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I always thought multiplication meant repeated addition. Consider

$$4 \times 3 = 12.$$

This the same as

$$4 + 4 + 4 = 12.$$

Now consider

$$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}. $$

If I use repeated addition approach, then I get

$$\frac{1}{2} + \frac{1}{2} = 1. $$

So the repeated addition approach doesn't really work.

I was helping my nephew with his maths homework and I was using the repeated addition approach. Then multiplying fractions came up and now I'm confused. Is there an easy answer to this?? Anything I could read. I'm very interested in trying to understand it. Right now it feels like I know nothing. lol

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    $\begingroup$ Multiplication is more of a scaling or stretching operation than repeated addition. So when you multiply by $1/2$ you're really just shrinking everything down to half the size just as multiplying by $2$ doubles everything. $\endgroup$ Jan 12 at 14:40
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    $\begingroup$ $\frac12\times\frac12$ would be addition of half copy of $\frac12$, not $2$ copies. $\endgroup$
    – peterwhy
    Jan 12 at 14:40
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    $\begingroup$ should I delete the post --- Personally, I think your error might be worth having available for others to see in the future. Maybe you can answer your question, but you'll need to use correct math formatting in both the question and answer. However, I suspect others might downvote your question anyway (and perhaps also an answer, if you give one?), so maybe it's not worth it. $\endgroup$ Jan 12 at 14:55
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    $\begingroup$ In your repeated addition scenario $\frac12 + \frac12$ is actually $2 \cdot \frac12$ which is why it equals $1$. $\endgroup$ Jan 12 at 15:05
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    $\begingroup$ Maybe you'll find this analogy useful? $\endgroup$
    – JonathanZ
    Jan 12 at 15:11

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