6/a + 6/b

Question

6/a + 6/b

jim_thompson5910 · Answer

what is the LCD

anonymous · Answer

6     6
-  + -  this is what it looks like
a      b

jim_thompson5910 · Answer

what are the denominators in this case

anonymous · Answer

a and b

jim_thompson5910 · Answer

since they have no common factors between them (other than 1), this means that the LCM of a and b is ab

you just multiply the two terms if they have no common factors between them

jim_thompson5910 · Answer

so this means that the LCD is ab

how can we use this to add the fractions?

anonymous · Answer

well i adding but that wasn't it either

jim_thompson5910 · Answer

in order to add the fractions, the denominators must be the same

jim_thompson5910 · Answer

to get them to the same expression, we need to get them equal to the LCD

jim_thompson5910 · Answer

in the fraction 6/a, what is missing to get the LCD?

anonymous · Answer

im not sure

jim_thompson5910 · Answer

what was the LCD again?

anonymous · Answer

a and b do i need to flip them

jim_thompson5910 · Answer

the LCD is ab

jim_thompson5910 · Answer

so if we have the denominator 'a'

and an LCD ab

what's missing?

anonymous · Answer

b

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

so you need to multiply top and bottom of the first fraction 6/a by b like this

$$\large \frac{6}{a} \times \frac{b}{b}$$

$$\large \frac{6\times b}{a\times b}$$

$$\large \frac{6b}{ab}$$

jim_thompson5910 · Answer

do you see what to do with the other fraction?

anonymous · Answer

and with 6/b i do the same

jim_thompson5910 · Answer

yes, you multiply top and bottom by ______ (fill in the blank)

anonymous · Answer

a

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

doing that means you'll have this

$$\large \frac{6}{b} \times \frac{a}{a}$$ 

$$\large \frac{6\times a}{b\times a}$$ 

$$\large \frac{6a}{ab}$$

jim_thompson5910 · Answer

So

$$\large \frac{6}{a} + \frac{6}{b}$$

turns into

$$\large \frac{6b}{ab} + \frac{6a}{ab}$$

what's next?

anonymous · Answer

then it looks like 12ab/ab

jim_thompson5910 · Answer

close, but you cannot add 6a and 6b to get 12ab

jim_thompson5910 · Answer

the only thing you can do is this

$$\large \frac{6b}{ab} + \frac{6a}{ab}$$

$$\large \frac{6b+6a}{ab}$$

anonymous · Answer

6a + 6b

jim_thompson5910 · Answer

yep, that's all you can do is add the numerators, but not actually combine them because they aren't like terms

jim_thompson5910 · Answer

optionally you could factor out 6, but that's extra work

anonymous · Answer

Thanks

jim_thompson5910 · Answer

you're welcome