What improper fraction has been represented?

Using Improper Fractions

﻿Hello, it's Miss Jones here, ready for today's maths lesson. Hope you're feeling good and ready to start. Let's have a look at what we're going to be doing today. In today's lesson, we're going to be converting mixed numbers into improper fractions. We're going to start by using representations to connect mixed numbers with improper fractions, then you've got an explore task, then we're going to think about how we can use multiplication to convert mixed numbers into improper fractions, finally, you've got your main task and your quiz. Before we get started, let's think about what we need. You need something to write with and something to write on, such as a pencil and piece of paper, you might also want to use a ruler today to help you draw number lines, but if you haven't got one, don't worry, you can sketch them. If you need to, pause the video now. If you've got everything you need, let's get started. To start with today, we've got something to warm our brains up. Which square has exactly half shaded blue? Pause the video now to see if you can explore this. Okay, let's have a look together. So we know what one half means, one half means the square needs to be split into two equal parts, so we need the same amount shaded blue as there is white. Now looking at this, we can see there are nine smaller squares all together, five of them are shaded blue, and four of them are white, so here, this is not shaded in blue because there is more blue than white. However, this one, we can see that exactly half the square is shaded white, half the square is shaded blue, so this one is shaded in half, half blue, half white. This one is also shaded in half, half blue and half white. These two are not, let's have a look why. Well, you might need to count the squares or the half squares in order to work this one out. I can see that one, two wholes are shaded blue, and then these two make another whole, three, four, five are shaded blue, which is more than half. In this one, you've got one whole shaded blue, then these two make another whole, one, two, three, four are shaded blue, which is less than half. So the only two that were shaded in half were the two I've ticked here. Okay, here I have a mixed number, one and three quarters. How do I know it's a mixed number? Well, because it's written as an integer plus a fractional part. I can represent that mixed number using some fraction bars, here. This green bar represents one whole, and this green bar underneath it represents three quarters. Now, when I'm thinking about a mixed number, I'm thinking about how many wholes there are, we have one whole, and then we have a fractional part. Now if I wanted to think about this as an improper fraction, instead of thinking about how many wholes there are, I need to think about how many parts there are, or how many quarters there are. So to do that, I can divide all of this into quarters, including my whole. So I've divided my whole into four quarters, and then I've still got three quarters underneath, so how many quarters do I have all together? We could say that we have four quarters, from the whole number, plus three quarters underneath, so all together we have seven quarters, this is an improper fraction where the numerator is greater than the denominator. We could then write our equation at the top, one and three quarters is equivalent to seven quarters, this is our improper fraction, and this is our mixed number. So let's think about what we did there, we thought about how many quarters were in our whole, which were four quarters, and then added them to the numerator, three quarters. Let's look at another one, this time we've got two and two fifths. Now we can represent that, again, with our fraction bars, here I've got my two wholes, and here I've got my two fifths. But if we wanted to represent this as a mixed number, what might we need to do? Well, we could think about how many fifths we have all together by dividing our wholes into five parts here. So here we have five fifths in one whole, so in two wholes we have 10 fifths plus our fractional part as well. So, if one whole is equal to five fifths, two wholes would be equal to 10 fifths. We have our 10 fifths, which is from our whole number, number two, then we add on our fractional part, which we can see in our numerator here, all together we have 12 fifths. Two and two fifths is the same as 12 fifths. It's time for your let's explore task, I'd like you to have a go now at converting these mixed numbers into improper fractions. Draw or use fraction bars to represent each one to show your thinking, and explain why they're equivalent. Now to help you, use these questions, think about, firstly, how many parts are in the whole? Then, how many parts are in the fractional part? And then add those together, how many parts all together? Okay, off you go, have a little explore, and then we'll have a look at them together. Okay, let's go through these. As we're doing so, I want you to think about, were you using multiplication as you were working out these improper fractions? Okay, one and three quarters is equal to seven quarters, so that would be four quarters added to three quarters. Two and four fifths is equal to 14 fifths. Three and two thirds is equal to 11 thirds. Two and one third is equal to seven thirds. And three and one half is equal to seven halves. Let's go back to my question, where did you use multiplication? Hmm, well looking at this last one, to work out three and a half we needed to think about how many parts were in three. Now we needed to do three lots of the whole, so three lots of two parts, so you could have said that we multiply this whole by our denominator, and then added on the fractional part. Let's have a look at that in another example. Okay, here I've got another mixed number, two and three quarters, and I'm going to convert it into an improper fraction. So I need to think about how many parts are in the whole, and then add on the number of parts in my fraction. I can use a representation, which I've got here, two wholes and three quarters. Now, first of all we need to work out how many parts are in the whole, so I'm going to divide all of this into quarters, I know that in one whole there are four, but in two wholes there are eight, I'm multiplying the whole number, number two, by the number of parts, number four. Two times four is equal to eight, there are eight parts in my integer, in the whole number, but then I need to add on the fractional part, I've got three more parts here, so I add on the three, and all together I have 11 parts, I have 11 quarters all together. So, we multiply the whole number by the denominator, the amount of parts, two times four, and then we added on the numerator, three. Let's look at another example, three and four fifths, which we can represent like this. So, we need to first of all think about how many parts we have all together to work out the improper fraction, then we need to multiply the whole by the number of parts, and then add on the fractional part, in other words we need to work out how many parts are here, where we have three lots of our denominator, five, and then add on these parts, which are four parts. All together we have three lots of five, which is 15, added four, which is 19 parts. Three and four fifths can be written as 19 fifths. For your independent task, I'd like you to have a go at converting the following mixed numbers into improper fractions, you can use fraction bars if you want to show your thinking, but I'd also like you to think about using our multiplication rules as well, multiply the whole number by the number of parts and then add on the fractional part. Pause the video now to have a go at your task and then come back and we'll look at the answers. Okay, hopefully you've paused the video, had a go at your task, and you've come back, let's have a look at the answers. Two and one quarter is equal to nine quarters, if we think about our whole, two is worth eight quarters, then we add on the one, our numerator, to get nine quarters. Let's go to this next one at the bottom here, two and two sevenths is equal to 16 sevenths. One and one sixth is equal to seven sixths. Two and five eighths is equal to 21 eighths. One and one third is equal to four thirds. Three and three quarters is equal to 15 quarters. Two and five sevenths is equal to 19 sevenths. Three and two thirds is equal to 11 thirds. Three and and a half is equal to seven halves, and two and two fifths is equal to 12 fifths. How did you get on? If you have got any corrections, have a go at them again and think about our rules. Okay, if you're done, it's time to complete the quiz. Thanks, everyone, bye bye.

One and one third is equivalent to....

Three and two fifths is equivalent to,,,

How else could I write two and two fifths

How else could I write five halves?

Which is greater?

Converting Mixed Numbers into Improper Fractions

In this lesson we will explore representations to connect mixed numbers and improper fractions, before using multiplication more formally to convert mixed numbers into improper fractions.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Converting mixed numbers into improper fractions

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

Adding fractions (up to one whole)

Subtracting fractions

Adding fractions (with a total greater than one)

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?

What is the sum of the fractions?

What mixed number is being represented?

Calculate:

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

Lesson overview:Converting mixed numbers into improper fractions

Core Content

Fractions: