Add or subtract the following fractions. FoM Ch 4 Drill 16

[DanielleT248]

Add or subtract the following fractions. Put answers in their most simplified form.

24 / 3√2 - 4 / √2
A) 2√2
B) 4
C) 8√2

The answer is A. I follow the explanation given in the book for how they arrived at that answer, but I am having trouble understanding where I went wrong in my calculation. I keep coming up with 4√2 when I try to solve on my own.

Approach 1: I multiplied 4 / √2 by 3 / 3 to get 12/3√2. Now I have 24 / 3√2 - 12 / 3√2 = 12 / 3√2 = 4√2

Approach 2: I simplified 24 / 3√2 to get 8 / √2. Now I have 8 / √2 - 4 / √2 = 4√2

Thank you!!

[DanielleT248]

I finally figured this out after spending more time on roots and exponents then coming back to this problem.

My answer of 4 / √2 is equivalent to the correct answer of 2√2 after I multiply 4 / √2 by √2 / √2 to get rid of the root in the denominator. I thought I was having an issue with my calculations, but I was really having trouble reducing/simplifying my final answer that last step.

[esledge]

Hi Danielle, yep, that's it, and that move of multiplying by root2/root2 is called "rationalizing the denominator." The GMAT will generally not leave roots in the denominator, so that move is a good one to know.

[In your initial post, you appeared to be dropping the "divided by" slash in the last step, too, to write 4root2 instead of 4/root 2, though that might just have been a typing error.]

Thanks for following up!

[DanielleT248]

Thank you! Yes, it was a typing error in my initial post.

[esledge]

Thought so! Thanks for following up.