Lesson 6: Lesson Six--Subtracting fractions
Lesson Six-Subtracting fractions and mixed numbers (like and unlike denominators, including borrowing).
Section One: Subtraction of fractions, no borrowing
The same rules that apply to adding fractions and mixed/whole numbers--the necessity of a common denominator and reducing your answer if possible--also apply to subtraction of fractions.
If you have a common denominator, simply subtract the numerators.
Example: 4/5 - 2/5 = 2/5.
Example: 6/10 - 2/10 = 4/10 = 2/5.
Example: 3 2/7 - 1 1/7 = 2 1/7.
If you have unlike denominators, find the LCD by finding the LCM, convert the fractions to those with common denominators, then subtract:
Example: 13/15 - 2/5: The LCD = 15, so, since 2/5 = 10/15, 13/15 - 10/15 = 3/15 = 1/5.
Example: 5 7/12 - 2 3/8: the LCD = 24, so, since 5 7/12 = 5 14/24 and 2 3/8 = 2 9/24, the answer is 5 14/24 - 2 9/24 = 3 5/24, which cannot be reduced.
Example: 6 - 2 3/4.
Though you can add 6 + 2 3/4 to get 8 3/4, unfortunately, you can't do that with subtraction!
When subtracting a mixed number or fraction from a whole number, you MUST convert the whole number into a MIXED NUMBER!
Let's convert 6 into a mixed number--this is important in preparing to borrow in section 2!
When you convert any whole number into a mixed number, keeping in mind you have to have a common denominator, you in fact BORROW one whole from the whole number, which means that the whole number you started with is now one less to include the fraction.
Let's convert 3 into a mixed number with a denominator of 4.
3 = 2 4/4. Why? Since 4/4 = 1, you are adding the whole number 2 and the fraction 4/4=1, or 2 + 1 = 3! So, 3 = 2 4/4.
Let's convert 5 into a mixed number with a denominator of 7.
5 = 4 7/7.
Finally, convert that 6 into a mixed number so you can subtract 2 3/4 from it:
Since 6 = 5 4/4, 6 - 2 3/4 = 5 4/4 - 2 3/4 = 3 1/4.
Let's do one more like this:
10 - 4 5/9. Since 10 = 9 9/9, 10 - 4 5/9 = 9 9/9 - 4 5/9 = 5 4/9.
