WEBVTT
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Anthony knows how to add and subtract zero, 0.25, 0.5, 0.75, and one.
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Look at how he uses these numbers to help him estimate sums of decimal numbers.
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By rounding to the nearest multiple of 0.25, he finds that 1.31 plus 0.42 is about 1.75.
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Estimate the sum by rounding each number to the nearest multiple of 0.25.
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2.17 plus 1.89 equals what.
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And then, estimate the difference by rounding each number to the nearest multiple of 0.25.
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4.69 subtract 0.42 equals what.
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There’s a lot to read and take in in this problem.
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So let’s go through it step by step.
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Firstly, we’re told that Anthony knows how to add and subtract five numbers.
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These are zero, 0.25, 0.5, 0.75, and one.
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These are all multiples of twenty-five hundredths or 0.25.
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And because Anthony finds it easy to add and subtract using these numbers, he uses them to help him estimate sums and differences of decimal numbers.
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And we’re given a diagram to show us exactly what he does.
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And it’s worth taking a moment just to look at it to try to understand what’s happening.
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Firstly, Anthony has a calculation to work out.
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He needs to find the sum of 1.31 plus 0.42.
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And we can see this vertical calculation on the left.
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And we can imagine Anthony saying to himself, I don’t want to find out the exact amount.
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I just need to find an estimate.
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So what I’ll do is round both numbers to the nearest multiple of 0.25 because I know how to add and subtract those.
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And so, this is what he does.
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And he uses a number line to help.
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Now, this number line is interesting.
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Firstly, we can see that all the multiples of 0.25 have been marked.
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They each have a slightly longer line than the other lines on there.
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And of course, we can see the labels there as well.
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So these multiples of 0.25 are very clear.
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But as well as the longer notches, we can also see there are some smaller marks on the number line too.
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If we look at where these are placed, we can see that these represent tenths.
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So, for example, if we’re looking for where 0.81 is going to be, we can find eight-tenths and use this to help us.
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So these small notches are very useful.
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The first number in Anthony’s calculation is 1.31.
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So we know Anthony must locate 1.31 on his number line, which is where the pink circle is.
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And then, he looks for the nearest multiple of 0.25 that he can round this to.
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We can see that the pink circle is in between 1.25 and also 1.5.
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And it’s nearest to 1.25 And so, the first number in Anthony’s estimate is going to be 1.25.
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The second number in Anthony’s addition is 0.42.
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So once again, he locates this on a number line.
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And in this time, he marks it with a blue circle.
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This time, the multiples of 0.25 that the blue circle’s in between are 0.25 itself and 0.5.
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And 0.42 is nearest to 0.5.
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So Anthony uses this as the second number in his estimate.
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And because he knows how to add these numbers quickly, he knows that 1.25 plus 0.5 equals 1.75.
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And this number is his estimate.
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By rounding to the nearest multiple of 0.25, he finds that 1.31 plus 0.42, that’s his original calculation, is about 1.75.
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Now, we’re asked to solve two problems of our own.
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To give us space to do this, let’s remove Anthony’s example.
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Our first calculation is an addition.
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We need to estimate the sum by rounding each number to the nearest multiple of 0.25.
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Again, we can sketch a number line, just like Anthony’s, to help us.
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The multiples of 0.25 are using larger notches and the smaller notches represent tenths.
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Now, we can round each of our decimals to the nearest multiple of 0.25.
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Firstly, 2.17.
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If this is where two is on our number line, then this small notch will be two and one-tenth or 2.1.
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And this second one must be 2.2.
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So we can say that 2.17 will be around about here on the number line.
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Which multiple of 0.25 is this nearest to?
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It’s nearest to 2.25.
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So the first number in our estimated calculation is going to be 2.25.
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But what number are we going to add to it?
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Let’s locate 1.89 in our number line.
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Here’s where 1.8 will be.
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And the second arrow represents 1.9.
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1.89 is very, very close to 1.9, so we can draw this dot here.
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And we can see that the multiple of 0.25 that this is nearest to is the number two.
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So the second number in our estimation that we need to add is two.
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Notice how we write the digit two in the ones place.
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Now, just like Anthony did, we can find the estimate by adding these numbers quickly.
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2.25 plus two equals 4.25.
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Our estimation for the answer to 2.17 plus 1.89 is 4.25.
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In the second calculation, we need to find the difference between two numbers.
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But we still need to use the same rounding method.
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The first number in our subtraction is 4.69.
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4.69 is only one hundredth away from 4.7.
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If we locate 4.7 on our number line, we can draw a circle.
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So we can say that the multiple of 0.25 that 4.69 is nearest to is 4.75.
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The first number in our estimation is going to be 4.75.
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But what number do we need to subtract?
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This time, we need to locate 0.42 on a number line.
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0.42 is two hundredths greater than 0.4.
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So if we find where 0.4 is in our number line, it will be just past that, perhaps about here.
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We can see that the nearest multiple of 0.25 to 0.42 is 0.5.
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We round the number up.
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The second number in our subtraction is 0.5.
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Now, we can find the difference by subtracting our two estimated numbers.
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In the hundredths place, we have five.
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And in our second number, we don’t have any hundredths.
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So we could actually put zero there as a placeholder.
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Five take away zero equals five.
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Seven-tenths take away five-tenths leaves us with two-tenths.
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And before we subtract the ones digits, we need to remember we’re working with decimals here.
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So we need to include a decimal point in our answer.
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Four ones take away zero ones equals four.
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In this problem, we’ve estimated the sum and the difference of pairs of decimal numbers by rounding them to the nearest multiple of 0.25.
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Our estimate for the sum of 2.17 and 1.89 is 4.25.
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And our estimate for the difference between 4.69 and 0.42 is also 4.25.