Subtracting Unlike Fractions

Example:  Subtract 4/8 - 1/10 then reduce your answer.

Step 1.  You have to find like denominators.  So find the Least Common Denominator for 8 & 10.  8 and 10 both go into 40 so I will use that as my new denominator.

Step 2.  Change the numerators.   In my denominator, 8x5=40 so I have to take my numerator also by that number, 4x5=20 so 4/8=20/40. In my other fraction I took the denominator 10x4=40 so I have to take my numerator 1x4=4 so 1/10=4/40.

Step 3.  Now that I have the same denominators, 20/40 -  4/40, I can simply subtract my numerators 20-4=16.  I keep the same denominator so my difference is 16/40.

Step 4.  The problem said to reduce my answer so I see that both 16 & 40 can be divided by 4.  So my reduced answer is 4/10.  This can still be reduced by dividing by 2 so it is reduced to 2/5.  So my final answer is 4/8 - 1/10=2/5.

You can do the same thing when subtracting unlike Mixed Numbers.

Example:  Subtract 40& 4/5 - 12 &2/3 then reduce your answer.

 Step 1.  You have to find like denominators.  So find the Least Common Denominator for 5 & 3.  5 and 3 both go into 15 so I will use that as my new denominator.

Step 2.  Change the numerators.   In my denominator, 5x 3=15 so I have to take my numerator  by the same thing, 4x3=12 so 4/5 turns into 12/15.  In my other denominator, 3x5=15 so I have to take my numerator 2x5=10 so 2/3 turns into 10/15.

Step 3.  Now that I have the same denominators, 12/15 - 10/15, I can simply subtract my numerators 12-10=2.  I keep the same denominator so my difference is 2/15.

Step 4.  Now I need to go back and subtract my whole numbers from the original problem.  40 – 12= 28.

Step 5.  Combine the whole numbers with your new fraction. Go back and find your remainder fraction which was 2/15 and add that to your whole number.  28& 2/15 is your answer.

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Updated on January 20, 2010