How to Calculate Fractions of Amounts

Hi, I'm Rebecca, and in this film we're going to look at how to find fractions of a set. So let's have a look at a problem. David has 15 marbles and he gives three fifths to Ellie. How many marbles does he give to Ellie? So I've got 15 marbles here. The denominator in my fraction is 5. So I'm going to sort my marbles into 5 equal groups. And I'm sharing them equally. And you could get pupils to do this with real counters. So now I've sorted my marbles into five equal groups and we can see that there are three marbles in, in each group. So 1/5 of 15 is equal to 3, but I don't want 1/5. I'm asked 3/5. So there's one set, two sets and three. So you can see easily that 3/5 of 15 is actually 3, 6, 9. So he gives nine marbles to Ellie. It's really important that children understand that when we're finding fractions of a set, that they take the amount of objects in the set and divide that by the denominator, then multiply it by the numerator. Let's have a look at applying that rule in another problem. So Jamal has 42 pounds and he spends four sixths of that on some new books. How much does he spend? Well, the denominator here is 6. So we need to divide 42 by 6, which is 7, but we're not asked for 16 of 42, 7 pounds, we're asked for 4 sixths. So we need to multiply our 7 pounds by 4, which would give us 28 pounds. So he spends 28 pounds on books. Now, it's very important that children understand that this rule applies when you are multiplying or finding a unit fraction of a set. So let's see how that works. Here we're asked for 18 of 16. We got to divide our 16 by 8, which is 2, but we're still going to multiply that by the numerator, which is 1, and 2 times 1 is 2. So 18 of 16 would be equal to 2, and that's how you find fractions of a set.