Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
Let's evaluate each statement step by step.
### Statement (i)
[tex]\[ \frac{-3}{8} \geq 0 \][/tex]
First, consider the fraction [tex]\(\frac{-3}{8}\)[/tex]:
- The numerator is -3, which is negative.
- The denominator is 8, which is positive.
- A negative number divided by a positive number is negative.
Since [tex]\(\frac{-3}{8}\)[/tex] is negative, it is not greater than or equal to 0. Therefore, the statement [tex]\(\frac{-3}{8} \geq 0\)[/tex] is False.
To correct the statement:
[tex]\[ \frac{-3}{8} < 0 \][/tex]
### Statement (ii)
[tex]\[ \text{If } \frac{1}{2} > \frac{1}{3} \text{ then } \frac{1}{2} - \frac{1}{3} \text{ is positive.} \][/tex]
First, verify that [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex]:
- To compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex], convert them to a common denominator.
- The least common denominator of 2 and 3 is 6.
Convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
[tex]\[ \frac{1}{3} = \frac{2}{6} \][/tex]
Clearly, [tex]\(\frac{3}{6} > \frac{2}{6}\)[/tex], so [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex] is true.
Next, verify the condition:
[tex]\[ \frac{1}{2} - \frac{1}{3} \][/tex]
To subtract these fractions, again convert to a common denominator:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
[tex]\[ \frac{1}{3} = \frac{2}{6} \][/tex]
Now subtract:
[tex]\[ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} \][/tex]
Since [tex]\(\frac{1}{6}\)[/tex] is positive, the statement [tex]\(\frac{1}{2} - \frac{1}{3}\)[/tex] is positive is true.
Therefore, the statement in (ii) holds:
[tex]\[ \frac{1}{2} > \frac{1}{3} \text{ implies } \frac{1}{2} - \frac{1}{3} \text{ is positive.} \][/tex]
Thus, this statement is True.
### Summary:
- Statement (i): False. Corrected statement: [tex]\(\frac{-3}{8} < 0\)[/tex]
- Statement (ii): True
The results of the evaluation are:
[tex]\[ \text{(i) False} \][/tex]
[tex]\[ \text{(ii) True} \][/tex]
### Statement (i)
[tex]\[ \frac{-3}{8} \geq 0 \][/tex]
First, consider the fraction [tex]\(\frac{-3}{8}\)[/tex]:
- The numerator is -3, which is negative.
- The denominator is 8, which is positive.
- A negative number divided by a positive number is negative.
Since [tex]\(\frac{-3}{8}\)[/tex] is negative, it is not greater than or equal to 0. Therefore, the statement [tex]\(\frac{-3}{8} \geq 0\)[/tex] is False.
To correct the statement:
[tex]\[ \frac{-3}{8} < 0 \][/tex]
### Statement (ii)
[tex]\[ \text{If } \frac{1}{2} > \frac{1}{3} \text{ then } \frac{1}{2} - \frac{1}{3} \text{ is positive.} \][/tex]
First, verify that [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex]:
- To compare [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex], convert them to a common denominator.
- The least common denominator of 2 and 3 is 6.
Convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
[tex]\[ \frac{1}{3} = \frac{2}{6} \][/tex]
Clearly, [tex]\(\frac{3}{6} > \frac{2}{6}\)[/tex], so [tex]\(\frac{1}{2} > \frac{1}{3}\)[/tex] is true.
Next, verify the condition:
[tex]\[ \frac{1}{2} - \frac{1}{3} \][/tex]
To subtract these fractions, again convert to a common denominator:
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
[tex]\[ \frac{1}{3} = \frac{2}{6} \][/tex]
Now subtract:
[tex]\[ \frac{3}{6} - \frac{2}{6} = \frac{1}{6} \][/tex]
Since [tex]\(\frac{1}{6}\)[/tex] is positive, the statement [tex]\(\frac{1}{2} - \frac{1}{3}\)[/tex] is positive is true.
Therefore, the statement in (ii) holds:
[tex]\[ \frac{1}{2} > \frac{1}{3} \text{ implies } \frac{1}{2} - \frac{1}{3} \text{ is positive.} \][/tex]
Thus, this statement is True.
### Summary:
- Statement (i): False. Corrected statement: [tex]\(\frac{-3}{8} < 0\)[/tex]
- Statement (ii): True
The results of the evaluation are:
[tex]\[ \text{(i) False} \][/tex]
[tex]\[ \text{(ii) True} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.