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Fractions

Subtraction

Think for a moment about a pie divided into 12 equal pieces. Each piece is 1/12. If we take some away, to find out how much pie we have left, we subtract the number of pieces taken from the original amount.

77 over 125 over 12= 2 over 12

7/12 − 5/12 = 2/12 = 1/6.

To subtract two fractional numbers with the same denominator, we simply subtract the numerators and keep the same denominator.

          a/b - c/b = (a-c)/b

Example

7 over 8 minus 3 over 8 equals 4 over 8 equals 1 over 2

If the pieces of the pie are of different sizes, we have to cut our pie into smaller equal sized pieces so we can subtract them. Consider having one piece that is 11/12 and another that is 2/3. We can divide each piece into 1/12-sized pieces. Then they are easy to subtract.

11 over 122 over 3= 1 over 4

11/12 − 2/3 = 11/12 − 8/12 = 3/12 = 1/4

 

Subtraction of two fractional numbers with different denominators can be carried out in a manner similar to addition.

Method 1: a/b - c/d = (a*d - b*c)/(b*d)

Method 2: Use the LCM as with addition.


Examples

1/9 - 1/12 = (1*4)/(9*4) - (1*3)/(12*3) = (4-3)/36 = 1/36

7 over 9 minus 3 over 8 equals 56 over 72 minus 27 over 72 equals 29 over 72

More Examples

 

Exercise

Now try a few of these exercises. These involve only positive fractions. Reduce your answer if possible. Practice makes perfect!

       

Working space

 

Answer

       


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Subtraction of Signed Fractions

When you have mastered positive fractions, it is only a small step to extend your prowess to both positive and negative fractions. Just as for adding, we simply carry the sign with the numerator. The rest of the method is the same. You will need to be competent at subtracting signed numbers before you tackle signed fractions.

If a/b > c/d then a/b - c/d is always positive.   If a/b < c/d then a/b - c/d is always negative.

 

Examples

2/5 - 7/5 = (2-7)/5 = -5/5 = -1

2/3 - 4/5 = (2*5 - 3*4)/(3*5) = (10-12)/15 = -2/15

More Examples

Exercise

       

Working space

 

Answer

       


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