Is 5 fifths equal to 5 tenths?

Updated: 4/28/2022
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11y ago

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5/5 = 1

5/10 = 1/2 or one half

The top (or first before the slash) number in a fraction is the numerator.

The bottom (2nd after the slash) number in a fraction is the denominator.

The bottom number tells you the TOTAL number of parts there are in that fraction.

The top number tells you how many parts of the total exist in the case.

When the top number and the bottom number are the same, that means that all of the parts are there.

If this were a pie, we would cut it into 10 parts. The 10 would be the denominator and would go on the bottom of the fraction.

Then, if we put five of those parts on one plate and the other five on another plate, the number 5 would be the number of parts out of the original 10 that existed on each plate and 5 would go on the top of the fraction.

What we do with fractions is divide. 5/10 is the same as writing 10 divided by 5 or 5 divided 10. 10 divided by 5 equals 2, and we would see that 2 is correct when we looked at the two plates on which we put 5 slices of pie each out of the original 10 total slices.

Another way to write this 5/10, now that we have divided the top into the bottom then is to put the new answer we got in the division above on the bottom and a 1 on the top. The reason for the 1 is because 5 divided by 5 equals 1. Whatever we divide into the bottom, we MUST divide also into the top number.

So the total equation (reducing to the lowest denominator) would look like this:

5/10 equals

(5 divided by 5) / (10 divided by 5 equals)


So the answer becomes 5/10 = 1/2

By the same token, 10/20 = 1/2 also, because when 10 is divided by 10 it is also 1, and when 20 is also divided by 10, it is also 2. So:

10/20 =

(10/10) / (10/20) =


10/20 = 1/2

We can do this with any number on top (including zero*) and any number on the bottom (except zero*) but, of course it won't always reduce to 1/2. For instance,

2/10 = (2/2) / (2/10) = 1/5

Now, we have discovered that 2/10 is equal to 1/5

The reason this is so is because if we had that same pie which was cut now into 10 pieces and we separated the slices into 2 on every dish, it would take 5 dishes to hold an exactly equal number of slices all of which total 10, AND if we instead cut that pie into 5 pieces and divided it instead into 1 piece on each plate, it would still take 5 plates to hold all 5 pieces with each plate now having only 1 slice of pie.

* The bottom (or 2nd number after the slash) can NEVER be zero since no real number can be divided into zero. Plainly, if there are 0 parts of the pie, we can't divide that pie up now to give different people a slice because someone already ate it all and left 0 pieces. It is not possible to divide 0 by any real number.

However, there CAN be 0 on the top of a fraction because now we are talking about how many parts of the whole (the whole, remember, is enumerated on the bottom of the fraction.) So, it IS possible to divide by 0, although it wouldn't make a lot of sense in the real world of pie since who wants 0/10 of pie. That would mean that he didn't get ANY AT ALL, while someone or a bunch of people ran off with the 10 slices.

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Q: Is 5 fifths equal to 5 tenths?
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