MATH 156
posted by NENAS
How do you add and subtract fractions? Provide an example and demonstrate the steps you would take to arrive at the answer. What strategies would you use to help a student struggling with the concepts of adding and subtracting fractions?

Ms. Sue
These sites all have excellent explanations of adding and subtracting fractions.
http://www.math.com/school/subject1/lessons/S1U4L3GL.html
http://www.themathpage.com/Arith/addfractionssubtractfractions1.htm
http://www.coolmath.com/fractions/fractions12addingsubtractingdifferentdenominators01.html
http://jamit.com.au/htmlFolder/FRAC1007.html 
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Dawson
It's easy to add and subtract like fractions, or fractions with the same denominator. You just add or subtract the numerators and keep the same denominator. The tricky part comes when you add or subtract fractions that have different denominators. Since only like fractions can be added or subtracted, we first have to convert unlike fractions to equal like fractions. We want to find the smallest, or least, common denominator, because working with smaller numbers makes doing the math easier. The least common denominator, or LCD, of two fractions is the smallest number that can be divided by both denominators. Rewrite the fractions as equivalent fractions with the LCM as the denominator. Then add or subtract only the numerators and keep the denominator the same. For mixed numbers, you add the whole numbers and add the fractions separately, or change them to improper fractions then find the LCD. Then, add or subtract and simplify.
I prefer to write the multiples of both denominators until I find a common multiple.
Let’s solve the problem: ¾ + 1/6
Simply start writing all the multiples of both denominators, beginning with the numbers themselves. For example: Multiples of 4 are 4, 8, 12, 16, and so on (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12, … wait, stop! That's the number we're looking for, 12, because it's the first one that appears in both lists of multiples. It's the least common multiple, which we'll use as our least common denominator.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.
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