I have a Mathematics Major at Our Lady of the Lake and I love math! I believe it is a very interesting subject and an awesome language. Mathematics is truly everywhere and we use math in every day. I chose math at my major because I truly want to help students to learn the language and to not be intimidated by the math language. I want people to understand not only the language but how and why we use Mathematics. I want to improve students problem solving and critical thinking skills to help them not only in school but in life.

## Comments

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.