Adding and Subtracting Fractions With Unlike Denominators
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## How to Add and Subtract Fractions and Mixed Numbers With Unlike Denominators

When adding fractions with like denominators , we do two things:

2️⃣ Copy the denominator.

How do we add fractions with unlike denominators?

Some add the numerators, and then the denominators.

✖️ This is not how to do it!

To add fractions, they must have a common denominator.

Tip: common means the same.

So, how can we add two fractions with unlike denominators?

The trick is to rewrite each fraction as an equivalent fraction with a common denominator.

Tip:

Equivalent fractions are fractions that have different numerators and denominators, but the same value as the original fraction.

We can make equivalent fractions by multiplying both the numerator and denominator of a fraction by any number.

Tip: When we multiply by 4/4, it's the same as multiplying by 1, which doesn't change the number. We just make it easier to work with.

### Finding a Common Denominator

One quick way to get a common denominator is to multiply the denominators of both fractions.

We can then turn each addend into an equivalent fraction with this common denominator, 12!

That's a lot of words. 😅 Let's show you what that means with our example.

Let's start with the first addend, 3/4. How do we turn it into an equivalent fraction with a denominator of 12?

We ask ourselves what number can we multiply 4 by to get 12?

Tip: this is the same as asking what's 12 ÷ 4.

Yes, 3!

So we multiply the numerator by 3 as well.

We found an equivalent fraction.

We've turned the first addend, 3/4, into an equivalent fraction with our common denominator, 9/12. 👏

Next, we repeat the same steps for the second addend, 2/3.

We turn it into an equivalent fraction with a common denominator of 12.

We ask ourselves, what number times 3 gets 12?

It's 4! So we multiply the numerator, 2, by 4 as well to find our equivalent fraction:

Now we've turned the second addend into an equivalent fraction with our desired denominator, 12.

Finally, we can add the two fractions with common denominators:

### So, What Did You Learn?

To add fractions with unlike denominators, first find a common denominator, then turn each of those fractions into equivalent fractions with that common denominator, and then add them.

### Subtracting Fractions with Unlike Denominators

Subtracting fractions is just like adding fractions.

To subtract fractions, they must have a common denominator.

Let's turn each fraction above into an equivalent one with a common denominator of 10.

After switching to equivalent fractions, we're able to subtract.

Can we still simplify this fraction? 🤔

Not anymore.

3/10 is our final answer. ✅

Great work.

Mixed numbers are made up of whole numbers and fractions.

You can add or subtract mixed numbers by turning them to improper fractions first.

Improper fractions are fractions where the numerator is greater than the denominator.

Let's try it with an example:

We convert the mixed numbers to improper fractions.

To do this, we multiply the denominator of the fraction with the whole number part, and add that product to the numerator.

For example, to convert 2 1/4:

4 x 2 = 8
8 + 1 = 9

Then, just copy the denominator.

The addition now looks like this:

Then, you can turn each fraction into an equivalent one with a common denominator, as we did in the examples above.

Let's convert it back to a mixed fraction.

71/12 in mixed fraction is 5 11/12. ✅

Great work.

### Subtracting Mixed Numbers

Subtracting mixed numbers is just like adding mixed numbers.

We turn them into improper fractions first.

Let's practice.

We convert these into improper fractions.

The new subtraction looks like this:

Now, let's find the Least Common Denominator (LCD).

The denominators are 2 and 5.

So we start by listing multiples of 5.

5, 10...

Is 5 a multiple of 2?

No, it's not! ✖️

Is 10 a multiple of 2?

Yes, it is. ✅

10 is a multiple of 2. We can stop listing multiples because we've found the LCD.

Let's find equivalent fractions with the LCD.

The addition problem now looks like this

65/10 - 28/10 = 37/10

Let's convert it back to mixed number.

Excellent work, learning how to add and subtract mixed numbers.

Now, complete the practice.

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