Video: KS2-M19 • Paper 1 • Question 32

2 1/2 − 3/4 = _.


Video Transcript

Two and a half take away three-quarters equals what.

In this problem, we are asked to take away a fraction from a mixed number. If we look carefully at the fraction part of the mixed number and compare it to the number that we’re taking away, we can see that the denominators are different. Halves have a denominator of two. And quarters have a denominator of four. So you might think that, in order to solve the problem, the first thing we need to do is to convert the first fraction so that the denominators are the same. But there is actually a quicker way to find the answer. It’s a sort of question we can work out mentally.

We know that we start with two and a half. But let’s look at the fraction that we’re taking away. How can we partition three-quarters to make it easier to subtract from two and a half? Well, we know that three-quarters is the same as two-quarters plus another quarter. How is partitioning three-quarters like this helpful? Well, these two-quarters are exactly the same as one-half. So we can say that three-quarters is the same as a half and a quarter. And because our mixed number has a half at the end of it, it’s now going to be easier to subtract from.

We could start by subtracting a half. Here’s a calculation we can do in our heads. Two and a half take away a half leaves us with two. We said that three-quarters was made up of a half and a quarter. We’ve already subtracted a half. So now all we need to do is to take away a quarter. We know that a whole take away a quarter leaves us with three-quarters. So two wholes take away a quarter leaves us with one and three-quarters.

Another way we could find the same answer is by imagining a number line, a number line that shows from zero to two and a half. Now let’s imagine what that number line might look like if it showed every quarter. We can see that we can express each fraction as a number of quarters. So to answer the question, we’d need to start on two and a half, which is the same as two and two-quarters, and then count back three-quarters. One takes us to two and a quarter. Two takes us to two. And three-quarters takes us to one and three-quarters. That’s another way to find the same answer.

So far, we’ve written the answer as a mixed number. But are there any other ways that we could write the same answer? Well, firstly, we could convert the mixed number into an improper fraction. How many quarters are there in one and three-quarters? Well, we know that one whole is equal to four-quarters. And so the number of quarters in one and three-quarters is the same as four plus three or seven-quarters. So if we had written the answer as seven-quarters, that would’ve been just as good as writing it as a mixed number.

Finally, there’s one more way we could write our answer. And that’s as a decimal. We know that three-quarters as a decimal is written as 0.75. And so one whole and three-quarters equals 1.75. So in this problem, we’ve looked at two different methods that we could use to find the answer. And then, once we found the answer, we looked at three different ways that we could write the answer. All of them would be correct.

Two and a half take away three-quarters equals one and three-quarters or seven-quarters or 1.75.

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