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Use the symbol for is less than, is equal to, or is greater than to compare the numbers on each pair of cards.
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23,099, what, 23,851; 11,273, what, 9,768; and then finally 25,938 plus 1,000, what, 26,819 plus 100.
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In this question, we’re given three pairs of cards, and we’re told that we need to compare the numbers on each pair.
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Let’s start with the first two numbers.
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How are we going to compare these?
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Well, we know that to compare two numbers means to look at the digits in those numbers and their place value.
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And a good way of doing this is using a place value grid.
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Let’s sketch one for these numbers by writing both numbers in the grid on top of each other.
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We can compare them digit by digit.
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So, our first number has a digit two in the ten thousands place, three in the thousands place.
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It has zero hundreds, nine tens, and nine ones.
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It’s 23,099.
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The number on the second card also has five digits, and some of these digits are very similar.
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There’s a two in the ten thousands place, a three in the thousands place.
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This particular number has an eight in the hundreds place, a five in the tens place, and a one in the ones place.
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Now that we’ve recorded both of our numbers in a place value grid, it is going to be a lot easier to compare them digit by digit and.
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To do this, we need to begin with the digits that have the largest value.
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These are the digits that have the most effect on the number.
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In other words, we need to start by looking at the ten thousands place.
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Both our numbers have the digit two in this place, so we can’t separate one number as being larger than the other just by looking at this digit.
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We’re going to need to carry on and look at the next digit alone.
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If we compare the two digits in the thousands place, we can see that these are the same too.
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We still can’t separate out our numbers.
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We’re going to have to compare the hundreds digits.
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Thankfully, we can see that these are different.
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And so, we now can tell which of our numbers is larger.
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The number on the first card has a zero in the hundreds place, and the number on the second card has an eight in the hundreds place.
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And it doesn’t matter about the tens and ones.
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We know which of our numbers is larger just by looking at the hundreds digit.
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Our second number is greater than the first.
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But of course, when we compare two numbers, we read them across from left to right.
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So, we need to use the less than symbol.
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23,099 is less than 23,851.
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Now, let’s compare our second pair of cards.
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Now, we could use a place value grid again to compare these numbers, but can you see something interesting about them?
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They both have a different number of digits.
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This is going to make them really quick to compare.
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In fact, we don’t really need to use the place value grid.
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Our first number has five digits, so the highest value digit is a ten thousands digit.
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But our second number only has four digits.
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So, the highest value digit is only worth thousands.
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A whole number with five digits is always going to be larger than a whole number with four digits.
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So, as we read our numbers from left to right, we’re going to need to use the symbol is greater than.
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11,273 is greater than 9,768.
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And if we complete our place value grid, we can see that the first number has a one in the ten thousands place.
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But our second number doesn’t have anything.
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Now, let’s compare our final pair of cards.
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These are interesting because each one has an addition written on it.
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For us to compare these values, we’re going to need to find the total on each card.
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On our first card, we have 25,938 plus 1,000.
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Now, what happens if we add 1,000 to a number?
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Well, there’s a change to the thousands digit.
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The number 25,938 has a five in the thousands place.
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But if we add one more 1,000, that five is going to become a six.
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So, the value of our first card is 26,938.
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The addition on our second card is 26,819 plus 100.
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And we know when we add 100 to a number, it’s the hundreds digit that changes.
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26,819 has the digit eight in the hundreds place.
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But if we add one more 100, our number will contain nine hundreds.
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So, the value of this particular card is 26,919.
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This time, both of our values have the same number of digits.
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So, we’re going to need that place value grid again.
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Starting with the place that has the largest value, we can see that both numbers have a two in the ten thousands place, so we can’t separate them out yet.
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If we compare the thousands digit, these are the same, so will a hundreds digit.
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But we can see that that the tens digit are different.
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And this helps us now to compare the two numbers.
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26,938 has a three in the tens place, and 26,919 only has a one in the tens place.
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That’s how we know the value on the first card is greater than the value on the second.
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We’ve used place value grids and also in the second example our knowledge of the number of digits to help us compare the numbers on these pairs of cards.
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23,099 is less than 23,851.
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11,273 is greater than 9,768.
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And the value of 25,938 plus 1,000 is greater than the value of 26,819 plus 100.