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Answer :
Morgan's statement that [tex]\(\frac{1}{2} + \frac{1}{4} = \frac{2}{6}\)[/tex] is incorrect. Let's go through the correct process step-by-step to understand why.
### Step 1: Identifying the Fractions
We need to add the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex].
### Step 2: Finding a Common Denominator
To add fractions, we need a common denominator. The denominators in this case are 2 and 4. The least common denominator (LCD) is 4.
### Step 3: Converting Fractions to Have the Same Denominator
1. Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with 4 as the denominator.
[tex]\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\][/tex]
2. [tex]\(\frac{1}{4}\)[/tex] already has the denominator 4, so it remains [tex]\(\frac{1}{4}\)[/tex].
### Step 4: Adding the Fractions
Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}
\][/tex]
### Conclusion
Morgan is incorrect because:
1. [tex]\(\frac{2}{6}\)[/tex] is not equal to [tex]\(\frac{1}{2}\)[/tex]. In fact, [tex]\(\frac{2}{6}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
2. The correct sum of [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
Morgan's error was in the addition of the fractions and the simplification process. The correct answer to the sum is [tex]\(\frac{3}{4}\)[/tex].
### Step 1: Identifying the Fractions
We need to add the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex].
### Step 2: Finding a Common Denominator
To add fractions, we need a common denominator. The denominators in this case are 2 and 4. The least common denominator (LCD) is 4.
### Step 3: Converting Fractions to Have the Same Denominator
1. Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with 4 as the denominator.
[tex]\[
\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
\][/tex]
2. [tex]\(\frac{1}{4}\)[/tex] already has the denominator 4, so it remains [tex]\(\frac{1}{4}\)[/tex].
### Step 4: Adding the Fractions
Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{2}{4} + \frac{1}{4} = \frac{2 + 1}{4} = \frac{3}{4}
\][/tex]
### Conclusion
Morgan is incorrect because:
1. [tex]\(\frac{2}{6}\)[/tex] is not equal to [tex]\(\frac{1}{2}\)[/tex]. In fact, [tex]\(\frac{2}{6}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
2. The correct sum of [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
Morgan's error was in the addition of the fractions and the simplification process. The correct answer to the sum is [tex]\(\frac{3}{4}\)[/tex].
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