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 Beverly Mackie BellaOnline's Math Editor

Fractions - Adding Mixed Numbers

Learn how to Add mixed numbers with like and unlike denominators.

I. Adding Mixed Numerals with Like Denominators
II. Adding Mixed Numerals with Unlike Denominators

Steps
1. Add numerators
2. Do NOT Add the denominators; the denominator remains the same.
3. Add whole numbers
4. Examine your answer. If an improper fraction exist, convert into a mixed numeral. If not, go to step 6.
5. Add the whole number in step 4 to the whole number in step 3 and keep the new fraction.
6. Reduce, if necessary

Example: 13 4/8 + 3 6/8 =

1. Add numerators --- 4 + 6 = 10
2. The denominator remains the same. 8
3. Add whole numbers 13 + 3 = 16
4. Examine your answer. 13 4/8 + 3 6/8 = 16 10/8 The fraction 10/8 is an improper fraction and must be converted to a mixed number. Thus 10/8 = 1 2/8.
5. Add the whole number in step 4 to the whole number in step 3 and keep the new fraction. 16 + 1 2/8 = 17 2/8

6. Reduce 17 2/8 = 17 1/4

7. In summary, 13 4/8 + 3 6/8 = 16 10/8 = 17 2/8 = 17 1/4

II. Adding Mixed Numerals with Unlike Denominators

Remember: Denominators must be the same in order to subtract or add fractions

Example: 9 5/7 plus 3 4/6
Good Math Detectives will notice the denominators are not the same.

Steps
1. Find the least common multiple between the two denominators. Most commonly referred to as the least common denominator (LCD)
2. Find the equivalent fraction for each fraction using the LCD. (As a result, the denominators will be the same.)
3. Add the numerators (The denominators are NOT Added.)
4. The denominator remains the same.
5. Add the whole numbers.
6. Examine your answer. If an improper fraction exist, convert into a mixed numeral. If not, go to step 8.
7. Add the whole number in step 6 to the whole number in step 5 and keep the new fraction.

8. Reduce, if necessary

1. Find the least common denominator (LCD) : To find the LCD, use prime factorization. (refer to GCF and LCM by Prime Factorization article) The prime factorization for 6 is 2 * 3. The number 7 is a prime number. The LCD for 42 = 2*3*7 . It just so happens, if you were to multiply the denominators, the answer is still 42. (Please refer to the Prime Factorization article for a more detailed explanation.)

2. Find the equivalent fraction for each fraction using the LCD.
Since the new denominator is 42. New numerators are needed. 4/6 = ?/42
Ask yourself , the denominator,6, times what number equals 42. It is 7. Since, the denominator was multiplied by 7, the numerator must be multiplied by 7. Thus the equivalent fraction for 4/6 using 42 as the denominator is 28/42. . Next, 5/7 = ?/42. Ask yourself , the denominator,7, times what number equals 42. It is 6. Since, the denominator was multiplied by 6, the numerator must be multiplied by 6. Thus, the equivalent fraction for 5/7 using 42 as the denominator is 30/42.
Now, the problem reads: 9 30/42 + 3 28/42 =

3. Add the numerators: 30 + 28 = 58

4. The denominator remains the same: 42

5. Add the whole numbers: 9 + 3 = 12
Therefore: 9 30/42 + 3 28/42 = 12 58/42

6. Examine your answer.9 30/42 + 3 28/42 = 12 58/42 The fraction 58/42 is an improper fraction and must be converted to a mixed number. Thus 58/42 = 1 16/42.
7. Add the whole number in step 6 to the whole number in step 5 and keep the new fraction. 12 + 1 16/42 = 13 16/42

5. Reducing is necessary because 16 and 42 have at least one common factor.
16/42 = 8/21 (If necessary, refer to article on reducing at the end of this article.)

Therefore: 9 5/7 plus 3 4/6 = 9 30/42 + 3 28/42 = 12 58/42 = 13 16/42 = 13 8/21

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