Calculate:

Subtracting Fractions

﻿Hi, welcome to today's math lesson with me Ms. Jones. Hope you're feeling ready for today's lesson. I certainly am. I'm ready to go. So let's find out what we're going to be doing today. In today's lesson, we'll be adding fractions where our total is greater than one. Start off by adding onto one whole and adding fractions that's greater than one whole. You've got an independent task and the quiz. You'll need today a pencil and piece of paper. Pause the video now to going back what you need and then come back. If you've got everything, let's get started. I've got a starter to warm our brains up here, complete the diagram so that each row and column of three add up to 180. Pause the video now time to go. Let's have a look at this together. So we know that each row and each column needs to add it to 180. I know that rows mean anything going across column anything going down like this. So, I'm looking at this row here to start with. The reason I've chosen this row to start is because I've already got two of my parts, so I can work out my third part. In some of the other rows and columns, it seems like for most of them, I only have one part. This is a really good starting point. So, I've got 50 and 60, which total to 110. I know that if I add 70, I total to 180 that's check. 50 and 70 together make 120. I know that because I know five and seven make 12, so I'm using my known fact. 120 added to 60 makes 180. Once I've worked at this row, I can use that to fill in any other columns. If anyone was stuck with how to start this, you can always pause again and finish it off. Because now I can see in this column, I've got two parts so I can work on my third part. 70 and 30 I know make 100 because I know my bonds, 7 and 3 make 10, 70 and 30 make a 100. So this one needs to be 80. Now we get to little bit more tricky as I've got a column here for then with two unknown parts. I've got a row here to fill in with two unknown parts. But I know that all of these need to make 180. So you might need to use a little bit of trial and improvement here. Well, let's have a think about what we need. We need 50 and something. Now I know that this is 20 more than this one, which is interesting. Let's try putting in a value. If we have 60 here, I know that 60 and 30 make 90. So here I will need another 90. Here for 60 and 50, which we know that here I've already used this fact 50 and 60, I knew that the missing part was 70. So if it's 70 in here, it should work. Now it looks like they could have been more than one way to work this out. This value might have been something else in your version which might've resulted in a different value here and here. Make sure that each row and column add up to 180 though to check your correct. Adding to one whole, what needs to be added to make one whole? Well, we can use our denominators here to help us think about this answer. We're working in thirds here, but here we've got our answer written as an integer. If we write one whole in terms of thirds, that might make it a little bit more clearer to us. One whole is equivalent to 3/3. So now we've got 1/3 added to something is equivalent to one whole or 3/3. Here's a palm model to help us think about this. So our whole is one. We've got 1/3 as our part, so we need to think about what our missing part is. I put in 3/3 which we know is equivalent to one whole. We can see that our missing value here is 2/3. 1/3 added to 2/3 is equivalent to one. I'd like you to have a go at these ones. What needs to be added to make one whole? Pause the video now to try this. Hopefully you've had a quick go at those. Remember, you can use a bar model or a fraction bar to help you work these out. And also think about how many of the denominator that you're using. So for the 4/5 would be equivalent to one whole. So for the first one, I know that one whole is equivalent to 5/5. So, I'm missing amounts here or I'm missing part needs to be 1/5 because 4/5 added to 1/5 will make 5/5 which is equivalent to one. Here, I know that in terms of 12ths, one whole is equivalent to 12/12. So our missing part is 2/12. 10/12 added to 2/12 is equal to 12/12 or one whole. Here, I know that in terms of ninths, one whole is equivalent to 9/9. So our missing part is 7/9. 2/9 added to 7/9 is equivalent to 9/9 or one whole. I'd like you to have a go at a few more and just say these out loud for me, use the sentence them hmm plus hmm is equal to one whole. Pause the video now to have a go. Hopefully you've had a go at saying those sentences, so 2/5 added to 3/5 is one equal to one whole. 1/9 added to 8/9 is equal to one whole. And 3/7 added to 4/7 is equal to one whole. Bullets about adding fractions which total greater is than one whole. Here we've got 3/6 added to 5/6 is equal to? How do I know that our answer is going to be greater than one? Well, we know that one would be equivalent to 6/6, and three and five is going to total more than six. Lets have a look at a bar model to try and make sense of this. So I've got one whole here and I know that our first part is 3/6 which I've marked here. 3/6 is equivalent to half so they take up half of my whole. Then I'm going to add 5/6. So what we can see here is all together we have got 8/6. And if we were to write this as an improper fraction, we could write it like this. But how about if we wanted to write it as a mixed number? Well, we know that 6/6 are equivalent to one whole. So we could replace 6/6 with one. And you can see from this diagram that we could also write our answer as one and 2/6. Both of these are correct. Sometimes the question might ask you to write you answer as an improper fraction. And sometimes it might ask you to write your answer as a mixed number. So you need to know how to do both or convert one to the other. Let's think about how we got to our mix number here. We thought about how many sixths are in one whole, which we knew was 6/6 and then what was left over which was 2/6 has been put as a numerator here. Let's have a look at one more. 7/8 added to 6/8. Well, if we wanted to write this as an improper fraction, our denominator stays the same and we can add together our numerators, seven plus six is equal to 13. 7/8 added to 6/8 is equal to 13/8. But what if I wanted to write this as a mixed number? Well, I know that 8/8 make one whole. Here we have 13/8 which is equivalent to 8/8 one, plus another 5/8. So we're thinking about how many eights are in 13 and how many are leftover and that becomes our numerator. It's time for your independent task. I'd like you to have a go at these which all have a total of one or more. Now I'd like you to write your answer as an improper fraction and a mixed number. Once you finish come back to the video. Hopefully you've had a chance to complete your task. Let's go through the answers. Write you answer as an improper fraction and a mixed number. So we had 5/6 added to 2/6 is equal to 7/6 or one and 1/6. 7/8 added to 6/8 is equal to 13/8 or one and 5/8. 2/3 added to 2/3 is equal to four thirds or one and 1/3. 3/4 added to 3/4 is equal to 6/4 or one and 2/4. You might've also said one and a half. 5/7 added 6/7 is equal to 11/7 or one and 4/7. 4/5 added 3/5 is equal to 7/5 or one and 2/5. How did you do? If you got any wrong, do not worry. Just have a look at the answer and see if you can spot where you went wrong for next time. Once you're done, it's time to complete the quiz. Thanks very much. Take care and bye bye.

What is the sum of the fractions?

What is the total?

Adding Fractions (With a Total Greater than One)

In this lesson, we will explore fractions that total one or greater than one using fraction bars to support understanding.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Adding fractions (with a total greater than one)

Fractions

Number

THEME

UNIT

Recognising fractions as different representations

Calculating unit fractions of quantities

Recognising  equivalent fractions

Recognising equivalent fractions (2)

Calculating non-unit fractions of quantities

Equivalent fractions

Fractions and division

Comparing fractions

Ordering fractions

Using mixed numbers

Using improper fractions

Converting mixed numbers into improper fractions

Adding fractions (up to one whole)

Subtracting fractions

Subtracting fractions (2)

Comparing non-unit fractions of quantities

Reasoning with fractions

Which representation shows three quarters?

What does the denominator tell us?

What does the numerator tell us?

How else could I write five halves?

Which is greater?

What mixed number is being represented?

What improper fraction has been represented?

A packet of paper has 261 sheets. Two thirds of the packet has been used. How much paper is left?

Lesson overview:Adding fractions (with a total greater than one)

Core Content

Fractions: