# How do I solve this fraction addition problem?

$4\frac{2}{9} + -9\frac{1}{2}$ yeilds result of $-5\frac{13}{18}$ but WolframAlpha says the answer is $-5\frac{5}{18}$

fixed.

• Your pre-edit question was better for understanding what the issue was. Oct 19, 2014 at 23:51
• There was confusion. Sorry about that. The arithmetic is 4 and 2/9 plus -9 and 1/2. My answer from Wolfram is -5 and 5/18 but what I calculated was -5 and 13/18. Oct 20, 2014 at 0:05
• @kinesis was your question answered? Accept the most helpful post so we can close this if this is the case, and upvote where appropriate. If an answer satisfies you on your other posts, do the same. Oct 20, 2014 at 1:09

In $-9 \frac12$, the negative sign applies to the whole quantity. Thus the calculation should be

$4 \frac29+(-9 \frac12)=\frac{38}{9}+(-\frac{19}{2})=\frac{76}{18}-\frac{171}{18}=-\frac{95}{18}=-5 \frac{5}{18}$

• I do not get this answer on paper when I calculate it like this: $4\frac{2}{9} + (-9\frac{1}{2}) = 4\frac{2*2}{9*2} + (-9\frac{1*9}{2*9}) = -5\frac{11}{18}$ did the numerator of the answer wrong, but still is $-5\frac{11}{18}$ Oct 20, 2014 at 0:32
• Can you show your steps? Oct 20, 2014 at 0:33
• Steps added on previous comment. I was instructed by online tutorials and such that you do the whole parts last? I see this answer above saying that I make the second fraction a negative? 2*9 is not 38 and 1*9 is not 19... Oct 20, 2014 at 0:41
• So you have $4+\frac{4}{18}-(9+\frac{9}{18})=4+\frac4{18}-9-\frac9{18}=-5-\frac{5}{18}=-(5+\frac{5}{18})=-5\frac{5}{18}$ Oct 20, 2014 at 0:44
• @kinesis You can do the fraction parts first if you want (due to properties called "commutativity" and "associativity" of addition). But you need to make sure that the signs are correct: $-9\frac 9{18}$ equals $-9 - \frac 9{18}$, not $-9+\frac9{18}$. The negative sign applies to both parts.
– user137731
Oct 20, 2014 at 1:59

You can compute $4-9=-5$ and $\frac29-\frac12=\frac4{18}-\frac9{18}=-\frac5{18}$ separately, and then add them up. Or you could compute $4\frac29 + -9\frac12=\frac{38}9-\frac{19}2=\frac{76}{18}-\frac{171}{18}=\frac{-95}{18}=-5\frac5{18}$, though the latter is probably more error prone.

TeX \frac directive takes two arguments, but you use three in your formulas. This probably confuses WolframAlpha.

• So I did \frac{numerator}{denominator}{whole part} - What is correct? I'll fix it. Oct 19, 2014 at 23:25
• If you want to display it, just enter whole\frac{numerator}{denominator} and get $whole\frac{numerator}{denominator}$. To get the right input for WolframAlpha - do something like whole + \frac{numerator}{denominator} Oct 19, 2014 at 23:32
• I fixed it but it didn't update correctly. it is 4 2/9 + -9 1/2 Oct 20, 2014 at 0:03
• I didn't use any LaTeX formatting with WolframAlpha I just used (4 2/9) + (-9 1/2) Oct 20, 2014 at 0:11
• Wolfram's answer, (4 2/9) + (-9 1/2) = -95/18 = -5 5/18 looks right to me. How did you get yours? Oct 20, 2014 at 0:22

In mixed fractions (just as in decimal ones), the sign applies to both whole and fractional parts, so

$$4\frac{2}{9} + -9\frac{1}{2}=4\frac{2}{9}-\left(9+\frac{1}{2}\right)=(4-9)+\left(\frac{2}{9}-\frac{1}{2}\right)$$

Since $$4-9=-5$$ and $$\frac{2}{9}-\frac{1}{2}=\frac{2\times2}{9\times2}-\frac{1\times9}{2\times9}=\frac{4-9}{18}=\frac{-5}{18}$$ the final answer is $$-5+\frac{-5}{18}=-\left(5+\frac{5}{18}\right)=-5\frac{5}{18}.$$