Answer :
Let's find the error in the reasoning and show the correct calculation.
### Given Expression:
The expression we need to simplify and evaluate is:
[tex]\[
\frac{8}{12} \times 6
\][/tex]
### Incorrect Reasoning Breakdown:
1. Incorrect Step 1:
- [tex]\(\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6\)[/tex]
- This is incorrect because multiplying [tex]\(\frac{8}{12}\)[/tex] by 6 is not equivalent to swapping it to [tex]\(8 \times \frac{1}{12} \times 6\)[/tex].
2. Incorrect Step 2:
- The calculation goes to: [tex]\(8 \times \frac{1}{72}\)[/tex]
- The simplification from [tex]\(8 \times 1/12 \times 6\)[/tex] to [tex]\(8 \times 1/72\)[/tex] is invalid.
3. Further Steps:
- The steps resulting in [tex]\(\frac{1}{9}\)[/tex] are based on this incorrect calculation.
### Correct Calculation:
We need to correct the original expression:
1. Fraction Simplification:
- Start with simplifying the fraction [tex]\(\frac{8}{12}\)[/tex].
- [tex]\(\frac{8}{12}\)[/tex] reduces to [tex]\(\frac{2}{3}\)[/tex] (by dividing both the numerator and the denominator by 4).
2. Multiplication:
- Now multiply the simplified fraction by 6:
[tex]\[
\frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3}
\][/tex]
3. Final Simplification:
- Calculate [tex]\(\frac{12}{3}\)[/tex]:
[tex]\[
\frac{12}{3} = 4
\][/tex]
Therefore, the correct result of [tex]\(\frac{8}{12} \times 6\)[/tex] is 4.0.
### Given Expression:
The expression we need to simplify and evaluate is:
[tex]\[
\frac{8}{12} \times 6
\][/tex]
### Incorrect Reasoning Breakdown:
1. Incorrect Step 1:
- [tex]\(\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6\)[/tex]
- This is incorrect because multiplying [tex]\(\frac{8}{12}\)[/tex] by 6 is not equivalent to swapping it to [tex]\(8 \times \frac{1}{12} \times 6\)[/tex].
2. Incorrect Step 2:
- The calculation goes to: [tex]\(8 \times \frac{1}{72}\)[/tex]
- The simplification from [tex]\(8 \times 1/12 \times 6\)[/tex] to [tex]\(8 \times 1/72\)[/tex] is invalid.
3. Further Steps:
- The steps resulting in [tex]\(\frac{1}{9}\)[/tex] are based on this incorrect calculation.
### Correct Calculation:
We need to correct the original expression:
1. Fraction Simplification:
- Start with simplifying the fraction [tex]\(\frac{8}{12}\)[/tex].
- [tex]\(\frac{8}{12}\)[/tex] reduces to [tex]\(\frac{2}{3}\)[/tex] (by dividing both the numerator and the denominator by 4).
2. Multiplication:
- Now multiply the simplified fraction by 6:
[tex]\[
\frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3}
\][/tex]
3. Final Simplification:
- Calculate [tex]\(\frac{12}{3}\)[/tex]:
[tex]\[
\frac{12}{3} = 4
\][/tex]
Therefore, the correct result of [tex]\(\frac{8}{12} \times 6\)[/tex] is 4.0.
