When subtracting fractions with different denominators, we follow the same process we used for adding unlike fractions. But since everybody doesn’t start with addition, we provide the same level of detail for subtraction.
First of all, when subtracting fractions with different denominators, the first step in the Rule says that we must change these fractions so that they have the “same denominator“.
Here are the steps for subtracting fractions with different denominators. We will break-down each step just like before to make sure you’ve got it. Then we will subtract some tougher numbers. And finally, we will help you pull everything together. Okay!
So, here are the steps.
- Build each fraction so that both denominators are equal. Remember, when subtracting fractions, the denominators must be equal. So we must complete this step first. What this really means is that you must find what is called a Common Denominator. Most of the time you will be required to work the problem using what’s called the Least Common Denominator (LCD). In either case you will build each fraction into an equivalent fraction.
- Re-write each equivalent fraction using this new denominator
- Now you can subtract the numerators, and keep the denominator of the equivalent fractions.
- Re-write your answer as a simplified or reduced fraction, if needed.
But keep in mind, if you are doing homework, be sure to answer the problems in the form asked for in the assignment.
Okay let’s start with…
The Basics for Subtracting Fractions with Different Denominators
Subtract: 1/2 – 1/3
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Notice that the overall size of our point of reference
(The Whole) is EXACTLY the same.
Step #1 in our rule tells us that the denominators must be equal. And the easiest way to find a common denominator is to just multiply the denominators.
So let’s do that now…
2 x 3 = 6
The Common Denominator for 1/2 and 1/3 is 6
Step #2 – Re-write each equivalent fraction using this new denominator.
Since…
1/2 is equivalent to 3/6
And…
1/3 is equivalent to 2/6
We re-write our equation to read…
Subtract: 3/6 – 2/6
Now we are ready to do Step #3 – Subtract the numerators, and keep the denominator of the equivalent fractions (which is 6).
So, we end up with…
3/6 – 2/6 = (3 – 2 )/6 = 1/6
–
=
Finally, Step #4 – Re-write your answer as a simplified or reduced fraction, if needed.
In our example, the answer (1/6) is already in its simplest form. So, no further action is required!
That’s It!
A quick and easy way to subtract fractions with different denominators.
Remember, always show your answer in the form asked for in your instructions.
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