{2}\)[/tex]\)
11. [tex]\(2 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{3}{4}\)[/tex]\)
12. [tex]\(2 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3\)
13. [tex]\(3 + \(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{1}{4}\)[/tex]\)
14. [tex]\(3 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{1}{2}\)[/tex]\)
15. [tex]\(3 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{3}{4}\)[/tex]\)
16. [tex]\(3 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4\)
17. [tex]\(4 + \(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{1}{4}\)[/tex]\)
18. [tex]\(4 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{1}{2}\)[/tex]\)
19. [tex]\(4 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{3}{4}\)[/tex]\)
So the sequence in decimals is:
[tex]\[ [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75] \][/tex]
### Part (c) Count in fifths from [tex]\(\frac{2}{5}\)[/tex] to [tex]\(3 \frac{3}{5}\)[/tex]:
We start at [tex]\(\frac{2}{5}\)[/tex] and add [tex]\(\frac{1}{5}\)[/tex] incrementally until we reach [tex]\(3 \frac{3}{5}\)[/tex].
1. [tex]\(\frac{2}{5}\)[/tex]
2. [tex]\(\frac{2}{5} + \(\frac{1}{5}\)[/tex] = [tex]\(\frac{3}{5}\)[/tex]\)
3. [tex]\(\(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = [tex]\(\frac{4}{5}\)[/tex]\)
4. [tex]\(\(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1\)
5. [tex]\(1 + \(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{1}{5}\)[/tex]\)
6. [tex]\(1 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{2}{5}\)[/tex]\)
7. [tex]\(1 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{3}{5}\)[/tex]\)
8. [tex]\(1 \(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{4}{5}\)[/tex]\)
9. [tex]\(1 \(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2\)
10. [tex]\(2 + \(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{1}{5}\)[/tex]\)
11. [tex]\(2 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{2}{5}\)[/tex]\)
12. [tex]\(2 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{3}{5}\)[/tex]\)
13. [tex]\(2 \(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{4}{5}\)[/tex]\)
14. [tex]\(2 \(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3\)
15. [tex]\(3 + \(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{1}{5}\)[/tex]\)
16. [tex]\(3 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{2}{5}\)[/tex]\)
17. [tex]\(3 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{3}{5}\)[/tex]\)
So the sequence in decimals is:
[tex]\[ [0.4, 0.6000000000000001, 0.8, 1.0, 1.2, 1.4, 1.5999999999999999, 1.7999999999999998, 1.9999999999999998, 2.1999999999999997, 2.4, 2.6, 2.8000000000000003, 3.0000000000000004, 3.2000000000000006, 3.400000000000001] \][/tex]
### Part (a) Count in thirds from [tex]\(\frac{1}{3}\)[/tex] to [tex]\(3 \frac{2}{3}\)[/tex]:
We start at [tex]\(\frac{1}{3}\)[/tex] and add [tex]\(\frac{1}{3}\)[/tex] incrementally until we reach [tex]\(3 \frac{2}{3}\)[/tex].
1. [tex]\(\frac{1}{3}\)[/tex]
2. [tex]\(\frac{1}{3} + \frac{1}{3} = \frac{2}{3}\)[/tex]
3. [tex]\(\frac{2}{3} + \frac{1}{3} = 1\)[/tex]
4. [tex]\(1 + \frac{1}{3} = 1 \frac{1}{3}\)[/tex]
5. [tex]\(1 \frac{1}{3} + \frac{1}{3} = 1 \frac{2}{3}\)[/tex]
6. [tex]\(1 \frac{2}{3} + \frac{1}{3} = 2\)[/tex]
7. [tex]\(2 + \frac{1}{3} = 2 \frac{1}{3}\)[/tex]
8. [tex]\(2 \frac{1}{3} + \frac{1}{3} = 2 \frac{2}{3}\)[/tex]
9. [tex]\(2 \frac{2}{3} + \frac{1}{3} = 3\)[/tex]
10. [tex]\(3 + \frac{1}{3} = 3 \frac{1}{3}\)[/tex]
11. [tex]\(3 \frac{1}{3} + \frac{1}{3} = 3 \frac{2}{3}\)[/tex]
So the sequence in decimals is:
[tex]\[ [0.3333333333333333, 0.6666666666666666, 1.0, 1.3333333333333333, 1.6666666666666665, 1.9999999999999998, 2.333333333333333, 2.6666666666666665, 3.0, 3.3333333333333335 ] \][/tex]
### Part (b) Count in quarters from [tex]\(\frac{1}{4}\)[/tex] to [tex]\(4 \frac{3}{4}\)[/tex]:
We start at [tex]\(\frac{1}{4}\)[/tex] and add [tex]\(\frac{1}{4}\)[/tex] incrementally until we reach [tex]\(4 \frac{3}{4}\)[/tex].
1. [tex]\(\frac{1}{4}\)[/tex]
2. [tex]\(\frac{1}{4} + \(\frac{1}{4}\)[/tex] = [tex]\(\frac{1}{2}\)[/tex]\)
3. [tex]\(\(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = [tex]\(\frac{3}{4}\)[/tex]\)
4. [tex]\(\(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1\)
5. [tex]\(1 + \(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{1}{4}\)[/tex]\)
6. [tex]\(1 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{1}{2}\)[/tex]\)
7. [tex]\(1 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 1 [tex]\(\frac{3}{4}\)[/tex]\)
8. [tex]\(1 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2\)
9. [tex]\(2 + \(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{1}{4}\)[/tex]\)
10. [tex]\(2 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{1}{2}\)[/tex]\)
11. [tex]\(2 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 2 [tex]\(\frac{3}{4}\)[/tex]\)
12. [tex]\(2 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3\)
13. [tex]\(3 + \(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{1}{4}\)[/tex]\)
14. [tex]\(3 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{1}{2}\)[/tex]\)
15. [tex]\(3 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 3 [tex]\(\frac{3}{4}\)[/tex]\)
16. [tex]\(3 \(\frac{3}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4\)
17. [tex]\(4 + \(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{1}{4}\)[/tex]\)
18. [tex]\(4 \(\frac{1}{4}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{1}{2}\)[/tex]\)
19. [tex]\(4 \(\frac{1}{2}\)[/tex] + [tex]\(\frac{1}{4}\)[/tex] = 4 [tex]\(\frac{3}{4}\)[/tex]\)
So the sequence in decimals is:
[tex]\[ [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75] \][/tex]
### Part (c) Count in fifths from [tex]\(\frac{2}{5}\)[/tex] to [tex]\(3 \frac{3}{5}\)[/tex]:
We start at [tex]\(\frac{2}{5}\)[/tex] and add [tex]\(\frac{1}{5}\)[/tex] incrementally until we reach [tex]\(3 \frac{3}{5}\)[/tex].
1. [tex]\(\frac{2}{5}\)[/tex]
2. [tex]\(\frac{2}{5} + \(\frac{1}{5}\)[/tex] = [tex]\(\frac{3}{5}\)[/tex]\)
3. [tex]\(\(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = [tex]\(\frac{4}{5}\)[/tex]\)
4. [tex]\(\(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1\)
5. [tex]\(1 + \(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{1}{5}\)[/tex]\)
6. [tex]\(1 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{2}{5}\)[/tex]\)
7. [tex]\(1 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{3}{5}\)[/tex]\)
8. [tex]\(1 \(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 1 [tex]\(\frac{4}{5}\)[/tex]\)
9. [tex]\(1 \(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2\)
10. [tex]\(2 + \(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{1}{5}\)[/tex]\)
11. [tex]\(2 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{2}{5}\)[/tex]\)
12. [tex]\(2 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{3}{5}\)[/tex]\)
13. [tex]\(2 \(\frac{3}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 2 [tex]\(\frac{4}{5}\)[/tex]\)
14. [tex]\(2 \(\frac{4}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3\)
15. [tex]\(3 + \(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{1}{5}\)[/tex]\)
16. [tex]\(3 \(\frac{1}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{2}{5}\)[/tex]\)
17. [tex]\(3 \(\frac{2}{5}\)[/tex] + [tex]\(\frac{1}{5}\)[/tex] = 3 [tex]\(\frac{3}{5}\)[/tex]\)
So the sequence in decimals is:
[tex]\[ [0.4, 0.6000000000000001, 0.8, 1.0, 1.2, 1.4, 1.5999999999999999, 1.7999999999999998, 1.9999999999999998, 2.1999999999999997, 2.4, 2.6, 2.8000000000000003, 3.0000000000000004, 3.2000000000000006, 3.400000000000001] \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.