Lesson 6: Lesson Six--Subtracting fractions

Section Two: Subtraction of fractions with borrowing

Since you already learned how to borrow in doing subtraction of fractions from whole numbers, learning to subtract fractions when the numerator of the first fraction is too small to subtract the numerator of the second fraction from should NOT be the total frustration you remember that it was in school!

And, since you already know to borrow one whole from the whole number, converting the borrowed whole into a fraction with the necessary denominator, and since Cambridge GED gives a great example of the process of borrowing on the top of page 96, I will not give a complete explanation of the whole process of borrowing with fractions, but will give you the shortcut way to do it.

Why won't I give you the "longcut" method when the shortcut will do? Because as a homeschooling mother I had to teach my son how to borrow to subtract mixed numbers, and because I taught him the way Example 4 on page 96 is done, it took him FIVE years to learn how to subtract fractions with borrowing instead of the ONE year it should have taken! That's because my son, who has a great deal of number sense, became confused by long-winded explanations that they give in textbooks.

So, here's the shortcut!

Example: 6 1/2 - 2 5/8:

The LCD is 8, so we have 6 4/8 - 2 5/8, which cannot be done, so we have to borrow one from the 6, but what about the 4/8 - 5/8? Instead of telling you to borrow 1 from the whole number 6, making it 5 8/8 then adding 4/8 to it, I will tell you to do this:

Borrow 1 from the 6 to make 5, then simply add the numerator 4 and the denominator 8 to get 5 12/8 (think about it--isn't 5 12/8 the same as 6 4/8?), from which you can subtract 2 5/8. Thus, 5 12/8 - 2 5/8 = 3 7/8.

Here's another: 15 1/3 - 6 3/4:

The LCD is 12, so that 15 1/3 - 6 3/4 = 15 4/12 - 6 9/12, which you can't do, so you borrow, and 15 4/12 = 14 16/12; thus 14 16/12 - 6 9/12 = 8 7/12.

In any case, make sure your answer is reduced!

BTW, if you subtract a whole number from a mixed number, you simply subtract and not worry about borrowing.

13 2/3 - 7 = 6 2/3. That's it!

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