Question

now, find fractions that are equivalent to \\(\frac{1}{4}\\). what do you notice about the relationship between the numerator and the denominator in each fraction? the denominator is? times the numerator. (options: 2, 3, 4, 5)

Explanation:

Step1: Find equivalent fractions

Multiply numerator/denominator by same non-zero integer:
$\frac{1}{4} = \frac{1\times2}{4\times2} = \frac{2}{8}$, $\frac{1\times3}{4\times3} = \frac{3}{12}$, $\frac{1\times4}{4\times4} = \frac{4}{16}$, $\frac{1\times5}{4\times5} = \frac{5}{20}$

Step2: Analyze numerator-denominator ratio

For each fraction, calculate $\frac{\text{denominator}}{\text{numerator}}$:
$\frac{4}{1}=4$, $\frac{8}{2}=4$, $\frac{12}{3}=4$, $\frac{16}{4}=4$, $\frac{20}{5}=4$

Answer:

1. Equivalent fractions: $\frac{2}{8}$, $\frac{3}{12}$, $\frac{4}{16}$, $\frac{5}{20}$
2. The denominator is always 4 times the numerator for each equivalent fraction.
3. 4