How to Add and Subtract Fractions

Common Questions

Can I add/subtract fractions with different denominators?

Yes! But it takes a couple steps, check out our guide below.

Common Questions

When we add or subtract fractions, we need to remember two rules:

  1. We can only add and subtract fractions if the denominators (the bottoms of the fractions) are the same.
  2. When we add/subtract, we only add/subtract the numerators. The denominator stays the same 😎.

Let's think about why these rules are true. Pick two fractions with different denominators to add or subtract.

Cool, we can use a circle to imagine this problem. One full rotation represents 1, and since our first fraction is -, we'll divide the circle into equal sections.

Nice job! Now, what fraction of the circle is filled-in? Hint: Divide the number of filled-in sections by the total number of sections.

Exactly! Let's go over what happened here. We started with this equation:

Both our fractions have the same denominator: . This is like dividing a circle into equal sections. Our first fraction then represents out of sections, and our second fraction represents out of sections.

So, you can see in our circle above, out of sections are filled-in, representing our first fraction . out of sections are purple, representing our second fraction .

Because our sections are the same size, we can them for a total of 0 out of sections.

Similarly, looking back at our equation, we can see that by subtracting the numerators and keeping the denominator the same, we also get:

If that all makes sense, scroll back up and try two fractions with different denominators.

So, remember, you always need the denominators to be the same to add or subtract, and to make them the same, you might need to multiply each fraction by different numbers.

It's kind of like the difference between equity and equality.

Equality means giving everyone the same resources.

Equity means giving everyone the different resources they need to get to the same place.

If one denominator is 3 and the other denominator is 4, to get them both to the same place, we need to multiply 3 by 4 and 4 by 3. This is equity. Equality would be multiplying them both by the same number, which would still leave us with different denominators.

Nice! So let's review the steps.

  1. Check if the denominators are the same. If they are, skip to step 3. If they aren't, go to step 2.
  2. We need to make the denominators the same, and the easiest way to do this is multiplying the first fraction by the second denominator and multiplying the second fraction by the first denominator. Let's look at an example:
  3. When we have the same denominators, or total number of sections, we add the fractions by adding the numerators, and we subtract the fractions by subtracting the numerators:

That's it! Just remember these three steps and you're good to go 🥳!