Subtracting Mixed Numbers with Different Denominators and Borrowing

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Example 1 Mixed Number Subtraction with Different Denominators and Borrowing

Suppose you wanted to take 3 and 1/3 and subtract 1 and 3/4

3	1		1	3
	---	-		---	=		---
	3			4

The first step in subtracting any mixed number problem is to be sure you have a common denominator for the fractions.

1		4		4
---	x	---	=	---
3		4		12

Thus 1/3 equals 4/12. Now change 3/4 to twelfths.

3		3		9
---	x	---	=	---
4		3		12

As you see 3/4 equals 9/12 when you multiply both the numerator and denominator by 3/3.

It is now time to borrow because 3 and 4/12 minus 1 and 9/12 cannot be subtracted since the first fraction is less than the second fraction.

3	4		1	9
	---	-		---	=		---
	12			12

You will need to sometimes need to borrow when subtracting mixed numbers. The only time you need to borrow is when the top(first) fraction is less than the bottom(second) fraction. In this example 9/12 cannot be subtracted from 4/12. There will not be enough to subtract the second fraction from the first fraction.

3	4		1	9			?
	---	-		---	=		---
	12			12			12

It will be difficult to subtract 9/12 from 4/12 even though both fractions have the same denominator. Taking 9/12 from 4/12 cannot be done with being able to borrow.

You will have to borrow on this problem. To borrow first you must get a common denominator. This problem now has a common denominator. On the 3 and 4/12 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 4/12 will look like with its new name.

3	4		3-1	4+12		2	16
	---	=		---	=		---
	12			12			12

With 3 and 4/12 renamed as 2 and 16/12 so the subtraction can occur.

2	16		1	9		1	7
	---	-		---	=		---
	12			12			12

Now you may need to reduce the fraction in your answer. In this problem you will not need to reduce 7/12 in the answer 1 and 7/12.