And this is also clearly an entire whole. So this is also equal to a whole. And I think you see a pattern here. They all represent a whole. And you would also see this if you were to draw a number line. So this is 0. This is 1. We could keep on going. If I were to say, well, between 0 and 1, I just have 1, I divide it into one equal chunk, well, that's just this whole thing right over here.
And if I were to move one of those equal chunks, I would get to 1. If I divide it into two equal chunks and if I make two jumps-- one, two jumps-- I still end up at 1. If I divide it into three equal sections-- so let's say one, two, three equal sections-- and I make three jumps-- one, two, three-- I end up at 1 again.
Up Next. One is 12 inches in length, and the other is 1 foot in length. They are the same length — their lengths are just expressed in different ways. So in the end, we end up with this:.
How this was done mathematically is we took the original numerator of 4 and divided it by 4. What is done to one part of the fraction must also be done to the other, so we also divided the denominator of 8 by 4, resulting in a fraction of 1 over 2. Doing the same thing to both the numerator and the denominator guarantees that the original fraction and the final fraction are equal in value.
We reduce fractions when we can evenly divide the same number into both the numerator and the denominator. In our example, 4 can be divided into both. Note that the number 2 can also be divided into both the numerator and the denominator. If we divided both by 2, we would get:. Although this still works mathematically, we often want to get a fraction into its lowest terms, meaning to a point where it can no longer be reduced. The fraction 2 over 4 could be reduced even further to 1 over 2, so there is further work we could do, if we chose to.
Take the following fraction and reduce it to its lowest terms:. Step 1 : What we want to do here is take a look at both the numerator and the denominator and determine if there is a number that can go into both of them.
It might be easier if you write down numbers starting from 1 and then decide which numbers can go into both 8 and There you have it: the fraction has now been reduced to its lowest terms. The example shown above is fairly straightforward.
Once there are larger numbers involved, it is sometimes easier to work through the question in a couple of steps to slowly reduce the fraction. Take a look at the following example to see what I mean. Step 1 : Determine if there is a number that can go into both the numerator and the denominator. If there is more than one number, then use the larger number. This is a bit tougher than the first question, as the numbers are a lot larger and harder to work with.
Going back to our times tables, we can see that 6, 8, and 12 all go into Understanding improper fractions and mixed numbers. The latest news, articles, and resources, sent to your inbox weekly.
Maths Maths Worksheets. Year 3 age Year 4 age Year 5 age Year 6 age Maths Games. Year 1 age Year 2 age Year 3 age Year 4 age Year 5 age Year 6 age MTC and Times Tables. Free Maths Worksheets. It lets us know how much we're talking about. Since we're talking about one slice of pizza, our numerator is 1.
Let's look at another example. What if we divided the same pizza into 12 slices instead of 8? No matter what fraction you're trying to write, you always write it the same way—with the number of parts on the bottom, and the parts you're referring to on top.
You'd read that like this: one-eighth. When we read or talk about fractions, we use special numbers called ordinal numbers. A good way to remember this is that many of them are the same numbers you use when you're putting things in order : third, fourth, fifth, and so on. You might know some of these numbers already. A good rule to remember is that most ordinal numbers end in " th. What about fractions that don't have a 1 on top? Read these as if you were counting.
The top number will always be a "normal" number like the ones you use to count, and the bottom number is always an ordinal number. Sometimes you might see a fraction next to a whole number.
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