Lesson video

Hello, my name's Miss Parnham.

In this lesson, we're going to learn how to add mixed numbers.

Let's look at this example.

Our fist step is to convert these mixed numbers into improper fractions.

So 2 3/4 is equivalent to 11/4, and 3 1/6 is equivalent to 19/6.

We can't add these fractions until the denominators are the same.

So the lowest common multiple of four and six is 12.

So rewriting these as equivalent fractions gives us 33/12 plus the 38/12, which sums to give 71/12.

Now let's convert that into a mixed number to give our final answer of 5 11/12.

In this example, we will convert these mixed numbers into improper fractions just like before.

Here, we have 88/15 and 23/6.

The lowest common multiple of 15 and six is 30.

So multiplying 88 and 15 by two, and multiplying 23 and six by five, gives us these equivalent fractions.

Adding 176 and 115 together gives us an answer of 291/30, which when we simplify this will give us 9 21/30.

But we're not quite finished because 21/30 can be simplified further as these are both multiples of three.

So the final answer should be 9 7/10.

Here are some questions for you to try.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

Notice in parts E and F, you needed to simplify.

So if you've got 6 9/12 and 9 12/15, they're mathematically correct, but you needed to cancel common factors on those fractions to get the simplified answers.

Here is a further question for you to try.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

There isn't a right or wrong answer here, but whichever method you prefer, you need to give some sound reasoning to back up your choice.

Let's look at some examples involving negative fractions.

Just as before, we need to rewrite these mixed numbers as improper fractions, so 9/4 plus negative 23/6.

And the lowest common multiple of four and six is 12, so rewriting them as equivalent fractions with the same denominator gives us 27/12 plus negative 46/12.

Now we can calculate that as negative 19/12 and then convert to a mixed number for our final answer.

In this next example, again, we convert the mixed numbers to improper fractions.

So negative 22/15 plus 25/6.

And the lowest common multiple of 15 and six is 30.

So rewriting them as negative 44/30 plus 125/30 then gives us an answer of 81/30.

Here we have 2 21/30, but you may have spotted that this will simplify further because 21 and 30 are both in the three times table, so the final answer is 2 7/10.

Here are some questions for you to try.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

Notice that D and F are negative answers.

With mixed numbers, we need to ensure that the negative sign is written in front of it.

Here is a further question for you to try.

Pause the video to complete the task, and restart the video when you're finished.

Here are the answers.

The greatest and lowest totals can be found in a different way as described in the last part of the question.

So, because addition is associative, you may have still got the same answer for the greatest, but perhaps you did 6 1/2 plus 5 3/4.

And for the lowest, you may have done 2 3/5 plus 1 4/6.

You would get the same greatest and lowest answers anyway, so that's fine.

That's all for this lesson.

Thank you for watching.