Question

explain why the denominator 8 in \\(\frac{4}{8}\\) is not changed when adding the fractions.\\(\

$$\begin{align}\\frac{4}{8}&=\\frac{4}{8}\\\\ +\\frac{1}{4}&=\\frac{2}{8}\\\\ \\hline \\frac{6}{8}\\end{align}$$

\\)\\(\circ\\) a. since the numerators are 1 and 4, and 4 is a multiple of 1, you need to change only the 1 to match the 4.\\(\circ\\) b. since the denominators are 8 and 4, and 8 is a multiple of 4, you need to change only the 4 to match the 8.\\(\circ\\) c. since the denominators are 8 and 4, and 8 is a factor of 4, you need to change only the 4 to match the 8.\\(\circ\\) d. since the denominators are 8 and 4, and 8 is a multiple of 4, you need to change only the 8 to match the 4.

Explanation:

To add fractions, we need a common denominator. Here, the denominators are 8 and 4. We know that 8 is a multiple of 4 (since \( 4\times2 = 8 \)). When adding \( \frac{4}{8}+\frac{1}{4} \), we convert \( \frac{1}{4} \) to a fraction with denominator 8 (by multiplying numerator and denominator by 2, getting \( \frac{2}{8} \)), so we change the denominator 4 to match 8. Let's analyze the options:

• Option A: Focuses on numerators, which is incorrect as we need common denominators, not related to numerator multiples.
• Option B: Correctly states that 8 is a multiple of 4, so we change the 4 (denominator of the second fraction) to match 8.
• Option C: 8 is not a factor of 4 (factors of 4 are 1, 2, 4), so this is wrong.
• Option D: We need to change the smaller denominator (4) to match the larger one (8) since 8 is a multiple of 4, not the other way around, so this is incorrect.

Answer:

B. Since the denominators are 8 and 4, and 8 is a multiple of 4, you need to change only the 4 to match the 8.