Answer :
Sure, let's go through each part of the question step-by-step:
### Comparing Fractions
1. [tex]\( \frac{1}{8} \bigcirc \frac{5}{32} \)[/tex]:
- Convert [tex]\( \frac{1}{8} \)[/tex] to a denominator of 32: [tex]\( \frac{1}{8} = \frac{4}{32} \)[/tex].
- Compare [tex]\( \frac{4}{32} \)[/tex] and [tex]\( \frac{5}{32} \)[/tex]. These are not equal, so [tex]\( \neq \)[/tex].
2. [tex]\( \frac{3}{5} \bigcirc \frac{6}{10} \)[/tex]:
- Simplify [tex]\( \frac{6}{10} \)[/tex] to [tex]\( \frac{3}{5} \)[/tex].
- Both are equal, so [tex]\( = \)[/tex].
3. [tex]\( \frac{5}{7} \)[/tex] and [tex]\( \frac{15}{20} \)[/tex]:
- Simplify [tex]\( \frac{15}{20} \)[/tex] to [tex]\( \frac{3}{4} \)[/tex].
- [tex]\( \frac{5}{7} \)[/tex] is not equal to [tex]\( \frac{3}{4} \)[/tex], so [tex]\( \neq \)[/tex].
4. [tex]\( \frac{7}{28} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex]:
- Simplify [tex]\( \frac{7}{28} \)[/tex] to [tex]\( \frac{1}{4} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
5. [tex]\( \frac{3}{9} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex]:
- Simplify [tex]\( \frac{3}{9} \)[/tex] to [tex]\( \frac{1}{3} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
6. [tex]\( \frac{3}{10} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex]:
- These are not equal, as values differ, so [tex]\( \neq \)[/tex].
7. [tex]\( \frac{3}{12} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex]:
- Simplify [tex]\( \frac{3}{12} \)[/tex] to [tex]\( \frac{1}{4} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
8. [tex]\( \frac{8}{40} \)[/tex] and [tex]\( \frac{2}{5} \)[/tex]:
- Simplify [tex]\( \frac{8}{40} \)[/tex] to [tex]\( \frac{1}{5} \)[/tex].
- [tex]\( \frac{1}{5} \)[/tex] is not equal to [tex]\( \frac{2}{5} \)[/tex], so [tex]\( \neq \)[/tex].
### Simplifying Fractions
1. [tex]\( \frac{20}{50} \)[/tex]:
- Simplify to [tex]\( \frac{2}{5} \)[/tex].
2. [tex]\( \frac{42}{27} \)[/tex]:
- This fraction is already in simplest form, but it equals approximately 1.56 in decimal form.
3. [tex]\( \frac{14}{21} \)[/tex]:
- Simplify to [tex]\( \frac{2}{3} \)[/tex].
4. [tex]\( \frac{12}{16} \)[/tex]:
- Simplify to [tex]\( \frac{3}{4} \)[/tex].
5. [tex]\( \frac{16}{18} \)[/tex]:
- Simplify to [tex]\( \frac{8}{9} \)[/tex].
By following these steps, you can understand how each comparison and simplification was made. If you have any further questions or need more explanations, feel free to ask!
### Comparing Fractions
1. [tex]\( \frac{1}{8} \bigcirc \frac{5}{32} \)[/tex]:
- Convert [tex]\( \frac{1}{8} \)[/tex] to a denominator of 32: [tex]\( \frac{1}{8} = \frac{4}{32} \)[/tex].
- Compare [tex]\( \frac{4}{32} \)[/tex] and [tex]\( \frac{5}{32} \)[/tex]. These are not equal, so [tex]\( \neq \)[/tex].
2. [tex]\( \frac{3}{5} \bigcirc \frac{6}{10} \)[/tex]:
- Simplify [tex]\( \frac{6}{10} \)[/tex] to [tex]\( \frac{3}{5} \)[/tex].
- Both are equal, so [tex]\( = \)[/tex].
3. [tex]\( \frac{5}{7} \)[/tex] and [tex]\( \frac{15}{20} \)[/tex]:
- Simplify [tex]\( \frac{15}{20} \)[/tex] to [tex]\( \frac{3}{4} \)[/tex].
- [tex]\( \frac{5}{7} \)[/tex] is not equal to [tex]\( \frac{3}{4} \)[/tex], so [tex]\( \neq \)[/tex].
4. [tex]\( \frac{7}{28} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex]:
- Simplify [tex]\( \frac{7}{28} \)[/tex] to [tex]\( \frac{1}{4} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
5. [tex]\( \frac{3}{9} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex]:
- Simplify [tex]\( \frac{3}{9} \)[/tex] to [tex]\( \frac{1}{3} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
6. [tex]\( \frac{3}{10} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex]:
- These are not equal, as values differ, so [tex]\( \neq \)[/tex].
7. [tex]\( \frac{3}{12} \)[/tex] and [tex]\( \frac{1}{4} \)[/tex]:
- Simplify [tex]\( \frac{3}{12} \)[/tex] to [tex]\( \frac{1}{4} \)[/tex].
- They are equal, so [tex]\( = \)[/tex].
8. [tex]\( \frac{8}{40} \)[/tex] and [tex]\( \frac{2}{5} \)[/tex]:
- Simplify [tex]\( \frac{8}{40} \)[/tex] to [tex]\( \frac{1}{5} \)[/tex].
- [tex]\( \frac{1}{5} \)[/tex] is not equal to [tex]\( \frac{2}{5} \)[/tex], so [tex]\( \neq \)[/tex].
### Simplifying Fractions
1. [tex]\( \frac{20}{50} \)[/tex]:
- Simplify to [tex]\( \frac{2}{5} \)[/tex].
2. [tex]\( \frac{42}{27} \)[/tex]:
- This fraction is already in simplest form, but it equals approximately 1.56 in decimal form.
3. [tex]\( \frac{14}{21} \)[/tex]:
- Simplify to [tex]\( \frac{2}{3} \)[/tex].
4. [tex]\( \frac{12}{16} \)[/tex]:
- Simplify to [tex]\( \frac{3}{4} \)[/tex].
5. [tex]\( \frac{16}{18} \)[/tex]:
- Simplify to [tex]\( \frac{8}{9} \)[/tex].
By following these steps, you can understand how each comparison and simplification was made. If you have any further questions or need more explanations, feel free to ask!
