Question

1 the example uses 12 as the common multiple of 4 and 6. a. name a different common multiple of 4 and 6. b. if you used the common multiple from part a as the common denominator, how would the models in the example be different? how would they be the same? c. use the common multiple from part a as the common denominator to write equivalent fractions for \\(\frac{3}{4}\\) and \\(\frac{1}{6}\\). \\(\frac{3}{4}=\\) \\(\frac{1}{6}=\\)

Explanation:

Part a

Step1: Recall LCM and multiples

Multiples of 4: 4, 8, 12, 24, 36,...
Multiples of 6: 6, 12, 24, 30,...
Common multiples are numbers in both lists. A different one from 12 is 24.

• Different: The models (circles) would be divided into 24 equal parts (instead of 12). The number of shaded parts for equivalent fractions would change (e.g., $\frac{3}{4}=\frac{18}{24}$, $\frac{1}{6}=\frac{4}{24}$) as the denominator is larger.
• Same: The total shaded area (representing the sum) would be equal, and the original fractions’ values (and their visual proportion) remain the same (just divided into smaller parts).

Step1: Convert $\frac{3}{4}$ to denominator 24

Multiply numerator and denominator by 6: $\frac{3\times6}{4\times6}=\frac{18}{24}$

Step2: Convert $\frac{1}{6}$ to denominator 24

Multiply numerator and denominator by 4: $\frac{1\times4}{6\times4}=\frac{4}{24}$

Answer:

24

Part b