Multiplication

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Explain this!

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2/5 * 25 =10 and the proportion 2/5 = 10/25

Why or how does 10 in 2/5 * 25 =10 become equivalent to the numerator for 25 in the proportion 2/5 = 10/25 as if 2/5 is being raised to higher terms?
 
Always find the prime numbers to be able to simplify expressions and find equivalence

[MATH]10 = 2 \cdot 5[/MATH][MATH]25 = 5 \cdot 5[/MATH]
now

[MATH]\frac{10}{25} = \frac{2 \cdot 5}{5 \cdot 5}[/MATH], you can cancel similar numbers in numerator and denominator

which leaves you with [MATH]\frac{2}{5}[/MATH]
 
[math]\dfrac{2}{5} \times 25 = 10[/math]
What you do to one side you must do to the other so if we divide both sides by 25 we get
[math]\dfrac{2}{5} \times 25 \times \dfrac{1}{25} = 10 \times \dfrac{1}{25}[/math]
The 25 cancels on the right cancels leaving
[math]\dfrac{2}{5} = \dfrac{10}{25}[/math]
-Dan
 
Explain this! said:
2/5 * 25 =10 and the proportion 2/5 = 10/25

Why or how does 10 in 2/5 * 25 =10 become equivalent to the numerator for 25 in the proportion 2/5 = 10/25 as if 2/5 is being raised to higher terms?
Click to expand...
You say "...2/5 = 10/25 as if 2/5 is being raised to higher terms"

- by that, do you mean

\(\displaystyle \left[ \frac{2}{5}\right] ^2\), \(\displaystyle \left[ \frac{2}{5}\right] ^3\) ...... etc = \(\displaystyle \frac{4}{25}\) , \(\displaystyle \frac{8}{125}\)...... etc .......... corrected

2/5 is NOT being raised to higher terms - instead it is being multiplied by 1 (or 5/5) to get to equivalent number 10/25
 
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Subhotosh Khan said:
You say "...2/5 = 10/25 as if 2/5 is being raised to higher terms"

- by that, do you mean

\(\displaystyle \left[ \frac{2}{5}\right] ^2\), \(\displaystyle \left[ \frac{2}{5}\right] ^3\) ...... etc = \(\displaystyle \frac{4}{25}\) , \(\displaystyle \frac{8}{125}\)...... etc ............corrected

2/5 is NOT being raised to higher terms - instead it is being multiplied by 1 (or 5/5) to get to equivalent number 10/25
Click to expand...
I understand that the procedure for raising a fraction to higher terms involves multiplying both terms of the fraction by the same number.
2/5 * 5/5 = 10/25
I am not familiar with your calculation nor do I understand it.
 
Explain this! said:
I understand that the procedure for raising a fraction to higher terms involves multiplying both terms of the fraction by the same number.
2/5 * 5/5 = 10/25
I am not familiar with your calculation nor do I understand it.
Click to expand...
There was a typo in my response#4 ............................that I corrected (and noted)

Please read it again and see if it makes more sense.
 
Yes, I understand your procedure, but it is not what I have read or understood to be used as raising a fraction to higher terms.
I thank you for your reply nevertheless!
 
Explain this! said:
Yes, I understand your procedure, but it is not what I have read or understood to be used as raising a fraction to higher terms.
I thank you for your reply nevertheless!
Click to expand...
The term "raising" is used in mathematics - related to "power" or "exponent".
 
Explain this! said:
I understand that the procedure for raising a fraction to higher terms involves multiplying both terms of the fraction by the same number.
2/5 * 5/5 = 10/25
I am not familiar with your calculation nor do I understand it.
Click to expand...
By converting 2/5 to 10/25 - you are NOT raising (2/5) to higher terms.

You are converting 2/5 to an equivalent fraction.

Could you provide some reference - where 2/5 → 10/25 was defined as "raising a fraction to higher terms"?
 
Subhotosh Khan said:
By converting 2/5 to 10/25 - you are NOT raising (2/5) to higher terms.

You are converting 2/5 to an equivalent fraction.

Could you provide some reference - where 2/5 → 10/25 was defined as "raising a fraction to higher terms"?
Click to expand...
If we talk about "reducing a fraction to lowest terms" (which we do), then it makes perfect sense to talk about "raising a fraction to higher terms". I don't think I've ever seen the phrase, but that doesn't make it wrong. In fact, a search for "raising a fraction to higher terms" turns up many sources.

He never said "raising to a power". The word "power", not "raising", is what determines the meaning of the phrase. You're reading too much into the word "raising", though I understand why you would initially misread it that way.
 
Dr.Peterson said:
If we talk about "reducing a fraction to lowest terms" (which we do), then it makes perfect sense to talk about "raising a fraction to higher terms". I don't think I've ever seen the phrase, but that doesn't make it wrong. In fact, a search for "raising a fraction to higher terms" turns up many sources.

He never said "raising to a power". The word "power", not "raising", is what determines the meaning of the phrase. You're reading too much into the word "raising", though I understand why you would initially misread it that way.
Click to expand...
I stand corrected.
 
Subhotosh Khan said:
By converting 2/5 to 10/25 - you are NOT raising (2/5) to higher terms.

You are converting 2/5 to an equivalent fraction.

Could you provide some reference - where 2/5 → 10/25 was defined as "raising a fraction to higher terms"?
Click to expand...

I have no reference to provide. I just used 2/5 as an example in 2/5 * 25. Yes, I understand that 2/5 and 10/25 are equivalent, but I also thought that 2/5 is raised to higher terms by multiplying 2 and 5 by whatever number one desires.

Here is a video that shows a fraction being raised to higher terms. It ever uses the "higher names", but "higher terms" is just as common.

 
There is a vocabulary problem here.

In your first video, it is very carefully explained about raising to higher NAMES. I do not know whether this is standard technical vocabulary in discussions of arithmetic. In mathematics more advanced than basic arithmetic, there is a technical term called "raising to a power." It is entirely different in meaning. It is unfortunate that both phrases have the word "raising."

The basic idea in your first video is this.

One times any number equals that number. Basic rule.

Any number (except 0) divided by itself equals one. Another basic rule.

You good with those?

Now if we put them together we get

[MATH]\dfrac{2}{5} = 1 \times \dfrac{2}{5}.[/MATH] First of those rules. Thus

[MATH]1 \times \dfrac{2}{5} =\dfrac{5}{5} \times \dfrac{2}{5}.[/MATH] Second basic rule.

[MATH]\dfrac{5}{5} \times \dfrac{2}{5} = \dfrac{5 \times 2}{5 \times 5} = \dfrac{10}{25}.[/MATH] How we multiply fractions.

Thus, [MATH]\dfrac{2}{5} = \dfrac{10}{25}.[/MATH] Things equal to the same third thing are themselves equal.

We have found a higher name for an equivalent fraction. As I say, I do not know whether that phrase "higher name" is standard, but I have no objection to it at all. I would, however, avoid the term "raise" because of the great opportunity for confusion.
 
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The basic idea in your first video is this.

One times any number equals that number. Basic rule.

Any number (except 0) divided by itself equals one. Another basic rule.

You good with those?

Yes, I understand those basic rules.

I have not heard or read anything that uses ':higher name." I have heard and read "higher terms." "Terms" refer to the numerator and denominator of the fraction. "Higher" is just what becomes of the terms when they are multiplied by the same number. They are larger or "higher," as it were. than before.

I want to thank you for your comments,
 
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