Single number &

Question

Hi guys,I'm poor at math and feel difficulty in understanding some meaning.If you have any idea after checking some below, would you comment some here for me.It would be a great help for me.Thanks~pb------------Q1: What's the meaning of "single number" here?  Is there any special meaning in "single" besides "one"?What single number raised to a power is 75/45 ?[for your reference, the answer is  (1.75)5.] Q2: I asked about this before but still in doubt. So ask sos once again.Does "dividing out" have same meaning with "dividing"? And what's the meaning of "dividing out two of five factors"?(Is it same with this: dividing five factors into two groups?)65 ÷ 62 = 63, because we are dividing out two of the five factors of 6, leaving three factors of 6, or 63

Anonymous · Accepted Answer

Pb03--

Q1: What's the meaning of "single number" here? Is there any special meaning in "single" besides "one"?

What single number raised to a power is 7⁵/4⁵ ?

[for your reference, the answer is (1.75)⁵.]

In this case, "single number" does mean "one number," as opposed to a series of numbers, or an equation. Since in math it is possible for multiple answers to satisfy a given equation, sometimes phrases like "what single number" are used to clarify that they are looking for "one" number, and not another equation.

For example, another "correct" answer could be (1 + 0.75)⁵instead of (1.75)⁵.

It does not have any other special meaning, such as the phrases "whole number" or "rational number" do.

Pb03--

Q2: I asked about this before but still in doubt. So ask sos once again.

Does "dividing out" have same meaning with "dividing"? And

what's the meaning of "dividing out two of five factors"?

(Is it same with this: dividing five factors into two groups?)

6⁵ ÷ 6² = 6³, because we are dividing out two of the five factors of 6, leaving three factors of 6, or 6³

In this case, they are using the phrase "dividing out" in the sense of removing from the original population. For example, let's say you have a herd of 30 sheep, 15 males and 15 females. If you remove all the males, you could say you "divided out the males from the herd" in the sense of "separated out" or "removed."

In this specific example, 6⁵ consists of 6 multiplied by itself five times. So, there are "five factors of 6" present originally: 6 x 6 x 6 x 6 x 6. If you divide by 6 x 6, you "divide out," or "remove" two of those original five factors of 6, leaving only three.

6 x 6 x 6 x 6 x 6 6 x 6

------------------ = 6 x 6 x 6 x ------ = 6 x 6 x 6 x 1 = 6 x 6 x 6 = 6^3.

6 x 6 6 x 6

You started with five factors of 6, and were left with three factors of 6, after "dividing out" the other two factors of six.

Avangi · Answer

I'm not too good at it either - but until someone else comes along:

I would not call either of these expressions particularly elegant.
Sometimes the term "dividing out" is used in place of the term "cancelling out." For example, if you have 3xy over (divided by) 7xz (or 3xy/7xz), in "simplifying" it, you could say the x's cancel out, leaving 3y over 7z, or 3y/7z. You "divide out" the x's, so to speak. It's just an algebraic operation.

Re your other example, your author obviously doesn't consider "seven to the fifth power divided by four to the fifth power" a "single number." However, he does consider "one point seven five to the fifth power a single number.
In the same spirit, you could say that a number raised to a power is a single (only one) number, while the expression "12/3" could be considered as two numbers, in the sense of "twelve divided by three," as an arithmetic example. Of course, it could also be considered a fraction, which would be a "single number."

CalifJim · Answer

Pb03Does "dividing out" have same meaning with "dividing"?

Almost. "dividing out" implies removing, as Anon said.

Suppose you have a number that consists of five factors: 2 x 3 x 3 x 5 x 7 (= 630).

There are many ways to divide out two of the five factors.

You can divide out (remove) 2 and 3. Dividing 630 by 6 gives 105. So after dividing out two factors of 630 you may have 105.

Or you can divide out (remove) 3 and 5. Dividing 630 by 15 gives 42. So after dividing out two factors of 630 you may have 42.

You can easily see that the answer depends which factors you divide out.

Note that when you express these computations as fractions, it amounts to removing the same factor above and below the fraction line.

(2)(3)(3)(5)(7) = (2)(3)~~(3)~~(5)~~(7)~~ = (2)(3)(5)

(3) (7) ~~(3)~~ ~~(7)~~

CJ

Avangi · Answer

I'm a bit mistified. Removing the black sheep from the herd gives us a different herd, as removing a "two" and a "three" from "2x3x3x5x7" gives us a different answer. I'm unaquainted with this process as a mathmatical tool.
What it really amounts to is subtraction. Dividing the herd by the number of black sheep gives us a different answer than subtracting the number of black sheep.

However, cancelling out common factors above and below the fraction line is "simplification," and retains the integrity of the expression's "value." This is what I was referring to earlier.

I don't understand how randomly eliminating a factor can be taken as an example of "dividing it out."
Do you mean, "2x3x3x5x7 divided by 2x3"? I guess that's a possible interpretation, albeit an unfamiliar one.

The OP is asking about "dividing out" as a process used in the context of mathmatics. How would the "herd" analogy be used in mathmatics?

- A.

Edit. Note that in the OP's final example, we have a division exercise involving exponents, and the final expression is still equivalent to the beginning expression. We are, in effect, cancelling out exponents above and below the fraction (division) line.

CalifJim · Answer

Avangi Note that in the OP's final example, we have a division exercise involving exponents, and the final expression is still equivalent to the beginning expression. We are, in effect, cancelling out exponents above and below the fraction (division) line.

In the case of exponentiation we are simply dealing with cases in which the factors are all the same.

6*4 / 6**3 = 6*1 = 6

~~(6)(6)(6)~~(6) = (6)
~~(6)(6)(6)~~

CJ

CalifJim · Answer

AvangiWhat it really amounts to is subtraction. Dividing the herd by the number of black sheep gives us a different answer than subtracting the number of black sheep.

The sheep example wasn't the best. True.

"remove" is an ordinary language concept, not a mathematical one. In mathematics, "removal" can be any of several things, including subtraction anddivision. But still, it may have got the basic point across.

CJ

Avangi · Answer

Agreed.  <img class='emoticon' style='Width:19px;Height:19px;' data-delaysrc='https://uat-englishforward-forums-backend.s3.us-west-2.amazonaws.com/Emoticons/15.gif' src='https://uat-englishforward-forums-backend.s3.us-west-2.amazonaws.com/Emoticons/15.gif' alt='Emotion: geeked'/>   Thanks.    -   A.

Single number &

Top answer

Get the Weekly English Kit 📬

Related Questions