We’re gonna look at how to represent fractions on the number line. To do that, we’re gonna zoom in on the bit between zero and one, then divide it up into equal shares, then we’re gonna count along the divisions.
Let’s start by thinking about a half. So here’s the number line from zero to one, and if we want to represent a half, we can divide the gap between zero and one into two equal parts because two was the number on the bottom of the fraction.
Now let’s label the points on the number line zero out of two, one out of two, and two out of two. Zero out of two is just zero; one out of two, one over two, one divided by two is a half; and two out of two, two divided by two, is one.
So the bottom number here is two because we divided the gap between zero and one into two equal parts. And the number on the top counts the number of parts, so zero parts up to here, one part up to here, and two parts all the way up to here.
Now if we draw an arrow starting at zero and ending here at a half, it represents a half because it reaches a half. So we can read the number off here on our number line, and that arrow represents a half.
Next, let’s divide that bit between zero and one into three equal parts. So we’ve got three on the bottom of our fraction, and we’re counting up zero, one, two, three thirds. Now if we start off at zero and finish up here at one-third, this fraction, this arrow, mean a third.
Next we’ve split it up into four equal parts. And when we’re writing the numbers down on the number line, one-quarter is just that, can’t be simplified, so that’s one-quarter; two-quarters, well that’s the same as a half so I can write a half; three-quarters, that doesn’t simplify anymore so that’s just three-quarters; and four-quarters is just one. That’s all four parts; that’s the whole thing; that’s one.
Now if we draw an arrow starting at zero and reaching all the way up to the first bar that we’ve drawn, that’s a quarter. So that arrow and this number here represent a quarter.
Now just before we move on, we’ve split it up into five parts. So the only fractions that simplify Here are zero over five becomes zero and five over five becomes one. All of the other fractions we can just copy down to their place on the number line because they can’t be simplified. Now if we start at zero and we finish at the first division, that represents a fifth.
So we’ve seen how to represent unit fractions on the number line; that’s fractions with a one on top. Divide up the space between the zero and the one into equal shares, and then the end of the first part tells you the fraction one over that number of shares. Have a go at doing this one. Think about how many shares it’s been divided into and how would you represent one of those shares.
Okay first, we count up how many it’s been divided into. So starting counting from zero, one, two, three, four, five, six, seven, eight, nine, ten shares. Now we know it’s divided into ten shares; we can put the bottom on those fractions. And the next step is to write the fractions down at the bottom, but we need to simplify any that we can.
So first I’ve just copied down the fractions that can’t simplify. And now two-tenths, well if I divide the top by two and the bottom by two, that becomes one-fifth; four-tenths, if I divide the top by two and the bottom by two, I get-twofifths; five-tenths, divide the top by five and the bottom by five and I get one-half; six-tenths divide the top by two and the bottom by two and I get three-fifths eight-tenths; divide the top by two and the bottom by two and I get four-fifths. So now I’ve got my nice simplified fractions on the bottom.
So to get my unit fraction, I start at zero and I draw my arrow up to the first marker which is representing a tenth. Now we can represent other fractions by using more of the shares. So for example, one-third was one of the shares and two-thirds is just two of the shares.
So this arrow represents two-thirds and two-thirds is made up of one-third and-and another third; one-third plus one-third makes two-thirds.
Let’s explore quarters then. We’ve seen that one section filled in means one-quarter, two sections filled in means two-quarters, but two quarters can be simplified to a half. So this arrow represents a half. And extending that a bit further, one-quarter plus another quarter plus another quarter makes three-quarters.
Okay let’s test you on this then. What fraction does this arrow represent? Well we’ve counted up to five, so we’ve divided it into five sections. And none of those simplify, so we can write the fractions down between zero and one we’ve got an arrow going from the zero point to the first section so that’s one-fifth.
So what fraction does this arrow represent? Starting at zero, we can count up to six. So we’ve split it into six sections.
So putting six on the bottom of each of our fractions, some of them simplify so two-sixths is a third, three-sixths is a half, and four-sixths is two-thirds. But some of the other fractions, a sixth and five-sixths, don’t simplify. So we can fill out the numbers between zero and one. Starting from zero and going to the end of the arrow, that takes us up to the five-sixths point, so this arrow represents the fraction five-sixths.
Finally then, work out what fraction this arrow represents. We can split it into ten sections. Some of those numbers simplify and some don’t, and we’re starting from zero and we came all the way up to seven-tenths, so this represents seven-tenths.