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Two and a half take away three-quarters equals what.
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In this problem, we are asked to take away a fraction from a mixed number.
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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.
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Halves have a denominator of two.
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And quarters have a denominator of four.
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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.
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But there is actually a quicker way to find the answer.
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It’s a sort of question we can work out mentally.
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We know that we start with two and a half.
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But let’s look at the fraction that we’re taking away.
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How can we partition three-quarters to make it easier to subtract from two and a half?
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Well, we know that three-quarters is the same as two-quarters plus another quarter.
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How is partitioning three-quarters like this helpful?
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Well, these two-quarters are exactly the same as one-half.
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So we can say that three-quarters is the same as a half and a quarter.
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And because our mixed number has a half at the end of it, it’s now going to be easier to subtract from.
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We could start by subtracting a half.
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Here’s a calculation we can do in our heads.
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Two and a half take away a half leaves us with two.
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We said that three-quarters was made up of a half and a quarter.
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We’ve already subtracted a half.
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So now all we need to do is to take away a quarter.
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We know that a whole take away a quarter leaves us with three-quarters.
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So two wholes take away a quarter leaves us with one and three-quarters.
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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.
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Now let’s imagine what that number line might look like if it showed every quarter.
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We can see that we can express each fraction as a number of quarters.
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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.
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One takes us to two and a quarter.
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Two takes us to two.
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And three-quarters takes us to one and three-quarters.
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That’s another way to find the same answer.
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So far, we’ve written the answer as a mixed number.
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But are there any other ways that we could write the same answer?
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Well, firstly, we could convert the mixed number into an improper fraction.
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How many quarters are there in one and three-quarters?
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Well, we know that one whole is equal to four-quarters.
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And so the number of quarters in one and three-quarters is the same as four plus three or seven-quarters.
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So if we had written the answer as seven-quarters, that would’ve been just as good as writing it as a mixed number.
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Finally, there’s one more way we could write our answer.
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And that’s as a decimal.
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We know that three-quarters as a decimal is written as 0.75.
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And so one whole and three-quarters equals 1.75.
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So in this problem, we’ve looked at two different methods that we could use to find the answer.
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And then, once we found the answer, we looked at three different ways that we could write the answer.
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All of them would be correct.
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Two and a half take away three-quarters equals one and three-quarters or seven-quarters or 1.75.