Answer :
Sure! Let's go through the solution step by step for each part of the question:
### Factoring Rules:
1. The number that is a factor of any number that ends with 0 or 5:
The answer is 5. Any number that ends in 0 or 5 can be divided evenly by 5.
2. The number that is a factor of any even number:
The answer is 2. All even numbers can be divided evenly by 2.
3. The number that is a factor if both 2 and 3 are also factors:
The answer is 6. If a number has 2 and 3 as factors, it can also be divided evenly by 6 (since 6 = 2 × 3).
4. The number that is a factor of any number whose digits add up to 9 or a multiple of 9:
The answer is 9.
5. The number that is a factor of any number whose digits add up to 3 or a multiple of 3:
The answer is 3.
### Listing Factors:
6. Factors of 20:
The factors of 20 are: 1, 2, 4, 5, 10, and 20.
7. Factors of 36:
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
### Reducing Fractions:
8. Reducing [tex]\(\frac{15}{20}\)[/tex]:
The reduced form is [tex]\(\frac{3}{4}\)[/tex].
9. Reducing [tex]\(\frac{16}{18}\)[/tex]:
The reduced form is [tex]\(\frac{8}{9}\)[/tex].
10. Reducing [tex]\(\frac{4}{8}\)[/tex]:
The reduced form is [tex]\(\frac{1}{2}\)[/tex].
11. Reducing [tex]\(\frac{32}{40}\)[/tex]:
The reduced form is [tex]\(\frac{4}{5}\)[/tex].
### Finding Missing Numerator or Denominator:
13. Find the missing numerator in [tex]\( \frac{5}{x} = \frac{9}{15}\)[/tex]:
The missing numerator is 8.333 (approximately).
14. Find the missing denominator in [tex]\( \frac{x}{12} = \frac{2}{3}\)[/tex]:
The missing denominator is 18.
15. Find the missing numerator in [tex]\( \frac{1}{2} = \frac{x}{20}\)[/tex]:
The missing numerator is 10.
16. Find the missing numerator in [tex]\( \frac{x}{6} = \frac{20}{24}\)[/tex]:
The missing numerator is 5.
17. Find the missing numerator in [tex]\( \frac{x}{4} = \frac{6}{8}\)[/tex]:
The missing numerator is 3.
18. Find the missing denominator in [tex]\( \frac{4}{x} = \frac{7}{35}\)[/tex]:
The missing denominator is 20.
### Ordering Fractions From Least to Greatest:
- [tex]\(\frac{3}{10}, \frac{3}{8}, \frac{3}{7}, \frac{3}{5}, \frac{3}{4}\)[/tex]
### Converting Improper Fractions to Whole or Mixed Numbers:
19. [tex]\(\frac{5}{2}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(1\)[/tex], which is [tex]\(2 \frac{1}{2}\)[/tex].
24. [tex]\(\frac{18}{6}\)[/tex]:
- Converts completely to [tex]\(3\)[/tex].
25. [tex]\(\frac{21}{3}\)[/tex]:
- Converts completely to [tex]\(7\)[/tex].
26. [tex]\(\frac{20}{8}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(4\)[/tex], which is [tex]\(2 \frac{4}{8}\)[/tex] or [tex]\(2 \frac{1}{2}\)[/tex].
27. [tex]\(\frac{10}{4}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(2\)[/tex], which is [tex]\(2 \frac{2}{4}\)[/tex] or [tex]\(2 \frac{1}{2}\)[/tex].
28. [tex]\(\frac{15}{12}\)[/tex]:
- The mixed number is [tex]\(1\)[/tex] with a remainder of [tex]\(3\)[/tex], which is [tex]\(1 \frac{3}{12}\)[/tex] or [tex]\(1 \frac{1}{4}\)[/tex].
These steps explain how we arrive at the final answers for the questions provided.
### Factoring Rules:
1. The number that is a factor of any number that ends with 0 or 5:
The answer is 5. Any number that ends in 0 or 5 can be divided evenly by 5.
2. The number that is a factor of any even number:
The answer is 2. All even numbers can be divided evenly by 2.
3. The number that is a factor if both 2 and 3 are also factors:
The answer is 6. If a number has 2 and 3 as factors, it can also be divided evenly by 6 (since 6 = 2 × 3).
4. The number that is a factor of any number whose digits add up to 9 or a multiple of 9:
The answer is 9.
5. The number that is a factor of any number whose digits add up to 3 or a multiple of 3:
The answer is 3.
### Listing Factors:
6. Factors of 20:
The factors of 20 are: 1, 2, 4, 5, 10, and 20.
7. Factors of 36:
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
### Reducing Fractions:
8. Reducing [tex]\(\frac{15}{20}\)[/tex]:
The reduced form is [tex]\(\frac{3}{4}\)[/tex].
9. Reducing [tex]\(\frac{16}{18}\)[/tex]:
The reduced form is [tex]\(\frac{8}{9}\)[/tex].
10. Reducing [tex]\(\frac{4}{8}\)[/tex]:
The reduced form is [tex]\(\frac{1}{2}\)[/tex].
11. Reducing [tex]\(\frac{32}{40}\)[/tex]:
The reduced form is [tex]\(\frac{4}{5}\)[/tex].
### Finding Missing Numerator or Denominator:
13. Find the missing numerator in [tex]\( \frac{5}{x} = \frac{9}{15}\)[/tex]:
The missing numerator is 8.333 (approximately).
14. Find the missing denominator in [tex]\( \frac{x}{12} = \frac{2}{3}\)[/tex]:
The missing denominator is 18.
15. Find the missing numerator in [tex]\( \frac{1}{2} = \frac{x}{20}\)[/tex]:
The missing numerator is 10.
16. Find the missing numerator in [tex]\( \frac{x}{6} = \frac{20}{24}\)[/tex]:
The missing numerator is 5.
17. Find the missing numerator in [tex]\( \frac{x}{4} = \frac{6}{8}\)[/tex]:
The missing numerator is 3.
18. Find the missing denominator in [tex]\( \frac{4}{x} = \frac{7}{35}\)[/tex]:
The missing denominator is 20.
### Ordering Fractions From Least to Greatest:
- [tex]\(\frac{3}{10}, \frac{3}{8}, \frac{3}{7}, \frac{3}{5}, \frac{3}{4}\)[/tex]
### Converting Improper Fractions to Whole or Mixed Numbers:
19. [tex]\(\frac{5}{2}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(1\)[/tex], which is [tex]\(2 \frac{1}{2}\)[/tex].
24. [tex]\(\frac{18}{6}\)[/tex]:
- Converts completely to [tex]\(3\)[/tex].
25. [tex]\(\frac{21}{3}\)[/tex]:
- Converts completely to [tex]\(7\)[/tex].
26. [tex]\(\frac{20}{8}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(4\)[/tex], which is [tex]\(2 \frac{4}{8}\)[/tex] or [tex]\(2 \frac{1}{2}\)[/tex].
27. [tex]\(\frac{10}{4}\)[/tex]:
- The mixed number is [tex]\(2\)[/tex] with a remainder of [tex]\(2\)[/tex], which is [tex]\(2 \frac{2}{4}\)[/tex] or [tex]\(2 \frac{1}{2}\)[/tex].
28. [tex]\(\frac{15}{12}\)[/tex]:
- The mixed number is [tex]\(1\)[/tex] with a remainder of [tex]\(3\)[/tex], which is [tex]\(1 \frac{3}{12}\)[/tex] or [tex]\(1 \frac{1}{4}\)[/tex].
These steps explain how we arrive at the final answers for the questions provided.