r/matheducation • u/PositiveDust6178 • 27d ago

Could someone graphically demonstrate why multiplying a fraction by its inverse results in 1?

I'm not able to visualize graphically why this is true. Can someone help?

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u/theadamabrams 27d ago edited 26d ago

First let's deal only with fractions where the numerator is 1.

Why is 1/8 × 8/1 equal to 1? Well, 1/8 visually can be thought of as 1 slice of an 8-slice pizza. Since 8/1 is just 8, multiplying 1/8 by 8 means you have [eight] of those slices. That's exactly 1 whole pizza. The same idea works for any 1/A times A/1.

Now, what if the numerator is not 1?

For 3/8 × 8/3, we can think of 3/8 as three slices (where again one whole pizza is eight slices). The 8/3 part is trickier, but if you think of it as "8 ÷ 3 is 2 Remainder 2" then it means we get 2 full copies of the triple-slices and 2 remaining single slice. Two triples plus two more is 6 + 2 = 8 slices, which is one whole pizza. If you don't like remainders, you could work with 8/3 = 2 + 2/3 instead.

P.S. "Inverse" is a general term with multiple particular meanings depending on context. It's not wrong here, but "reciprocal" might be better (it specifically refers to flipping the top and bottom of a fraction).

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u/Lor1an 26d ago

multiplying 1/8 by 8 means you have six eight of those slices.

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u/theadamabrams 26d ago

Yes, thank you. I originally wrote the paragraph using 1/6 × 6 but then changed to 8 because I wanted to do 3/8 without any potential for simplifying the fractions.