Questions: Find the LCM. Then convert each expression to an equivalent expression with the denominator equal to the LCM. 6/4, 3/2, 17/4 The LCM is

Solution Steps

To solve this problem, we need to find the Least Common Multiple (LCM) of the denominators of the given fractions. Then, we will convert each fraction to an equivalent fraction with the denominator equal to the LCM.

1. Identify the denominators of the given fractions.
2. Calculate the LCM of these denominators.
3. Convert each fraction to an equivalent fraction with the LCM as the denominator.

The given fractions are \( \frac{6}{4} \), \( \frac{3}{2} \), and \( \frac{17}{4} \). The denominators of these fractions are \( 4 \), \( 2 \), and \( 4 \).

To find the Least Common Multiple (LCM) of the denominators \( 4 \), \( 2 \), and \( 4 \), we observe that:

• The prime factorization of \( 4 \) is \( 2^2 \).
• The prime factorization of \( 2 \) is \( 2^1 \).

The LCM is determined by taking the highest power of each prime factor: \[ \text{LCM}(4, 2, 4) = 2^2 = 4 \]

Next, we convert each fraction to have the denominator equal to the LCM, which is \( 4 \).

1. For \( \frac{6}{4} \): \[ \frac{6}{4} = \frac{6 \cdot (4/4)}{4} = \frac{6}{4} \]

2. For \( \frac{3}{2} \): \[ \frac{3}{2} = \frac{3 \cdot (2)}{2 \cdot (2)} = \frac{6}{4} \]

3. For \( \frac{17}{4} \): \[ \frac{17}{4} = \frac{17}{4} \]

Thus, the converted fractions are \( \frac{6}{4} \), \( \frac{6}{4} \), and \( \frac{17}{4} \).

Final Answer