Question

sort the numerical expressions, according to their products.

select \\(\frac{1}{8}\\), \\(\frac{1}{4}\\), or neither.

	\\(\frac{1}{8}\\)	\\(\frac{1}{4}\\)
\\(\frac{1}{4} \times \frac{1}{2}\\)
\\(\frac{1}{3} \times \frac{1}{5}\\)
\\(\frac{1}{4} \times \frac{1}{4}\\)

Explanation:

Calculate the product of the first expression

We multiply the numerators and denominators:

$$ \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4} $$

Calculate the product of the second expression

We multiply the numerators and denominators:

$$ \frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8} $$

Calculate the product of the third expression

We multiply the numerators and denominators:

$$ \frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15} $$

Since \(\frac{1}{15}\) is neither \(\frac{1}{8}\) nor \(\frac{1}{4}\), this expression belongs to "Neither".

Calculate the product of the fourth expression

We multiply the numerators and denominators:

$$ \frac{1}{4} \times \frac{1}{4} = \frac{1 \times 1}{4 \times 4} = \frac{1}{16} $$

Since \(\frac{1}{16}\) is neither \(\frac{1}{8}\) nor \(\frac{1}{4}\), this expression belongs to "Neither".

Answer:

Expression	Product	Category
\(\frac{1}{4} \times \frac{1}{2}\)	\(\frac{1}{8}\)	\(\frac{1}{8}\)
\(\frac{1}{3} \times \frac{1}{5}\)	\(\frac{1}{15}\)	Neither
\(\frac{1}{4} \times \frac{1}{4}\)	\(\frac{1}{16}\)	Neither