#### Dinnerout

##### New Member
Hi everybody,

How do you read the following expressions?:

1) 250:150=x:100

2) 120^5

• #### vachecow

##### Senior Member
Wel, is the first one supposed to multiplication? Because over here we just use the one dot. I have seen the second one, but it has been a while.

#### Focalist

##### Senior Member
Vc,

:

is another way of writing

÷

or

/

to represent division.

F

#### Silvia

##### Senior Member
Dinnerout said:
1) 250:150=x:100
250 is to 150 as X is to 100

I think it's called proportion.

#### Artrella

##### Banned
Dinnerout said:
Hi everybody,

How do you read the following expressions?:

1) 250:150=x:100

2) 120^5

The first one seems to be an equation, where you have to find "x"'s value.

so two hundred and fifty divided into a hundred and fifty equals "x" divided into a hundred

This is just a guess, I'm not a native!! But I also want to know how to read that!!

I don't know what the symbol in the second one means!

#### Ralf

##### Senior Member
If I'm not mistaken:
1) 250 divided by 150 equals (is equal to) x divided by 100
2) 120 raised by 5 or 120 raised to the 5th power

#### David

##### Banned
Artrella and Ralf are on the wrong track, I fear. This is a proportion, as indicated above. 120^5 is 120 to the 5th power, used when superscript numbers are not available.

#### Artrella

##### Banned
David said:
Artrella and Ralf are on the wrong track, I fear. This is a proportion, as indicated above. 120^5 is 120 to the 5th power, used when superscript numbers are not available.

Good to know David!! Thank you!!

#### Dinnerout

##### New Member
silviap said:
250 is to 150 as X is to 100

I think it's called proportion.

My American Theacher told me:

"Two hundred and fifty over one hundred and fifty, equals x over one hundred"

Is she right? Whether or not, let me know.

For the second question she told me:

"one hundred and twenty at the fifth".

#### David

##### Banned
Speaking in mathematical terms, your Teacher is right. If this were written as the equation

250/150=x/100, it could be read either "Two hundred fifty over one hundred fifty equals x over 100," or "Two hundred fifty divided by one hundred fifty equals x divided by 100."

However, if it is written as a proportion, 250:150=x:100, it should be read "Two hundred fifty is to one hundred fifty as x is to 100."

The same kind of relationship can be used for verbal relationships, when it is called an analogy: hat:head::glove:hand.

#### Artrella

##### Banned
Dinnerout said:
My American Theacher told me:

"Two hundred and fifty over one hundred and fifty, equals x over one hundred"

Is she right? Whether or not, let me know.

For the second question she told me:

"one hundred and twenty at the fifth".

I think she is right, over means divided into (fractions) At least in Spanish we say "over"

fraction
a number that results from dividing one whole number by another, or a small part of something:
¼ and 0.25 are different ways of representing the same fraction.

I'm not sure about the second one, I've found this definition.

power (MATHEMATICS) the number of times that a number is to be multiplied by itself:
2 to the fourth power is 2 times 2 times 2 times 2, which equals 16.

3 to the power 4 is usually written as 3*.

*
it means a number 4 (but I cannot write it properly)

#### elroy

##### Moderator: EHL, Arabic, Hebrew, German(-Spanish)
Dinnerout said:
My American Theacher told me:

"Two hundred and fifty over one hundred and fifty, equals x over one hundred"

Is she right? Whether or not, let me know.

For the second question she told me:

"one hundred and twenty at the fifth".

You would not say "at the fifth" but "to the fifth (power)." Technically, you should always say "power" but people do just say "to the fifth," I guess because it takes too much breath to always have to say "power."

#### Alfry

##### Senior Member
Dinnerout said:
Hi everybody,

How do you read the following expressions?:

1) 250:150=x:100

2) 120^5

1) 250 is to 150 as x is to 100

2) 120 raised to the fifth power (120 power 5)

#### modgirl

##### Senior Member
David said:
However, if it is written as a proportion, 250:150=x:100, it should be read "Two hundred fifty is to one hundred fifty as x is to 100."

That's exactly the way I read it. However, I'm not particularly good in math, so I didn't say anything because I didn't know if there were perhaps some alternative meaning of which I was unaware!

#### aigle491

##### Member
Artrella and Ralf are on the wrong track, I fear. This is a proportion, as indicated above. 120^5 is 120 to the 5th power, used when superscript numbers are not available.

In other words: 120^5 = 24,883,200,000

#### Focalist

##### Senior Member
Somewhere along the line I posted this:
The division sign resembles a dash or double dash with a dot above and a dot below (÷). It is equivalent to the words "divided by." This symbol is found mainly in arithmetic texts at the elementary-school level. It is rarely used by professional or academic mathematicians, scientists, or engineers.

Mathematically, the division sign is equivalent to the forward slash. Thus, for example, 4 ÷ 5 = 4/5 = 0.8, and -100 ÷ 10 = -100/10 = -10. In general, for any real number x and any nonzero real number y, the following is always true:

x ÷ y = x/y

The division sign is also mathematically equivalent to the ratio symbol, customarily denoted by a colon ( : ) and read "is to." Thus, for any real number x and any nonzero real number y, this equation holds:

x ÷ y = x:y
(Source)

But as it does not appear to have shown up yet, in the interests of general enlightment I hereby post it again..

F

#### Nick

##### Senior Member
Focalist said:
Vc,

:

is another way of writing

÷

or

/

to represent division.
NO NO NO!
This is a common mistake that really bugs me.

15:20 is a ratio. It is NOT even close to the same as the fraction 15/20. The ratio 15 to 20 means there are 15 of one thing and 20 of another. It can be expressed using TWO fractions: 15/35 and 20/35. It is not the same as 15/20.

Think of the score of a game. 9-14. One team got 9 points, the other team got 14 points. The fraction for team one is 9/23; the fraction for team two is 14/23.

#### modgirl

##### Senior Member
Nick, this may be another American/British situation. To me, as an American, I see 15:20 as a ratio.

Also, as an American, I see 1,300 as one thousand three hundred. However, Europeans see it as one point three. The way they would write one thousand three hundred would be: 1.300.

#### aigle491

##### Member
250:150=x:100

This is read like this: "250 to 150 equals x to 100"
This is a ratio and is comparing something to something else.
If this helps at all....

250/150=x/100
25000=150x
166.66666666=x

#### vachecow

##### Senior Member
silviap said:
250 is to 150 as X is to 100

I think it's called proportion.
Yes! Thats what it is! I knew it was familiar...

#### timpeac

##### Senior Member
modgirl said:
Nick, this may be another American/British situation. To me, as an American, I see 15:20 as a ratio.

Also, as an American, I see 1,300 as one thousand three hundred. However, Europeans see it as one point three. The way they would write one thousand three hundred would be: 1.300.

No - I would agree with you Americans here - this is a ratio. There is a total of 35 whatevers split in the ratio (or proportion) 15 to 20.

So for example if it is boys compared to girls in a class then out of the total 35 children 15/35 = 3/7 of the class are boys and 4/7 of the class are girls.

#### Artrella

##### Banned
Dinnerout said:
Hi everybody,

How do you read the following expressions?:

1) 250:150=x:100

2) 120^5

Well, Dinnerout, don't pay attention to my message. Since I am not an American native...

I agree with your teacher, we do the same in Argentina. It seems in the States they have different mathematics conventions. So, take what they say. To be on the safe side...

Bye, Art

#### Focalist

##### Senior Member
Nick said:
NO NO NO!Think of the score of a game. 9-14. One team got 9 points, the other team got 14 points. The fraction for team one is 9/23; the fraction for team two is 14/23.
And the ratio of Team 1 points to the total of points scored was 9:23, that of Team 2 was 14:23 -- or was it not?

F

#### Nick

##### Senior Member
Focalist said:
And the ratio of Team 1 points to the total of points scored was 9:23, that of Team 2 was 14:23 -- or was it not?
Ratio without "of X to Y" is like 9:14 -- you add them to find the total.

Ratio of Team 1's points to the total points is like 9:23 -- you don't add them because you know what is being compared, you are given the total. Generally, though, you don't use a ratio like this. One would normally use a fraction. This is a different definition of ratio, one which I do not like because it conflicts with the first definition. This is called a proportion (two ratios set equal to each other). Then they behave just like fractions because you can do the same mathmatical operation to both sides of the equation.