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how do i do this 1 5/6 + 3 4/15

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6 Answers

Hi, Lori,

When you're working with mixed numbers, you always want to make sure your fractions play nicely together. A fraction is just a proportion, meaning it can be scaled up or scaled down. To scale 5/6 and 4/15 so they'll be easily compatible with each other, you need to find a common denominator.

The smallest number that your existing denominators (the digits under/to the right of the slash) of 6 and 15 will both go into is 30. (6*5=30 and 15*2=30.) Keep your numerators (the digits over/to the left of the slash) in proportion by multiplying them by those factors as well, using equations that look like this:

(5/6)*(5/5)=25/30. So, your original value of 1 5/6 is equivalent to 1 25/30.
 
(4/15)*(2/2)=8/30. So, your original value of 3 4/15 is equivalent to 3 8/30.
 
Now you can add your newly-compatible mixed numbers together.

1 25/30 + 3 8/30 = 4 33/30.
 
Since we know that 33 is more than 30, we can break down that last fraction into 1 3/30, then add that to our value of 4 to get 5 3/30. You can simplify further by reducing 3/30 to 1/10 (again, because the values are in proportion - in this case, the denominators 30 and 10 both divide by 3) to get a final sum of 5 1/10.
 It is easier just follow Steve 's way adding mixed numbers.
 
 Use associate law of of addition separate the whole numbers from integer
 
    1 5/6 + 3 4/15
 
   ( 1 +3 ) + ( 5/6 + 4/15) =
 
        4  + 5/6 + 4/15
 
        4  +  (25/30 + 8/30)
       
        4  + 33/30
      
       4 + 1 1/10 =
 
       5 1/10
 
         
 
       
 
Hi Lori;
1 5/6 + 3 4/15
Currently, you have whole numbers and fractions.  It is easier to work with only one.  In this circumstance, we want fractions.
The denominator, bottom number, of the final fraction will be the same as the current fraction, 6.  The final fraction will be x/6.
We must establish the numerator, number one top.
1 5/6
multiply (1)(6)=6
then add 6+5=11
This final numerator and denominator is 11/6.
 
3 4/15
(3)(15)=45
45+4=49
49/15
The equation is now...
(11/6)+(49/15)
We would like both denominators, numbers on bottom, to be the same.
The quickest technique is to realize that...
(6)(15)=90
Therefore...
(11/6)(15/15)=[(11)(15)]/[(6)(15)]=165/90
(49/15)(6/6)=[(49)(6)]/[(15)(6)]=294/90
The equation is now...
(165/90)+(294/90)
The denominator, number on bottom, will remain unchanged as we add the numerators, numbers on top...
459/90
Both the numerator and denominator can be divided by 9...
51/10
This is also...
5  1/10
This is because [(5)(10)]+1=51......51/10
 
1 5/6 + 3 4/15 =
 
1 + 5/(2*3) + 3 + 4/(3*5) =
 
1 + 3 + 5*5/(2*3*5) + 2*4/(2*3*5) =
 
4 + (5*5 + 2*4)/(2*3*5) =
 
4 + (25 + 8)/30 =
 
4 + 33/30 =
 
4 + (3*11)/(3*10) =
 
4 + (10 + 1)/10 =
 
4 + 1 + 1/10 =

5 1/10
1  5/6 = (1x6+5)/6 = 11/6
 
3  4/15 = (3x15+4)/15 = 49/15
 
11/6   + 49/15  
 
Take least common multiple of 6 and 15 which is 90
 
((11 x 15)+(49 x 6))/90
 
459/90 = 51/10

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