Math Skills: Fractions

Lesson 5: Lesson Five--Adding Fractions

Section Two: Adding fractions

Adding fractions that already have common denominators is easy: simply add the numerators and carry through the denominator.

1/6 + 4/6 = 5/6

2/7 + 3/7 = 5/7

2/9 + 1/9 + 3/9 = 6/9 = 2/3.

You must reduce your answer if possible!

Here's one that becomes a mixed number: 3/8 + 5/8 + 7/8 = 15/8 = 1 7/8

Here's one that becomes a whole number: 3/7 + 2/7 + 4/7 + 5/7 = 14/7 = 2

You ALWAYS add the numerators in a fraction PROVIDED YOU HAVE A COMMON DENOMINATOR!

If you have unlike denominators, you MUST find the lowest common denominator. Most fraction addition problems will be like this.

Example: 2/5 + 8/9

Since 5 and 9 are relatively prime to each other, the easiest way to get the lowest common denominator would be to multiply 9 x 5 = 45.

2/5 = 18/45 (multiply numerator and denominator by 9); 8/9 = 40/45 (multiply numerator and denominator by 5), then 2/5 + 8/9 = 18/45 + 40/45 = 58/45 = 1 13/45.

One more:

3/8 + 5/12

Since 8 and 12 are NOT relatively prime to each other and have a least common multiplier, you need to find it. Did you guess what it was?

The LCM = 24; thus, the LCD = 24, since it's the lowest number both 8 and 12 go into evenly.

3/8 = 9/24 (multiply numerator and denominator by 3); 5/12 = 10/24 (multiply numerator and denominator by 2). So 9/24 + 10/24 = 19/24, which cannot be reduced since 19 is prime.

You can also add mixed numbers, or mixed and whole numbers. If you are adding a whole number and one fraction, you don't have to worry about common denominators: 1 + 1/2 = 1 1/2.

Adding one mixed number and a whole number is the same: 2 + 1 2/3 = 3 2/3, just adding the whole numbers.

But let's add two mixed numbers: 5 4/7 + 2 2/3.

First find the LCD. Since 3 and 7 are relatively prime to each other, the LCD will be 3 x 7 = 21.

5 4/7 = 5 12/21. 2 2/3 = 2 14/21. Thus, you get 5 4/7 + 2 2/3 = 5 12/21 + 2 14/21 = 7 26/21. This must be reduced because you can NEVER leave an improper fraction in your answer!

First reduce 26/21 by dividing 21 into 26, and you get 1 5/21.

But did you forget the whole number 7 you got before? MANY PEOPLE DO! Make sure you don't! Add 7 and 1 5/21 = 8 5/21. That's your answer!

If you remember to add the original whole number to the reduced improper fraction you got originally, adding mixed numbers will be no problem!

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