# How to make sense of fractions concretely I can solve fractions abstractly, for example,

How to make sense of fractions concretely
I can solve fractions abstractly, for example, $\frac{5}{2}$ divided by $\frac{3}{2}$, you can flip $\frac{3}{2}$ so that $\frac{5}{2}$ multiplied by $\frac{2}{3}$. Specifically, math makes sense abstractly, but concretely it just won't make sense, like in word problems. I understand the concept of complex fractions I know how to solve them, but by applying it on practical use such as a shape it does not make sense. How to make sense of fractions concretely?? or perhaps there is a book that you can advice me that help solve this problem
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Kaylie Mcdonald
So what you would like to know is why
$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}$
to understand this you first need to understand $\frac{1}{x}\cdot x=1$. Knowng this we can see $\frac{c}{d}\cdot \frac{1}{\frac{c}{d}}=1\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\frac{1}{\frac{c}{d}}=\frac{d}{c}$ (just assume $\frac{c}{d}$ is $x$).
Therefore $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot \frac{1}{\frac{c}{d}}=\frac{a}{b}\frac{d}{c}=\frac{ad}{bc}$
as desired.

Maliyah Robles
In general, $\frac{a}{b}$ denotes the quantity x, which when multiplied by b gives a. In fact, this is the correct way to interpret $\frac{a}{b}$
In your case, $\frac{5/2}{3/2}$ denotes the quantity x, which when multiplied by $\frac{3}{2}$ gives us $\frac{5}{2}$ , i.e.,
$\frac{3}{2}x=\frac{5}{2}\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}x=\frac{5}{3}$

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