Answer :
Let's take a closer look at the problem and identify the error in the given work, then provide the correct calculation.
The original work is as follows:
1. [tex]\(\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6\)[/tex]
2. [tex]\(= 8 \times \frac{1}{72}\)[/tex]
3. [tex]\(= \frac{8}{72}\)[/tex]
4. [tex]\(= \frac{1}{9}\)[/tex]
The error occurs in step 2. The correct step should not be [tex]\(8 \times \frac{1}{72}\)[/tex]. Let's go through the correct steps:
1. Start with the original expression: [tex]\(\frac{8}{12} \times 6\)[/tex].
2. This is equivalent to [tex]\((8 \div 12) \times 6\)[/tex].
3. Simplify [tex]\(\frac{8}{12}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex], since both the numerator and denominator can be divided by 4.
4. Now, compute [tex]\(\frac{2}{3} \times 6\)[/tex].
5. This can also be written as [tex]\(\frac{2 \times 6}{3}\)[/tex].
6. Calculate the numerator: [tex]\(2 \times 6 = 12\)[/tex].
7. Divide the result by 3: [tex]\(\frac{12}{3} = 4\)[/tex].
Therefore, the correct calculation is [tex]\(\frac{8}{12} \times 6 = 4\)[/tex].
The correct answer to the problem is 4.
The original work is as follows:
1. [tex]\(\frac{8}{12} \times 6 = 8 \times \frac{1}{12} \times 6\)[/tex]
2. [tex]\(= 8 \times \frac{1}{72}\)[/tex]
3. [tex]\(= \frac{8}{72}\)[/tex]
4. [tex]\(= \frac{1}{9}\)[/tex]
The error occurs in step 2. The correct step should not be [tex]\(8 \times \frac{1}{72}\)[/tex]. Let's go through the correct steps:
1. Start with the original expression: [tex]\(\frac{8}{12} \times 6\)[/tex].
2. This is equivalent to [tex]\((8 \div 12) \times 6\)[/tex].
3. Simplify [tex]\(\frac{8}{12}\)[/tex] to [tex]\(\frac{2}{3}\)[/tex], since both the numerator and denominator can be divided by 4.
4. Now, compute [tex]\(\frac{2}{3} \times 6\)[/tex].
5. This can also be written as [tex]\(\frac{2 \times 6}{3}\)[/tex].
6. Calculate the numerator: [tex]\(2 \times 6 = 12\)[/tex].
7. Divide the result by 3: [tex]\(\frac{12}{3} = 4\)[/tex].
Therefore, the correct calculation is [tex]\(\frac{8}{12} \times 6 = 4\)[/tex].
The correct answer to the problem is 4.
