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What are the missing numbers in the sequence, zero, 0.25, what, 0.75, one, what, and what?
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To begin with, let’s write out the numbers in our sequence in a row, which will help us compare them.
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Zero, 0.25, then we have a missing value, then 0.75, followed by one.
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And then, there are two more missing numbers on the end.
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To be able to spot the rule for a sequence, we need to compare how numbers change from one to the other.
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But if we look at the number sequence we’ve been given, there are several missing numbers.
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This means there are only two parts that we can compare.
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We can work out how a number changes to get from 0 to 0.25.
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And we can also see how a number changes to get from 0.75 to 1.
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Hopefully, the rule will be the same both times.
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And then, we’ll have a rule for the whole sequence.
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Let’s try to find the rule.
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First of all, how do we get from 0 to 0.25, or twenty-five hundredths?
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Well, because we’re starting from zero.
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We can work this out quickly.
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We’re adding 0.25.
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0.25 is the same as a quarter, or twenty-five hundredths.
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So, we could say we’re counting in quarters, or even adding twenty-five hundredths every time.
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The idea of counting in quarters is important when we get to our next pair of numbers, 0.75 and one.
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Is the rules still to add 0.25?
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This is where the idea of adding a quarter comes in useful.
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0.75 is the same as three-quarters.
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And if we add a quarter to three-quarters, we get one whole.
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So, 0.75 plus 0.25 does equal one.
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We’ve found the rule to the sequence.
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Now, let’s apply our rule to find the missing numbers.
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Our first missing number is found by adding 0.25 to 0.25.
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Twenty-five hundredths plus another twenty-five hundredths equals fifty hundredths.
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We can write this simply as 0.5.
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Another way of thinking of this is a quarter plus a quarter equals a half.
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To find our second missing number, we need to add 0.25 to 1.
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And the answer is 1.25.
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In other words, one plus a quarter equals one and a quarter, or one plus twenty-five hundredths equals one and twenty-five hundredths.
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And to find our final missing number, we need to add another twenty-five hundredths to 1.25.
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The answer is one and fifty hundredths, or 1.5.
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The rule for our sequence was to add 0.25 every time.
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And so, the three missing numbers, from left to right, are 0.5, 1.25, and 1.5.