Question
Tammy said the product of 5/7 and 1 1/4 is 1 3/4
How can you tell that this answer is wrong?
answers:The answer cannot be a mixed number.
This is the correct product.
1 1/4 times a number greater than
cannot result in a product greater than the number.
5/7 times a number greater than
cannot result in a product greater than the number.
How can you tell that this answer is wrong?
answers:The answer cannot be a mixed number.
This is the correct product.
1 1/4 times a number greater than
cannot result in a product greater than the number.
5/7 times a number greater than
cannot result in a product greater than the number.
Answers
GPT-4o mini
To determine if Tammy's answer is wrong, we should first calculate the actual product of \( \frac{5}{7} \) and \( 1 \frac{1}{4} \).
1. Convert \( 1 \frac{1}{4} \) to an improper fraction:
\[
1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}
\]
2. Now, multiply \( \frac{5}{7} \) by \( \frac{5}{4} \):
\[
\frac{5}{7} \times \frac{5}{4} = \frac{5 \times 5}{7 \times 4} = \frac{25}{28}
\]
3. We should convert \( \frac{25}{28} \) to a mixed number to compare with \( 1 \frac{3}{4} \):
- Since \( 25 \) is less than \( 28 \), \( \frac{25}{28} \) is less than 1. Thus, it cannot be written as a mixed number greater than or equal to \( 1 \).
Now we analyze Tammy's assertion:
- **Tammy claimed the product is \( 1 \frac{3}{4} \)**, which is equal to \( \frac{7}{4} \) as an improper fraction. Notice that \( \frac{7}{4} \) is greater than \( 1 \).
- Since \( \frac{25}{28} \) is less than \( 1 \), this shows that the product cannot be \( 1 \frac{3}{4} \) (since that would imply a value greater than \( 1 \)).
Now let’s review the options provided:
1. The answer cannot be a mixed number.
2. This is the correct product.
3. \( 1 \frac{4}{4} \) times a number greater than cannot result in a product greater than the number.
4. \( \frac{5}{7} \) times a number greater than cannot result in a product greater than the number.
### Correct Choice:
The best choice to demonstrate why Tammy's answer is wrong is:
**"5/7 times a number greater than cannot result in a product greater than the number."**
This is relevant to the scenario because multiplying a fraction (less than 1) by \( 1 \frac{1}{4} \) (which is greater than 1) cannot yield a product that is greater than \( 1 \).
1. Convert \( 1 \frac{1}{4} \) to an improper fraction:
\[
1 \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}
\]
2. Now, multiply \( \frac{5}{7} \) by \( \frac{5}{4} \):
\[
\frac{5}{7} \times \frac{5}{4} = \frac{5 \times 5}{7 \times 4} = \frac{25}{28}
\]
3. We should convert \( \frac{25}{28} \) to a mixed number to compare with \( 1 \frac{3}{4} \):
- Since \( 25 \) is less than \( 28 \), \( \frac{25}{28} \) is less than 1. Thus, it cannot be written as a mixed number greater than or equal to \( 1 \).
Now we analyze Tammy's assertion:
- **Tammy claimed the product is \( 1 \frac{3}{4} \)**, which is equal to \( \frac{7}{4} \) as an improper fraction. Notice that \( \frac{7}{4} \) is greater than \( 1 \).
- Since \( \frac{25}{28} \) is less than \( 1 \), this shows that the product cannot be \( 1 \frac{3}{4} \) (since that would imply a value greater than \( 1 \)).
Now let’s review the options provided:
1. The answer cannot be a mixed number.
2. This is the correct product.
3. \( 1 \frac{4}{4} \) times a number greater than cannot result in a product greater than the number.
4. \( \frac{5}{7} \) times a number greater than cannot result in a product greater than the number.
### Correct Choice:
The best choice to demonstrate why Tammy's answer is wrong is:
**"5/7 times a number greater than cannot result in a product greater than the number."**
This is relevant to the scenario because multiplying a fraction (less than 1) by \( 1 \frac{1}{4} \) (which is greater than 1) cannot yield a product that is greater than \( 1 \).