﻿Hello again, I'm Mr Cannon. In our last lesson we were learning how to express fractions in their simplest form. I left you with this fractions to simplify. Did you have a go, what did you need to do? First you need to identify the highest common factor of the numerator and the denominator. Its quite easy for the fraction 7/28. Because I know that seven is a factor of 28 the denominator. So next I need to divide the numerator by seven and the denominator by seven. This gives me 1/4, which I know, is the simplest form of the fraction. Because its a unit fraction, Its abit tricky to identify the highest common factor for 4/14. Because I know four isn't a factor of 14. Seven is a factor of 14, its bigger than four so it can't be a factor. I'll try two 'cause I know that two is a factor of four and a factor of 14. I divide the numerator by two and the denominator by and I get 2/7. Now, I need to remember to check if 2/7 is the simplest form of the fraction. So we need to think are there any common factors for two and seven? Well, there is only one, so 2/7 must be in its simplest form. Remember when we simplify 4/14 to 2/7, we're preserving the proportional relationship between the numerator and the denominator. Size of the fraction doesn't change. 4/14 and 2/7 are the same points on the number line. Like we saw in the previous lesson. Sometimes the hardest placed fraction is the last part. Checking whether a fraction is in its simplest form. Lets practise that abit more. Here are some fractions. Lets look together and see if we can workout, how I should solve them into the Venn diagram. Straight away I'm thinking 3/15 is not in its simplest form. Can you think why? That's right, I've sported that three the numerator is a factor of 15 the denominator. So if I divide them both by three I'll get a unit fraction. Remember we can't simplify unit fractions any further. What about 9/17, nine isn't a factor of 17 and they are not in the same times table. In fact, I cannot think of any times table, where 17 is a product. Except the 1x17 times table and they don't help me here. So 9/17 is already in its simplest form. Lets look at 15/30, that isn't in its simplest form either. And there are a few different ways, I can think about this time. Firstly look at the vertical relationship. 15 is half of 30, so I know that I can simplify 15/30 to 1/2. I have also spotted that 15 and 30 are products in the same times tables. The three times table, the five times table. And finally the numerator 15 is a factor of the denominator. Now its your turn, pause the video and sort this fractions into the Venn diagram. Are they in their simplest forms or not. Did you have a go? I hope so. Lets see if you sorted this fractions in the same way that I did earlier. What about 5/15 did you spot that five is a factor of 15? The numerator is a factor of the denominator? What will that give us? That's going to be a unit fraction isn't it? Not in its simplest form. The next one was 16/28, abit trickier. 16 isn't a factor of 28, they do have some common factors. Two, one obviosly, four, four is going to be the highest common factor. So 16/28 is going to go into the "Not in it simplest form" circle too. Now 2/5, do I have to put 2/5 into one of the circles? Sometimes, when we use a Venn diagram, we put things on the outside of the circles. If they won't go into one of the sets. Can I put 2/5 on the outside? What do you think? But with this question its either in its simplest form or it isn't. So it has to go in one of the cicles. The highest common factor of two and five is one. So its already in its simplest form. And it goes here. Is that what you found? Okay, here is another challenge. My friend sorted this fractions earlier, but one of them is in the wrong place. Can you spot which one it is? Pause the video and have a think. We're going to use this sentence stems, to help explain our thinking. So you want to practise saying them either in your head or out loud. I'll start with the fractions, which I think are in the right places. 15/45 is not in its simplest form. 'Cause 15 is a common factor of the numerator and the denominator. 6/8 is not in its simplest form because two is a common factor of the numerator and denominator. So 9/24 is the one that's in the wrong place. 9/24 is not in its simplest form because three is a common factor of the numerator and denominator. Both nine and 24 are in the three times table. So lets move it to its correct place. In this lesson your practise activity will look like this. The fractions have already been simplified. You have to workout which numbers are missing. You'll need to look for the connections between numerators or denominators that have already been given to you. In the first example, we know that the numerator is one. But what's the denominator? I know to get from 12 to one, I need to divide 12 by 12. Remember, when we simplify, we are not changing the size of the fraction. So we need to keep that proportional relationship between the numerator and the denominator. I have to divide the denominator 36 by 12 as well. And that gives me a denominator three. The simplified fraction is 1/3. Pause the video now, have a go at the other two examples for yourself. What did you notice? Did you get the connections between the denominators in 21/28. 28 has been divided by seven to get four. So the numerator 21 must also be divided by seven which is three. 21/28 simplifies to 3/4. In the final example, you're already given the simplified fraction 2/3. So we need to work a little bit differently. The denominator 12 must have been divided by four, to give three in the simplified fraction. So I'll need to multiply the numerator two by four to give the missing numerator which is eight. Check it 8/12 is equivalent to 2/3. 8/12 simplifies to 2/3 highest common factor is four. The numerator and denominator could both be divided by four. Here are the practise activities, I want you to do the next time. Remember to look carefully for the connection to the proportional relationship between the numerator and the denominator stays the same. At the bottom there is a much trickier challenge for you to try. Thank you for your hard work in this lesson.

In this lesson, we will learn how to check whether a fraction is in its simplest form.

In this lesson, we will learn how to check whether a fraction is in its simplest form. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Lesson overview:Checking whether a fraction is in its simplest form

Core Content

Equivalent fractions: