Question

multiply. use the cross - cancel strategy to simplify the problem. \\(\frac{1}{8} \times \frac{1}{2}\\) answer as a fraction in simplest form. enter the numerator.

Explanation:

Step1: Cross - cancel if possible

We have the fractions $\frac{1}{8}$ and $\frac{1}{2}$. We check if we can cross - cancel. The denominator of the first fraction is 8 and the numerator of the second fraction is 1, and the denominator of the second fraction is 2 and the numerator of the first fraction is 1. Wait, actually, we can also look at 8 and 2. 8 and 2 have a common factor of 2. So we can divide 8 by 2 and 2 by 2.
After cross - canceling, the first fraction becomes $\frac{1}{4}$ (since $8\div2 = 4$) and the second fraction remains $\frac{1}{1}$ (since $2\div2=1$). But actually, when multiplying fractions $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$, and cross - canceling is a way to simplify before multiplying. The numerators are 1 and 1, and the denominators are 8 and 2. We can also just multiply the numerators and denominators directly first: $\frac{1\times1}{8\times2}=\frac{1}{16}$. Wait, let's do cross - canceling properly. The numerator of the first fraction is 1, denominator of the first is 8; numerator of the second is 1, denominator of the second is 2. The common factor between 8 and 2 is 2. So we divide 8 by 2 to get 4, and divide 2 by 2 to get 1. Now the fractions are $\frac{1}{4}\times\frac{1}{1}$.

Step2: Multiply the fractions

When we multiply $\frac{1}{4}\times\frac{1}{1}$, we multiply the numerators: $1\times1 = 1$, and multiply the denominators: $4\times1=4$? Wait, no, that's wrong. Wait, actually, cross - canceling is done between a numerator and a denominator of different fractions. So numerator of first fraction (1) and denominator of second fraction (2): no common factors. Denominator of first fraction (8) and numerator of second fraction (1): no common factors. Wait, maybe I made a mistake. Let's just multiply the fractions directly. The formula for multiplying two fractions $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$. So for $\frac{1}{8}\times\frac{1}{2}$, $a = 1$, $b = 8$, $c = 1$, $d = 2$. So numerator is $1\times1=1$, denominator is $8\times2 = 16$. So the fraction is $\frac{1}{16}$.

Answer:

1