Answered

Get detailed and accurate answers to your questions on IDNLearn.com. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

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 :

GinnyAnsweridn
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].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.