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Hello, my name is Miss Parnham.

In this lesson, we're going to be adding and subtracting fractions less than one.

In this lesson, you will need to know how to find equivalent fractions.

So if that is something you are unsure of, then work through those lessons first.

Let's have a look at this example.

We must write fractions with the same denominator before we can add or subtract them.

So in this case, 10 is a multiple of five.

So we can convert 2/5 into tenths and then we're able to solve.

So 2/5 is equivalent to 4/10.

7/10 subtract 4/10, gives us 3/10.

In this addition, 15 is a multiple of five.

So we can write 2/5 as 15nths.

2/5 is equivalent 6/15.

6/15 add 4/15 equals 10/15.

But here we have a common factor of five for the numerator and denominator, so we can simplify to 2/3.

In this example, four and six both need to be changed to find a common multiple and the lowest one is 12.

So we can rewrite them as 9/12 and 2/12 respectively.

Adding them together gives a final answer of 11/12.

In the final example, we have 31/45 and 3/10.

The lowest common multiple here with the denominators is 90.

So we can rewrite that as 62/90 subtract 27/90, that gives us 35/90.

But you've probably spotted that these are both multiples of five, so cancelling that common factor gives us a final answer of 7/18.

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 part e and part f needed you to simplify? So if you did get 8/12 for part e, you were nearly there, and 25/60 for part f, you were so close, but they needed to be simplified by cancelling common factors.

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.

Part c really needed you to do three things; First of all know what the range is and then be able to ascertain which is the smallest fraction, which is the largest fraction and then finally finding the difference between them.

So you probably already know that 1/3 is greater than 1/4.

So when comparing 1/4 with 2/9, you can think of 1/4 as 2/8 and then that's obviously greater 2/9.

So 2/9 is the smallest because you probably already realised that 5/12 is the greatest because it's only 1/12 less than 1/2.

Let's look at some examples involving negative fractions.

In this example, we need to change the fifths into tenths on the second fraction.

So 7/10 subtract negative 4/10 gives us 11/10, but this is an improper fraction, and we need to write it as a mixed number.

So think of it as 10/10 plus 1/10, which is of course one and 1/10.

In this example, we need to change fifths into 15ths for the second fraction.

So negative 7/15 plus 12/15 is 5/15.

But we can simplify this fraction further by dividing numerator and denominator by five, and therefore the final answer is 1/3.

In this next example, the lowest common multiple of nine and four is 36.

So we need to rewrite these fractions as 36ths.

Negative 32/36 plus 27/36 gives us negative 5/36.

Notice how the negative sign is at the front of the fraction.

You could also write the fraction with either the numerator or the denominator prefixed with a negative sign.

In this example, the lowest common multiple of six and 15 is 30.

So rewriting as 30ths gives us 25/30 subtract 28/30, which is negative 3/30.

Notice here we have the negative sign on the numerator.

This will simplify further to negative 1/10.

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.

Some of the questions have mixed number solutions.

If you gave it as an improper fraction, you were so close.

So part a, if you got 11/9 you were nearly there.

Part c, 23/20 and part f 17/16.

You just needed to make sure that you made those into mixed numbers.

And notice there were a couple of negative solutions there.

If you place the negative sign in front of either the numerator or the denominator, one or the other, that can still be marked right.

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.

Did you notice with a question like question four, if you make one mistake, it leads to other mistakes because every solution builds on what you've already discovered previously? That's all for this lesson.

Thank you for watching.