Question

1/3 + 1/5 = 1/x

Answer 1

To get rid of all this fraction business, multiply through by the Least Common Multiple of the denominators.

Since the denominators are relatively prime, our common denominator will be 3*5*x. So we'll multiply both sides by 15x,\[\large\rm \color{royalblue}{15x}\left(\frac13+\frac15\right)=\frac1 x\cdot \color{royalblue}{15x}\]

Answer 2

Distribute the 15x on the left side of the equation,\[\large\rm 15x\frac13+15x\frac15=15x\cdot\frac1x\]

Answer 3

Moved to Algebra

Answer 4

And make cancellations where appropriate,\[\large\rm \color{orangered}{5}\cancel{15}x\frac{1}{\cancel{3}\color{orangered}{1}}+\color{orangered}{3}\cancel{15}x\frac{1}{\cancel{5}\color{orangered}{1}}=15\cancel{x}\cdot\frac{1}{\cancel x\color{orangered}{1}}\]

Answer 5

Leaving us with,\[\large\rm 5x+3x=15\]

Answer 6

Combine like-terms,\[\large\rm 8x=15\]

Answer 7

Then simply divide by 8 as a final step, yayyyy math!

Answer 8

Hmm I made that cancellation step a lil bit more confusing than was necessary XD

Answer 9

is there a simplier way? im in 10th grade i dont want to be too complicated

Answer 10

There's a different way, yes.
I'm not sure if it's simpler tho :)

Instead of multiplying through by the LCM (I do that because I don't enjoy doing fraction math, it can get messy), you can simply look for a common denominator on the left side of the equation, and add.

Answer 11

oh so theres only two ways

Answer 12

\[\large\rm \frac13+\frac15=\frac1x\]So in this case, in order to get a common denominator, the first fraction needs a 5, and the second fraction needs a 3.

Answer 13

\[\large\rm \frac55\cdot\frac13~+~\frac33\cdot\frac15=\frac1x\]Which gives,\[\large\rm \frac{5}{15}+\frac{3}{15}=\frac1x\]and then add the numerators,\[\large\rm \frac{8}{15}=\frac1x\]And then take the reciprocal of both sides (the flip),\[\large\rm \frac{15}{8}=\frac{x}{1}\]And x/1 is simply x.

Answer 14

Only two ways? I dunno.
Those definitely seem like the simplest ways to do it tho :o

Answer 15

Since the denominators are relatively prime, our common denominator will be 3*5*x. So we'll multiply both sides by 15x,

Answer 16

i dont under stand this part lol its worded too complicated

Answer 17

Imagine your problem was instead: 1/2 + 1/4 = 1/x

We wouldn't need to multiply both sides by 2*4*x because 2 is contained within 4. It is a factor of 4. Simply multiplying by 4x would do the job for this alternate problem.

Answer 18

3 cant go into 5 so we chose 15

Answer 19

Yes, 3 can't go into 5, so we need a 3 AND also a 5. :D

Answer 20

how should i write it ?

Answer 21

If it makes more sense to you, you can multiply through by each denominator value one at a time.\[\large\rm \frac13+\frac15=\frac1x\]Multiplying both sides by 3,\[\large\rm 3\left(\frac13+\frac15\right)=3\left(\frac1x\right)\]gives us,\[\large\rm \frac33+\frac35=\frac3x\]so you can see that multiplying by 3 fixed the first fraction, but none of the others.\[\large\rm 1+\frac35=\frac3x\]Likewise, multiplying by 5 would fix the next fraction and no others.

Answer 22

Oh, like, how to put it into your own words type of thing? :U

Answer 23

yes but im writing it down ill show you how i finish it and if it sounds correct

Answer 24

why do we cancel?

Answer 25

Maybe I shouldn't have used the word cancel.
What I mean is, something is dividing evenly out of the numerator and denominator.

If you look at the way I did it last, we're left with a 3/3. Which simplifies to 1, yes?

So,
\[\large\rm 15x\cdot\frac13=\frac{15x}{3}\]

15 is 3 * 5,
So we know the factor of 3 within that 15 will divide evenly with the 3 in the denominator.

\[\large\rm \frac{5\cdot3\cdot x}{3}\quad=5x\frac{3}{3}\quad=5x\cdot 1\]

Answer 26

Trying to find the best way to explain this to you :D lol
fractions math can be hard to learn.

Answer 27

im more confused

Answer 28

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Zepdrix
And make cancellations where appropriate,\[\large\rm \color{orangered}{5}\cancel{15}x\frac{1}{\cancel{3}\color{orangered}{1}}+\color{orangered}{3}\cancel{15}x\frac{1}{\cancel{5}\color{orangered}{1}}=15\cancel{x}\cdot\frac{1}{\cancel x\color{orangered}{1}}\]
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 29

why do we make cancellations?

Answer 30

Oh.
We're multiplying both sides by this special value to hopefully get rid of any fractions. (All denominators should go away when we apply this process).

Answer 31

We're "cancelling out" the denominators.

Answer 32

ok