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A fruit vendor has four boxes containing 121 red apples each and nine boxes containing 91 yellow apples each.
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How many apples does the vendor have?
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In this problem, we have a fruit vendor who is selling two different types of apples, red and yellow.
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We’re told that he or she has four boxes that each contain 121 red apples each.
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This bar represents the number of red apples that they have.
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One way of writing this value is as a multiplication, 121 multiplied by four.
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We’re also told that the vendor has nine more boxes.
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And each of these nine boxes contain 91 yellow apples.
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Another way of representing the number of yellow apples is as 91 multiplied by nine, nine lots of 91.
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And our question asks us, how many apples does the vendor have?
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In other words, what is the total of red and yellow apples?
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What is the total of our bar model?
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And so to find the answer, we need to calculate two multiplications and then add them together to find the total.
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We need to find the answer to 121 multiplied by four, 91 multiplied by nine.
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And then add the two answers together.
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These are both multiplications that we can work out mentally.
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We don’t have to use written methods to find the answer.
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We know that two times two is four.
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So multiplying any number by four is the same as timesing it by two and then two again or, in other words, doubling it and then doubling it again.
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121 is a sort of number where the digits are easy to double quickly.
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They don’t affect any of the other digits.
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So if we double 121, we get the answer 242.
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And we could do the same with 242.
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242 doubled is 484.
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So the number of red apples that the vendor has is 484.
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Now let’s calculate the number of yellow apples that the vendor has.
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We need to find the answer to 91 multiplied by nine.
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What’s a quick mental method we could use for multiplying by nine?
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We know how to multiply by 10 quickly.
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Perhaps we could use this to help.
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When we multiply by 10, the digits shift one place to the left.
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So 91 multiplied by 10 equals 910.
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We found what 10 lots of 91 are worth.
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But to find in nine lots of 91, we need to subtract one lot of 91 from 910.
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91 is only nine less than 100.
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If we take away 100 from 910, we get the answer 810.
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But by taking away 100, we’ve subtracted nine too many.
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We only wanted to take away 91.
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So we need to add nine back onto our answer.
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The answer is 819.
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This is the number of yellow apples that the vendor has.
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To find the overall total number of apples that the vendor has, we need to add 484 and 819.
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Four plus nine equals 13.
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Eight tens plus one ten equals nine tens plus the 10 we have underneath equals 10 tens, which is the same as 100.
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Four hundreds plus eight hundreds equals 12 hundreds plus the 100 underneath equals 13 hundreds or 1300.
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To find the answer, we calculated 121 multiplied by four.
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And to do this, we doubled, then doubled again.
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We then calculated 91 multiplied by nine.
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Again, we used the mental method to find the answer.
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First, we multiplied by 10.
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And then we took off one lot of 91.
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Finally, we added our two answers to find the overall total.
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The number of apples that the vendor has altogether is 1303.