Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
