Audrina Jackson

2022-07-13

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

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

Kaylie Mcdonald

Beginner2022-07-14Added 19 answers

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 $\frac{c}{d}\cdot \frac{1}{\frac{c}{d}}=1\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}\frac{1}{\frac{c}{d}}=\frac{d}{c}$ (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.

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}$

to understand this you first need to understand $\frac{1}{x}\cdot x=1$. Knowng this we can see $\frac{c}{d}\cdot \frac{1}{\frac{c}{d}}=1\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}\frac{1}{\frac{c}{d}}=\frac{d}{c}$ (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

Beginner2022-07-15Added 1 answers

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.,

$\frac{3}{2}}x={\displaystyle \frac{5}{2}}\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}x={\displaystyle \frac{5}{3}$

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.,

$\frac{3}{2}}x={\displaystyle \frac{5}{2}}\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}x={\displaystyle \frac{5}{3}$

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