Expert Answers

An illustration of the letter 'A' in a speech bubbles

 This is probably the old-fashioned way, but, perhaps, it may be simpler:

Another way to solve this problem is just to find the lowest common denominator for the fractions as they are without converting the mixed number to an improper fraction. 

The lowest common denominator for 4 and 6 is 12 as 4 goes into 12  3 times and 6 goes into 12  2 times. 

So, convert 3/4 to 12ths by dividing 12 by 4=3.  Then, multiply 3 times the old numerator, 3 = 9.  Write the new mixed fraction as 6 9/12

Do the same for 5/6:  Divide 12 by 6 = 2; then multiply 2 times the old numerator, 5 = 10.  Rewrite the mixed fraction as 1 10/12

 Finally, add the mixed numbers that now have common denominators: 

  6 3/4 = 6 9/12

+ 1 5/6 = 1 10/12

____________________

 TOTAL =  7 19/12 = (Changing the improper fraction 19/12 to a mixed fraction makes 1  7/12  and adding it to 7) =  8  7/12 [ANSWER]

Approved by eNotes Editorial Team

Posted on

An illustration of the letter 'A' in a speech bubbles

The first thing you need to do is to get these fractions to have the same bottom number.  You should do this by finding their least common mutliple.  In this case, it is 12.

So now you want to get them both to be expressed in terms of something over 12.  To do that, you first have to convert the whole numbers into fractions.

6 3/4 becomes 27/4 and 1 5/6 becomes 11/6.

Now you need to multiply both to get them to be over 12.

27/4 = 81/12 and 11/6 = 22/12

Now you can just add them.  81 + 22 = 103

So your answer is 103/12.

You can simplify that to 8 7/12 because 103/12 = 8 remainder 7.

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial