Litzi M.

asked • 10/11/12

4 2/5+5 1/5

 i need help on adding mixed fractions

1 Expert Answer

By:

Nicole C. answered • 10/11/12

Increase confidence in math and science, chemistry, algebra II

Michael B.

All generally correct, but in this specific case converting to improper fractions is unnecessary.  You can treat each number as a sum of an integer and a fraction, and then use Associative/Commutative Properties:

(4 2/5) + (5 1/5) = (4 + 5) + (2/5 + 1/5) = 9 + 3/5 = 9 3/5

Report

11/13/12

Jay T.

There is an unanswered question regarding the term 'mixed fractions'. What if the two denominators are different? For example, what if the problem had read 4 2/5+5 1/3? In general, the following steps are used to solve this type of problem:
 
1) Convert both fractions to fractions having the same denominator. The easiest way to do this is to multiply the two denominators to get a common denominator, and then convert both fractions to fractions having the same value, but using that denominator. For this problem,
 
5 x 3 = 15 is the common denominator.
 
One could convert the whole thing to improper fractions as follows:
 
4 2/5 = ((4 x 5) + 2)/5 = 22/5
5 1/3 = ((5 x 3) + 1)/3 = 16/3
 
and then convert both fractions to improper fractions in terms of fifteenths:
 
22/5 = (22/5) x (3/3) = (22 x 3)/(5 x 3) = 66/15 because 3/3 = 1, so (22/5) x (3/3) = (22/5) x 1 = 22/5
16/3 = (16/3) x (5/5) = (16 x 5)/(3 x 5) = 80/15 because 5/5 = 1, so (16/3) x (5/5) = (16/3) x 1 = 16/3
 
In other words, multiply each of the original fractions by (opposite fraction's denominator/opposite fraction's denominator) to convert each fraction to its value using the same denominator.
 
Now, you can add the two directly:
 
4 2/5 + 5 1/3 = (66 + 80)/15 = 146/15 = 9 11/15
 
You can make this easier on yourself by recognizing that the whole numbers, 4 and 5, are of the same denominator, 1 and can be added directly to sum up to 9. Then you can use the above procedure on the fractions 2/5 and 1/3:
 
2/5 = (2 x 3)/(5 x 3) = 6/15
1/3 = (1 x 5)/(3 x 5) = 5/15
 
2/5 + 1/3 = (6 + 5)/15 = 11/15
 
Now add the whole number, 9 to the fraction to get 9 11/15.
 
What if problem was 4 2/5 - (5 1/3)? The same procedure can be used:
 
4 2/5 - 5 1/3 = 4 6/15 - (5 5/15) = (4 - 5) + (6/15 - 5/15) = -1 + 1 15 = -15/15 + 1/15 = (-15 + 1)/15
= -14/15
 
What if the fractions add up to an improper fraction?  Suppose the problem was 4 2/5 + 5 2/3 = ? The same procedure works here too.
 
4 2/5 + 5 2/3 = (4 + 5) + 6/15 + 10/15 = 9 + 16/15
Since 16/15 = 15/15 + 1/15 = 1 1/15,
 
9 16/15 = (9 + 1) + 1/15 = 10 1/15
 
Hope this addresses future questions on this.
 
 
Report

02/19/14

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