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Mathematics

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.

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I saw a question on how to add "mixed fractions'. The problem was to add 4 2/5 to 5 1/5 (= 9 3/5).However, mixed fractions can be more than this. Suppose denominators were not the same. Then what. Here is a comment I made that may help students having similar problems:
 
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.