problem canceling in multiplication of fractions now that i have a grasp on formatting mathematical fractions and whatnot i present you with my latest confusion
$$3\frac15 \times 1\frac23 \times 2\frac 34$$
converted into improper fractions
$$\frac{16}5 \times \frac 53 \times \frac{11}4$$
this much i understand. the following bit is whats driving me insane
$$\frac41 \times \frac13 \times \frac{11}1$$
i simply dont get how it goes from the improper fractions to the next set of fractions. apparently its called canceling but i cant see any sense in it

First, $\frac{16}5 \times \frac 53 \times \frac{11}4$ is the same as $\frac{16}1 \times \frac 13 \times \frac{11}4$, since we can cancel the $5$ from both numerator and denominator. And in turn, $\frac{16}1 \times \frac 13 \times \frac{11}4$ is the same as $\frac41 \times \frac13 \times \frac{11}1$, since we can cancel a factor of $4$ from both numerator and denominator.
It might be able to see the validity of these cancellations more easily if, instead of writing $\frac{16}5 \times \frac 53 \times \frac{11}4 = \frac{16}1 \times \frac 13 \times \frac{11}4 = \frac41 \times \frac13 \times \frac{11}1$, we instead write the equivalent $\frac{16\times5\times11}{5\times3\times4} = \frac{16\times1\times11}{1\times3\times4} = \frac{4\times1\times11}{1\times3\times1}$.
