Lesson video

Hello, my name is Miss Parnham.

In this lesson, we're going to be solving mixed fraction, addition and subtraction problems. The missing fractions from this addition grid are all unit fractions.

They have a numerator of one.

The shaded squares along the bottom contain the total of each column, and those on the right are the totals for each row.

Before we try to solve this problem, let's look at what happens when we add unit fractions.

In this example, we have 1/3 plus 1/4.

In order to add them, they need to have the same denominator.

So we rewrite them using the lowest common multiple of three and four, which is 12.

Adding those together, gives us 7/12.

Do you notice that seven is the sum of three and four? This has happened because in 1/3, the numerator and the denominator both had to be multiplied by four.

And in the 1/4, the numerator and the denominator both had to be multiplied by three.

And because the numerators are one, the four and the three crop up again.

So what happens is the numerator is sum of original denominators and the denominator is the product.

Looking at this example, the lowest common multiple of three and six is not their product of 18.

So when we have 2/6 and 1/6 together, we get 3/6 and we also can simplify that to 1/2.

So there's not much help here, when the fractions we are adding have a lowest common multiple that is not equal to their product.

So now let's look at the grid.

Do you notice that we have 35 as one of our denominators? 35 doesn't have that many factors.

Apart from 1/35, the only other two are five and seven.

So that would lead us to believe that the unit fractions being added together here are 1/7 and 1/5.

And if we add five and seven together, do you notice that we get 12? Now let's decide how to arrange them in that middle column.

Looking at the fractions down the right hand side, we have 10ths and 14ths.

So the fraction in the middle of the grid must be 1/7 and above that 1/5.

Now if we think of 1/5 as 2/10, then, the fraction in the top left hand corner must be 1/10.

So that when it's added onto 1/5, we get 3/10.

So the final gap that needs to be filled, if we consider 3/5 as being 6/10, then the missing fraction must be 5/10.

But no, it needs to be a unit fraction, but 5/10 will simplify to 1/2.

So that is a unit fraction and there's our final answer.

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.

I hope that the strategy we discussed helped you solve these problems more quickly than if you'd just use the trial and error method instead.

Let's look at a word problem.

White Rose United won 3/8 and lost 1/3 of their matches one season, what fraction of the matches did they draw? Whereas winning, losing and drawing are all the options, then all three fractions should sum to one.

So let's add to what we already know.

3/8 plus 1/3 must be rewritten with the lowest common multiple of eight and three as the denominator.

So 9/24 plus 8/24 is 17/24.

So 17/24 of the games were either won or lost, so the rest must have been drawn.

So if we subtract this from one, it means that 7/24 were drawn.

Now let's look at some sequences of fractions, and see if we can work out the next term.

Here we have 1/4, 3/8, 1/2, 5/8, 3/4.

It's going to be easier to rewrite these fractions with a common multiple.

And the lowest common multiple of all these denominators is eight.

So that's 2/8, 3/8, 4/8, 5/8, 6/8.

Of course, we can see a pattern.

The next fraction is going to be 7/8.

Let's look at a decreasing sequence.

We have 1/2, 3/10, 1/10, negative 1/10, negative 3/10.

Let's rewrite these fractions all as tens.

You may have noticed the pattern.

We have five, three, one, negative one, and negative three.

So the next one would obviously be negative 5/10.

But guess what? This will simplifying, so that's negative 1/2.

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.

Hopefully writing the sequence of fractions in part A, all as tens, helped you to see that this is a sequence increasing by 1/10 each time.

And in part B, writing every fraction in the sequence as twelves, helped you to realise that this was decreasing by 3/12 or 1/4 from term to term.

Here's 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.

Probably the most challenging question on here is two 2/5 subtract negative one and something.

And to find that number by subtracting one and 3/4 from 2/5, will need you to make both into 20ths.

So you're going to need to change both denominators.

Let's solve this problem.

If we're told that the mode is one and 2/5, it means the most frequent value is one and 2/5.

So that's what's missing from both of these cards.

We're asked to find the total.

We can add these numbers up until they have the same denominator.

So the lowest common multiple of four, 10, and five is 20.

So rewriting these as improper fractions with the same denominator, all sums to 97/20.

But let's keep that as a mixed number, which is four and 17/20.

The range is the difference between the largest and smallest values.

The largest value is one and 2/5 because 2/5 is bigger than 3/10, because 2/5 is equivalent to 4/10.

And the smallest value is the only fraction we see here, 3/4.

So because we worked out the equivalent fractions with the same denominator before, we can use them again to find the answer of 13/20.

Here's a question for you to try.

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

Here are the answers.

You will recall that mode means most frequent.

So that means the missing data from Friday is going to be two and 1/2.

And the range is the largest value subtract the smallest.

And for the final part of the question, you should have calculated how far in total Amir had walked and you should have got 19 and 43/60.

So that's why the answer is five and 17/60.

That's all for this lesson.

Thank you for watching.