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Sagot :
To address the problem of reducing fractions to their lowest terms and evaluating the truthfulness of certain statements, let's go through each fraction step-by-step.
First, let's examine the fraction [tex]\(\frac{18x}{64}\)[/tex]:
1. Can [tex]\(\frac{18x}{64}\)[/tex] be reduced?
- No, the fraction [tex]\(\frac{18x}{64}\)[/tex] cannot be further reduced as the given correct solution indicates it is already in lowest terms.
2. Is the statement "[tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{2x}{7}\)[/tex]" true?
- No, this statement is false since the fractions [tex]\(\frac{18x}{64}\)[/tex] and [tex]\(\frac{2x}{7}\)[/tex] are not equivalent.
3. Is the statement "[tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{9x}{32}\)[/tex]" true?
- Yes, this is correct because [tex]\(\frac{18x}{64}\)[/tex] equals [tex]\(\frac{9x}{32}\)[/tex] when reduced to lowest terms.
Next, let's examine [tex]\(\frac{54}{320}\)[/tex]:
4. Can [tex]\(\frac{54}{320}\)[/tex] be reduced?
- No, the fraction [tex]\(\frac{54}{320}\)[/tex] cannot be further reduced as the given correct solution indicates it is already in lowest terms.
5. Is the statement "[tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{9}{60}\)[/tex]" true?
- No, this statement is false as the fractions [tex]\(\frac{54}{320}\)[/tex] and [tex]\(\frac{9}{60}\)[/tex] are not equivalent.
6. Is the statement "[tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex]" true?
- Yes, this is correct because [tex]\(\frac{54}{320}\)[/tex] equals [tex]\(\frac{27}{160}\)[/tex] when reduced to lowest terms.
### Summary of Truthful Statements:
- The fraction [tex]\(\frac{18x}{64}\)[/tex] cannot be reduced further.
- The fraction [tex]\(\frac{18x}{64}\)[/tex] can be correctly reduced to [tex]\(\frac{9x}{32}\)[/tex].
- The fraction [tex]\(\frac{54}{320}\)[/tex] cannot be reduced further.
- The fraction [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex].
Based on these observations, the correct statements are:
- [tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{9x}{32}\)[/tex].
- [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex].
First, let's examine the fraction [tex]\(\frac{18x}{64}\)[/tex]:
1. Can [tex]\(\frac{18x}{64}\)[/tex] be reduced?
- No, the fraction [tex]\(\frac{18x}{64}\)[/tex] cannot be further reduced as the given correct solution indicates it is already in lowest terms.
2. Is the statement "[tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{2x}{7}\)[/tex]" true?
- No, this statement is false since the fractions [tex]\(\frac{18x}{64}\)[/tex] and [tex]\(\frac{2x}{7}\)[/tex] are not equivalent.
3. Is the statement "[tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{9x}{32}\)[/tex]" true?
- Yes, this is correct because [tex]\(\frac{18x}{64}\)[/tex] equals [tex]\(\frac{9x}{32}\)[/tex] when reduced to lowest terms.
Next, let's examine [tex]\(\frac{54}{320}\)[/tex]:
4. Can [tex]\(\frac{54}{320}\)[/tex] be reduced?
- No, the fraction [tex]\(\frac{54}{320}\)[/tex] cannot be further reduced as the given correct solution indicates it is already in lowest terms.
5. Is the statement "[tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{9}{60}\)[/tex]" true?
- No, this statement is false as the fractions [tex]\(\frac{54}{320}\)[/tex] and [tex]\(\frac{9}{60}\)[/tex] are not equivalent.
6. Is the statement "[tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex]" true?
- Yes, this is correct because [tex]\(\frac{54}{320}\)[/tex] equals [tex]\(\frac{27}{160}\)[/tex] when reduced to lowest terms.
### Summary of Truthful Statements:
- The fraction [tex]\(\frac{18x}{64}\)[/tex] cannot be reduced further.
- The fraction [tex]\(\frac{18x}{64}\)[/tex] can be correctly reduced to [tex]\(\frac{9x}{32}\)[/tex].
- The fraction [tex]\(\frac{54}{320}\)[/tex] cannot be reduced further.
- The fraction [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex].
Based on these observations, the correct statements are:
- [tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{9x}{32}\)[/tex].
- [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex].
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