Borrowing when Subtracting Mixed Numbers

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You will need to sometimes need to borrow when subtracting. The only time you need to borrow is when the top fraction is less than the bottom fraction. There will not be enough to subtract the bottom fraction from the top fraction.The same pattern hold true for whole numbers.

Example 1 Simple Mixed Number Subtraction with Borrowing

3	1		1	3		?	?
	---	-		---	=		---
	8			8			8

You will have to borrow on this problem. To borrow first you must get a common denominator. This problem already has a common denominator. On the 3 and 1/8 you need to borrow.

First you need to take one from the whole number 3. The three will become a two.

Secondly on the fraction, add the numerator and denominator together. This number will be used as the new numerator.

This is what 3 and 1/8 will look like with its new name.

3	1		3-1	1+8		2	9
	---	=		---	=		---
	8			8			8

Why does this method work?? When you borrow one whole the numerator and denominator must be equal to each other to be equal to one whole. For example one whole equals 2/2, 3/3, 4/4, 5/5, etc. So to rename the mixed number, take one from the whole and add the numerator and denominator together for the fraction.

The fraction 3 and 1/8 will have to be written as an improper fraction 2 and 9/8 so that the subtraction can occur.

2	9		1	3		1	6
	---	-		---	=		---
	8			8			8

The fraction 6/8 will have to be reduced. Divide both the numerator and denominator by 2.

6	/	2		3
---		---	=	---
8	/	2		4

In lowest terms 6/8 equals 3/4. The final answer will be 1 and 3/4.