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This content is taken from the National STEM Learning Centre's online course, Maths Subject Knowledge: Fractions, Decimals, and Percentages. Join the course to learn more.
1.4

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: In the last step, we asked you to consider three different statements comparing the values of 2/5 versus 3/7. Now, it’s not immediately obvious which one’s larger, which one’s smaller, or whether they’re equal. To help us try and answer that question, we’re going to draw a diagram. Now, in our first diagram, we have a circle, which represents the whole. And we’ve split that into five equal parts and shaded two of them. That represents our 2/5. We’ve taken the same circle and split it into, again, equal parts, this time in sevens, to represent sevenths. And 3/7 is three of them coloured in.

Skip to 0 minutes and 42 seconds So by looking at these two diagrams, we can start to maybe compare the two fractions, but it’s quite difficult to tell even with this diagram that we’ve got.

Skip to 0 minutes and 51 seconds PAULA KELLY: And circles are quite tricky to split into our equal parts. This is obviously very important with fractions. We tried again with them rectangular diagrams here. Again, we have five equal parts. Two are shaded. Seven equal parts, three are shaded. We can see the relative size, but as we were saying, it’s quite hard to judge just how much larger or smaller each one is.

Skip to 1 minute and 14 seconds MICHAEL ANDERSON: So the rectangles look like a better method to help us compare fractions than the circles, but we still can’t really answer how much larger one fraction is than another. During the rest of the week, we’re going to explore a range of strategies that are going to help us compare two different fractions a lot more easily than the methods we’ve already covered.

# A fraction of a whole

Throughout the next few steps we’ll be looking at how we define a fraction. This will help us answer our starter problem: is $$\frac{2}{5}$$ greater than, less than or equal to $$\frac{3}{7}$$?

When comparing two fractions one method is to draw a picture to represent the size of each fraction, split the shape into the appropriate number of equal parts, and then shade in the correct number of parts to represent each fraction.

In the video above, we look at how this would apply to our starter problem. In some cases the pictorial representation will be enough to convince you which fraction is the largest, but if the fractions are similar it may be difficult to tell. In fact, a diagram often does not tell you is how much bigger one fraction is than another.

## Problem sheet

Complete questions 1 and 2 from this week’s worksheet.