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Cross-multiplying these fractions results in large numbers. To simplify, first reduce the fractions to their lowest terms, if possible.

Can [tex]\(\frac{18x}{64}\)[/tex] be reduced? What about [tex]\(\frac{54}{320}\)[/tex]?

Select all true statements:

A. Only one fraction can be reduced.
B. [tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{2x}{7}\)[/tex].
C. [tex]\(\frac{18x}{64}\)[/tex] can be reduced to [tex]\(\frac{9x}{32}\)[/tex].
D. [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{9}{60}\)[/tex].
E. [tex]\(\frac{54}{320}\)[/tex] can be reduced to [tex]\(\frac{27}{160}\)[/tex].

Sagot :

GinnyAnswer
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].
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