Adding & Subtracting Fractions

Adding Fractions If we were adding apples, 1 apple + 1 apple = 2 apples Same with fractions: You just add the tops and copy the bottom.

Adding Fractions Oops! What if we can’t just “copy the bottom” because the bottoms are different?

Adding Fractions We need a common denominator. It’s much easier to understand common denominators if you understand what common multiples are.

Multiples of a Number A multiple of a number is a number that you can get by multiplying your original number by a whole number. For example, the multiples of 6 would be 6, 12, 18, 24, 30, 36, 42, 48, . . .

12 and 24 are two of the many common multiples of 6 and 12. If you had two numbers like 6 and 12, a common multiple would be a number that is a multiple of each of them. Multiples of 6 6, 12, 18, 24, . . . Multiples of 12 12, 24, 36, 48, . . . 12 and 24 are two of the many common multiples of 6 and 12.

Least Common Multiples Even though 6 and 12 have many common multiples, we usually work with the smallest, or least common multiple. Multiples of 6 6, 12, 18, 24, . . . Multiples of 12 12, 24, 36, 48, . . . 12 is the least common multiple of 6 and 12.

Common Denominator In order to add or subtract fractions, you need to have a common denominator. The fractions must have the same number on the bottom.

Common Denominators Finding common denominators is the same as finding common multiples. The denominator is the number on the bottom of a fraction. Finding a common denominator for is the same as finding the common multiples of 6 and 12.

Least Common Denominator Although you can add fractions using any common denominator, most people like to work with smaller numbers so they use the least common denominator. It’s abbreviated L.C.D.

Adding Fractions To add these fractions, we must first transform them into equivalent fractions that have the same number on the bottom.

Adding Fractions We’ve already decided that the least common multiple of 6 and 12 is 12. Therefore the L.C.D. of our fractions is 12.

Adding Fractions We only have to change the first fraction so that it has a 12 on the bottom. We have to be careful not to change the value of the fraction when we change what it looks like!

Changing Fractions An easy way to change a 6 into a 12 is to multiply it by 2. If we multiply the bottom by 2, we must also multiply the top by 2.

Changing Fractions Why aren’t we changing the value when we multiply by 2 on the top and bottom?

Adding Fractions Now our problem is easy!

ALWAYS REDUCE FRACTIONS! ARF! We aren’t finished until we reduce the answer. ALWAYS REDUCE FRACTIONS!

Subtracting fractions Good news! Subtracting fractions is just like adding except that you subtract the tops and copy the bottom!

Remember: To add or subtract you need the bottoms of the fractions to be the same. If they aren’t the same, find a common denominator. L.C.D. is the least common denominator. Change the fraction by multiplying the top and the bottom by the same number. Add or subtract the tops and copy the bottom.