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