LI: I can simplify fractions
Today you shall be simplifying fractions to their simplest form using a numbers factors.
What we need to know
- Use your fraction wall to investigate fractions. When we simplify a fraction do we move up or down the fraction wall. Can you spot any patterns when the denominator is a multiple of the numerator?
- A common factor is a factor that can be exactly multiplied into both the numerator and he denominator, for example: a common factor of 4/6 is 2 as it exactly goes into 4 and also 6.
- We can use the common factors of the numerator and denominator to simplify fractions. We can do so by dividing both the numerator and denominator by the common factor. In our previous example if we divide 4/6 by the common factor of 2 then we find a simplified fraction of 2/3.
- What are the common factors of 5/10? What about 14/21?
- Simplify fractions to their simplest possible form using the common factors of the denominator and numerator.
LI: I can represent fractions on a number line.
Today you shall be showing whether a fraction is larger or smaller than another through the use of number lines.
What we need to know:
- To compare and order a set of fractions we can use the numerators when the denominators are the same. This is because we only need to identify whether the numerator of the fraction is larger or greater than the other, for example: 7/10 is greater than 4/10 as the numerator is larger and the denominators are the same.
- What about if the denominators are different however? In this instance, we shall need to make the denominators the same as each other in order to compare them. To do so we can use common factors or multiples of both denominators and divide or multiply by that number to modify the fractions.
- For example, if we were comparing 3/5 and 4/10, we know that the denominator 5 is a factor of 10 so we can alter the 4/10 to make the denominator 5 which will let us compare the two fractions.
- To do so we must divide 4/10 by 2. If we divide the denominator by 2 then we must also divide the numerator by 2.Therefore, 4/10 becomes 2/5. This can now be compared with 3/5.
- Place mixture of proper and mixed fractions on a number line to order and compare them.
LI: To be able to compare and order fractions with differing denominators.
In order to successfully complete this lesson, you should familiarise yourself with the process of simplifying a fraction to an equivalent. You should also revise your knowledge of common factors and multiples of a number. Use the video 'Simplify Fractions' on the link below to help you:
- Study the fractions: 5/8 and 3/5. Which is larger?
- At this point we would find it difficult to compare the two as their denominators are different!
- When we have completed the calculation and changed the denominators, we discover that 25/40 > 24/40. But how did we get this answer? What do you notice about the original denominators and the new denominators?
- They've both been multiplied by the other!
- Let's explain. 8 and 5 have common multiples which we can use to make the same denominators. The lowest common multiple of 8 and 5 is 40. This is what both denominators must become to then compare them.
- For 5 to become 40, we multiply by 8 and for 8 to become 40, we multiply by 5. Simple so far!
- But the numerator has also grown. But how?
- They've also been multiplied by the same number that their denominator was multiplied by! so 5/8 x 5 = 25/40 and 3/5 x 8 = 24/40.
- Now we are able to compare them!
- Try using the same method to compare these two fractions: 7/6 and 6/5.
- Complete the activity sheet by altering the denominators so that they are both the same and multiplying the numerator by the same number you used to multiply your denominator. Then compare the fractions to show which is greater and which is smaller.
LI: To be able to enhance my understanding of comparing fractions.
In this lesson, you shall further practice the use of comparing fractions but this time you shall also put more practice into studying the numerators. You will need a fraction wall to help you with your activity which is provided in your learning packs.
- How do you compare the fractions 4/7 and 3/4? Refer back to your last lesson of learning.
- Today, we are comparing fractions slightly differently. In some cases the lowest common multiple of the denominators are a very large number and would take a lot of time to work out. In these instances, we can use the lowest common multiple of the numerator instead.
- Look at the two fractions below:
6/11 and 3/5
- You will notice that the lowest common multiple of these numbers is rather high (55). It can be solved an alternative way which shall require far less multiplication. we know that 6 is in the 3 times table (3x2) so we can simply make the numerators the same instead. We must also remember to multiply the denominator by 2 as well.
- We therefore get two fractions: 6/11 and 6/10. Using our fraction wall to help us. We can see that the larger the denominator, the smaller the pieces of the fraction actually are. Therefore 6/11 < 6/10.
- Use the same technique to compare the fractions below:
- 5/7 and 15/19.
- When confident, apply what you have learnt about comparing fractions through their denominators or numerators to solve the problems on the activity sheet.
LI: I can add and subtract fractions with different denominators.
Before beginning this lesson, refer back to this weeks learning so far. Recall how you have compared fractions through converting their denominators to the same value and what you have had to do to the numerators when you have done this.
- Watch the following video to learn more about adding and subtracting fractions:
- Now that you have watched the video, apply what you have learnt to solve:
3/10 + 2/5
- How did you get on? Can you explain what you did to solve the question?
- Did you get any of the following answers: 5/15; 7/10 or 5/10?
- Let's check which was correct.
- To solve the question, both the denominators should be the same. We can multiply 2/5 by 2 to make the denominators the same.
- 2/5 x 2 = 4/10 as we also need to multiply the numerator.
- Now we have the question 3/10 + 4/10. We then add both the numerators together but do not add the denominators together.
- This gives us the answer of 7/10.
- Try doing the same for the following questions:
1) 7/9 - 1/3
2) 2/5 + 1/8
3) 9/11 - 3/7
- Move onto your activity sheet when confident.
LI: To be able to add mixed number fractions
Watch yesterday's video link from White Rose explaining how to add and subtract fractions with different denominators. You will be using this skill again, but enhancing it further through the use of mixed numbers.
- Before you begin, explain to somebody else what a mixed number is when we talk about fractions. What does it represent? Can you give an example of a mixed number?
- How could we also show a fraction that is larger than a whole but not as a mixed fraction?
- Considering what you have learnt from the video and yesterday's lesson. Attempt to solve: 1 whole and 1/3 + 1 whole and 3/8
- You could show the fractions as part of a bar graph like below to help you with your working out.
- We know that 1 whole add 1 whole makes 2 wholes, which we can see in the bar graph. But now we have to solve 1/3 + 3/8.
- To solve 1/3 + 3/8, we need to refer back to yesterday's learning of making the denominators the same. To do so we must find the lowest common multiple of 3 and 8. We can do so by multiplying the fraction by the other's denominator.
- 1/3 x 8 = 8/24 3/8 x 3 = 9/24
- So 8/24 + 9/24 = 17/24 but don't forget the 2 wholes!
- 1 1/3 + 1 3/8 = 2 17/24
- Use the same method for the following question:
1 1/4 + 2 2/5
- When complete, move onto your activity sheet.
Awards we have received so far.