<s>[INST] 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
 [/INST] We know that $\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}$ and that we can commute $\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{c}{b}\times\dfrac{a}{d}=\dfrac{c}{d}\times\dfrac{a}{b}$ and so on, of course in the nominator and denominatior. Then, in your exercise:
$$\frac{16}5 \times \frac 53 \times \frac{11}4=\dfrac{16}{4}\times\dfrac{5}{5}\times\dfrac{11}{3}=\dfrac{4}{1}\times\dfrac{1}{1}\times\dfrac{11}{3}=\dfrac{4}{1}\times\dfrac{1}{3}\times\dfrac{11}{1}$$
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