There are a couple of ways to do this.
You can turn both into improper fractions
(where numerator is larger than
denominator) and then add them...,
or you can add the whole numbers
together, add the fractions together,
then combine them.
1. Improper fractions then add:
5 3/5 + 2 2/3
to turn a mixed number into an improper fraction
you first multiply the whole number by the
denominator of the fraction, then add the
numerator to the product. Put the result over
the original denominator to create a new fraction.
5 3/5 = (5(5)+3)/5 = 28/5
2 2/3 = (3(2)+2)/3 = 8/3
so we have 28/5 + 8/3
Now we have to get a common denominator.
The least common multiple of 3 and 5 is 15.
Since any number divided by itself = 1...
(x/x=1 regardless of yhe value of x)..
So multiply 28/5 by 3/3 and 8/3 by 5/5
to get 15 as the common denominator.
28/5 + 8/3
= (28/5)(3/3) + (8/3)(5/5)
= [28(3)]/[5(3)] + [8(5)]/[3(5)]
= 84/15 + 40/15
since we now have a common denominator
we can add the numerators and put the sum
over the denominator.
84/15 + 40/15 = (84+40)/15 = 124/15
124/15 is a valid answer, but can it
be reduced? Look for any number that will
divide into both the numerator and the
denominator. In this case 124 and 15 have
no common factors. The factors of 15 are
1, 3, 5, 15 and, other than 1 which changes
nothing, neither 3, 5, nor 15 are factors
of 124. The fraction cannot be reduced.
Still, 124/15 is an improper fraction since
the numerator is larger than the denominator.
To turn this into a mixed number, divide
15 into 124 giving 8 remainder 4
because 124 = 15(8) + 4
The 8 will be the whole number part of the
final answer with the remainder 4 being
put over the denominator 15 to create th
fraction part. 124/15 = 8 4/15
Final answer: 5 3/5 + 2 2/3 = 8 4/15
**********************************
The other way is first add the whole numbers,
and fractions separately then combine. The
procedures explained above still apply to
adding the fractions
5 3/5 + 2 2/3
= 5 + 2 + 3/5 + 2/3
= 7 + 3/5 + 2/3
we need to add the fractions
3/5 + 2/3
= (3/5)(3/3) + (2/3)(5/5)
= 9/15 + 10/15
= (9 + 10)/15
= 19/15
= 1 4/15
7 + 3/5 + 2/3
= 7 + 1 4/15
= 8 4/15
Final answer: 5 3/5 + 2 2/3 = 8 4/15
This is just like the way we originally
did it, except dealing with smaller
fractions since we added them separately
from the whole numbers.
I hope this mskes sense to you. Let me
know if you have questions.
