Lesson video

Hello! My name is Ms. Parnham and in this lesson we're going to learn how to subtract mixed numbers.

Subtracting mixed numbers follows the same rules as subtracting fractions.

Let's take a look at an example.

The first step is to rewrite these mixed numbers as improper fractions.

So 15/4 subtracts 7/6.

Now we need to look at the denominators and determine the lowest common multiple.

This is 12.

So we rewrite these fractions as 12ths.

45/12, subtract 14/12, is 31/12.

But this is an improper fraction, so we rewrite this as a mixed number of 2 and 7/12.

In this next example, we start by converting the mixed numbers to improper fractions and then we find the lowest common multiple of 15 and 6, which is 30.

So these can be rewritten as equivalent fractions of 172/30, subtract 115/30.

This gives us an answer of 57/30.

But this is an improper fraction, so we rewrite this as a mixed number of 1 and 27/30.

But that's not quite the final answer, because 27/30 can be simplified further.

So the final answer is 1 and 9/10.

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.

Did you notice that the last two parts of this question could be simplified? So in part E, if you have 1 and 3/12 and for part F, if you have 3 and 6/15, then you're mathematically correct, but you need to cancel common factors in the fraction parts of these numbers in order to get your answer as simple as possible.

Here is another question 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 Jack made a little mistake.

He either assumed that subtraction is commutative, or he missed the sign of the fraction and it meant that his answer is incorrect.

Now let's look at an example involving negative mixed numbers.

Just like before, we need to convert these mixed numbers into improper fractions.

So we can rewrite these as as 9/4 subtract -7/6.

The lowest common multiple of 4 and 6 is 12, so we rewrite this as 27/12 subtract -14/12.

This gives us an answer of 41/12.

This is an improper fraction, so we convert it to a mixed number, 3 and 5/12.

In the next example, just like before, we convert these mixed numbers to improper fractions.

So we have -22/15 subtract 29/6.

The lowest common multiple of 15 and 6 is 30.

So rewriting these as equivalent fractions of 30 gives us -44/30 subtract 145/30.

This is -189/30.

This simplifies to -6 and 9/30, but this can be simplified further because 9/30 is equivalent to 3/10, so this is -6 and 3/10.

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.

In part E and F, you do need to simplify, so if you had 6 and 4/12 for part E, and for part F, -7 and 55/60, they're mathematically correct, but by cancelling common factors in the fraction parts of those numbers would mean that you could get your answer as simply as possible.

Here are some further questions for you to try.

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

Here are the answers.

You need to take extra special care with questions like number five, as one mistake can lead to a chain of errors, as each solution relies on the one before it being correct.

That's all for this lesson, thank you for watching.