A math question regarding this specefic reciprocal

[ingoi]

Can someone tell me how 2 is the reciprocal of 1/(1/2) , was reading the definition of reciprocal and it said if it was equal to 1 but when I put the reciprocal to test if it really is one I would get and answer of 4 so I am confused about this one.

[NeoZeon]

the reciprocal is 1/x, where the equation of is 1/x =1

 

so 1/(1/2 * x) = 1 

 

solve for x , x= 2

 

remember order of operations

 

1/(1/2) = 2 

 

so 2 * (1/x) = 2/x = 1 

 

solve for x again and you get 2. 

 

so the reciprocal should be 1/2

[Voldy21]

I'm super confused how you get 4 because at no time are you multiplying 2 with anything other than 1 in 1/(1/2) lol. Re-write it like this. 1 divided by 1/2 is also 1x(2/1). If you're dividing two numbers, you can flip over the denominator and then multiply the two numbers again. For instance let's say you have 1/3 divided by 1/4. You can multiply 1/3 by 4/1 and get 4/3. Flip the second part of it, or the denominator, and then multiply them.

[Speedyv]

1/(1/2) * 2/2  = 2/1

the reciprocal of (2/1) is 1/2

 

It should be 1/2 and not 2

[ingoi]

the reciprocal is 1/x, where the equation of is 1/x =1

 

so 1/(1/2 * x) = 1 

 

solve for x , x= 2

 

remember order of operations

 

1/(1/2) = 2 

 

so 2 * (1/x) = 2/x = 1 

 

solve for x again and you get 2. 

 

so the reciprocal should be 1/2

 

I'm super confused how you get 4 because at no time are you multiplying 2 with anything other than 1 in 1/(1/2) lol. Re-write it like this. 1 divided by 1/2 is also 1x(2/1). If you're dividing two numbers, you can flip over the denominator and then multiply the two numbers again. For instance let's say you have 1/3 divided by 1/4. You can multiply 1/3 by 4/1 and get 4/3. Flip the second part of it, or the denominator, and then multiply them.

EDIT: eh I just noticed you did 1/(1/2 * x) I thought you had to times the whole thing - correct me if im wrong or right. since I been doing (1/(1/2))*x and

(1/(1/2))*2 for checking if its equal to 1

        Still not to sure how you got the answer by rechecking with the reciprocal, does that mean you don't have to times it by the whole equation like I did below?

Well,from your equation wouldn't that make it x = 1/2 not x = 2? since it would go along like this

 

x/1  / 1/2  = 1-->   x/1*2/1 --> 2x = 1 --> x = 1/2 - which wouldn't make sense considering I know it should definitely be 2 - can you tell me my missing step?

 

Also I got 4 from doing this

Edit- I'm assuming 2 is the reciprocal so I was seeing if it was indeed a reciprocal if it followed the law

2/1   /  1/2 --->  2/1 * 2/1 = 4 - whcih if you punch it into a calculator would give you 4 as well o-o, but doesn't help the fact I still do not know why its not following the law of, reciprocals should equal to 1

[ionbasa]

A neat nmonit to help you out: "keep, change, flip"

See the example prolems here: http://www.softschools.com/math/topics/dividing_fractions/

[Voldy21]

EDIT: eh I just noticed you did 1/(1/2 * x) I thought you had to times the whole thing - correct me if im wrong or right. since I been doing (1/(1/2))*x and

(1/(1/2))*2 for checking if its equal to 1

        Still not to sure how you got the answer by rechecking with the reciprocal, does that mean you don't have to times it by the whole equation like I did below?

Well,from your equation wouldn't that make it x = 1/2 not x = 2? since it would go along like this

 

x/1  / 1/2  = 1-->   x/1*2/1 --> 2x = 1 --> x = 1/2 - which wouldn't make sense considering I know it should definitely be 2 - can you tell me my missing step?

 

Also I got 4 from doing this

Edit- I'm assuming 2 is the reciprocal so I was seeing if it was indeed a reciprocal if it followed the law

2/1   /  1/2 --->  2/1 * 2/1 = 4 - whcih if you punch it into a calculator would give you 4 as well o-o, but doesn't help the fact I still do not know why its not following the law of, reciprocals should equal to 1

Yes. (2/1) / (1/2) is 4 but that's something completely different than from what we're talking about. 

if you want to find the reciprocal of any number then you divide that number you want to get the reciprocal of by 1. So if you want to find the reciprocal of 1/2 then you put 1/(1/2). Using the rule I showed you it should be

 

(1)/(1/2) or (1)*(2/1) = 2. That's all there is. I don't know the exact equation that you're talking about so you'll have to show it to me.

 

 

the reciprocal is 1/x, where the equation of is 1/x =1

 

so 1/(1/2 * x) = 1 

 

solve for x , x= 2

 

remember order of operations

 

1/(1/2) = 2 

 

so 2 * (1/x) = 2/x = 1 

 

solve for x again and you get 2. 

 

so the reciprocal should be 1/2

You made it a little confusing. 

In the problem 1/(1/2 * x) = 1 the first thing you should do is what's inside the parentheses.

 

Therefore, it would be 1/(x/2) which would make it (1)*(2/x) which would make it (2/x)=1. Then you multiply x on both sides making it x=2.

 

You did some weird stuff. I think you distributed so that you divided 1 by everything in the parentheses? Is that what you did? Makes things a little confusing when you're doing it on this kind of format

[ingoi]

Yes. (2/1) / (1/2) is 4 but that's something completely different than from what we're talking about. 

if you want to find the reciprocal of any number then you divide that number you want to get the reciprocal of by 1. So if you want to find the reciprocal of 1/2 then you put 1/(1/2). Using the rule I showed you it should be

 

(1)/(1/2) or (1)*(2/1) = 2. That's all there is. I don't know the exact equation that you're talking about so you'll have to show it to me.

 

 

You made it a little confusing. 

In the problem 1/(1/2 * x) = 1 the first thing you should do is what's inside the parentheses.

 

Therefore, it would be 1/(x/2) which would make it (1)*(2/x) which would make it (2/x)=1. Then you multiply x on both sides making it x=2.

 

You did some weird stuff. I think you distributed so that you divided 1 by everything in the parentheses? Is that what you did? Makes things a little confusing when you're doing it on this kind of format

Ah I see now, also the formula per se was  a* 1/a =1  -which is pretty much just if you times by the reciprocal you should get one

 

Which was why I was multiplying the whole thing by 2. Does this mean instead of doing 2*(1)/(1/2) you would just do  2* 1/2?

 

Honestly I wasn't really sure since it was a fraction inside a fraction

[Voldy21]

Ah I see now, also the formula per se was  a* 1/a =1  -which is pretty much just if you times by the reciprocal you should get one

 

Which was why I was multiplying the whole thing by 2. Does this mean instead of doing 2*(1)/(1/2) you would just do  2* 1/2?

 

Honestly I wasn't really sure since it was a fraction inside a fraction

Okay, thank you for the formula and the formula is correct although you might as well say it's a/a=1. a*1 = a so it would be a/a=1. 

 

If you plug in 2 for a, because 2=a in this problem, you don't get 2*(1)/(1/2) you get 2*(1)/(2)=1 and that's true. Your problem was that you were plugging in the wrong numbers.

[ingoi]

Okay, thank you for the formula and the formula is correct although you might as well say it's a/a=1. a*1 = a so it would be a/a=1. 

 

If you plug in 2 for a, because 2=a in this problem, you don't get 2*(1)/(1/2) you get 2*(1)/(2)=1 and that's true. Your problem was that you were plugging in the wrong numbers.

Ah I see thanks.