How do I solve 6 3/4 + 1 5/6?

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mwestwood's profile pic

mwestwood | College Teacher | (Level 3) Distinguished Educator

Posted on

 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]

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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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.

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krishna-agrawala | College Teacher | (Level 3) Valedictorian

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The number 6 3/4 really is equal to 6 + 3/4. It can be rewritten as:

24/4 + 3/4 = 27/4

Similarly 1 5/6 = 1 + 5/6 = 6/6 + 5/6 = 11/6

Therefor:

6 3/4 + 1 5/6 = 27/4 + 11/6 = (12/12)*(27/4 + 11/6)

= (3*27)/12 + (2*11)/12 = (81 + 22)/12 = 103/12

= 96/12 + 7/12 = 8 + 7/12 = 8 7/12

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

6 3/4 + 1 5/6

In order to solve this you need to change the whole numbers to fractions, this is how you change them: 6 3/4 = multiply the denominator by the whole number and then add the numerator your fraction will become 27/4, and in order to change it decimal just divide 3 by 4 and take the whole number in units place, it will then become 6.75. Same process will then be applied to 1 5/6 and it will become 11/6, decimal= 1.83.

therefore,

27/4 + 11/6

3(27/4) + 2(11/6)                             (find the LCM, which in this case is 12) 

81/12 + 22/12

81+22/12

103/12

8.583 or 8 7/12 Answer

Or you can also you a calculator.

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

 6 3/4 + 1 5/6

First let's add the fraction ( 3/4 and 5/6 ) 

By adding the fraction you should get

38/24 now change this to a mixed number

By changing the improper fraction to a mixed number, you should get

1 7/12 now add this with 6 and 1 

By adding,  you should get

8 7/12 which is your answer

parama9000's profile pic

parama9000 | Student, Grade 11 | (Level 1) Valedictorian

Posted on

6 3/4=6x4+3/4=27/4

Similarly, 1 5/6=11/6

27/4=81/12

11/6=22/12

81/12+22/12=103/12=8 7/12

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted on

6 3/4 plus 1 5/6 so basically you first turn both into unsimplified fractions. So 27/4 and 11/6. Then you want to try to get a similar denominator or bottom part of the fraction. Both 4 and 6 have a least common denominator of 12 so 12 is your new denominator now hold this thought. You have to multiply 6 by 2 to get 12 so whatever you do to the bottom you do to the top. So it would be 22/12 and you need to multiply 4 by three so 81/12. Then you add 22 and 108 to get 103/12 and then just simplify to 8 7/12.

zumba96's profile pic

zumba96 | Student, Grade 11 | (Level 3) Valedictorian

Posted on

Change it into a mixed number

6 3/4 + 1 5/6

27/4+11/6 

Find the LCM

162/24 +44/24

206/24

8 7/12

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`6 3/4 + 1 5/6`

`4/4 xx 6/1 = 24/4 +3/4 = 27/4`

`6/6= 1`

`6/6 + 5/6 =11/6`

`27/4 + 11/6`

the denominators have a common multiple of 12 so multiply to get the denominators to equal 24

`27/4 xx 3 = 81/12`

`11/6 xx 2 = 22/12`

`81/12 + 22/12 = 103/12`

the answer is `103/12 ` but you can try to simplify it

12 goes into 103,  8 times which is 96

`103- 96 = 7` so seven is left over

you answer becomes `8 7/12`

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princessenotes | Student, Undergraduate | (Level 1) Honors

Posted on

First, you need the denominator to be the same.

24/4 + 3/4 = 27/4

11/6

6 3/4 + 1 5/6 = 27/4 + 11/6 = (12/12)*(27/4 + 11/6)

= (3*27)/12 + (2*11)/12 = (81 + 22)/12 = 103/12

= 96/12 + 7/12 = 8 + 7/12 = 8 7/12

If you need anymore help, please contact my teacher at helpmathtutor@gmail.com

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amitparmar | Student, Undergraduate | (Level 3) eNoter

Posted on

solve 63/4+ 15/6,

we may written as

63/4=15.75...............<1>

we may also written as

15/6=2.5..................<2>

for solving this question adding both equation

63/4+ 15/6=2.5+15.75

or,63/4+ 15/6=18.25

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

How do I solve 6 3/4 + 1 5/6?

Solution:

6 3/4 + 1 5/6?

As in algebra (where we group like terms), here, you can group whole numbers together.

Therefore, 6  3/4 + 1  5/6 = 6+3/4+1+5/6

= 6+1+3/4+1/6 , by commutative law.

=7  + (3/4+5/6).......................(1)

Fraction could be added by converting the  fractions into equivalent fractions with common dinominators.The common dinominator, here, for 4 and 6 is their LCM, that is ,12. So equivalent fraction of 3/4 with 12 as dinaminator is 3*3/(4*3) and that of 5/6=5*2/(6*2) . So , the expression at  (1) could now be rewritten like:

7 +  3*3/(4*3)+(5*2/(6*2)

=7 + 9/12+10/12

=7+(9+10)/12

=7 + 19/12

=7  + 1 + (19-12)/12

=8 + 7/12. Whole numbers added.

=8  7/12

 

 

 

 

 

 

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