Find the missing partial products to complete the given area model: 74 times 69. What number should we write instead of 𝑥? What number should we write instead of 𝑦?
So this model is representing the product, 74 times 69. At the top, we have 70 and four, and they add to be 74, on purpose. And over here, we have 60 and nine, and they add to be 69.
Let’s first look at 630. 630 is in the column of 70, in the row of nine. And 70 times nine is 630. 36 is in the column of four, and the row of nine. And four times nine is indeed 36. So since 𝑥 is in the column of 70, and the row of 60, we need to multiply 70 and 60 together. And 70 times 60 is equal to 4200. So to answer the question “What should we write instead of 𝑥?,” we should write 4200.
Now for 𝑦, 𝑦 is in the column of four, and the row of 60. And 60 and four multiply to be 240. So we should rewrite 𝑦 as 240. So once again, we’ll replace 𝑥 with 4200 and we replace 𝑦 with 240.
So while this might be our answer, how does it make sense? Well, 74 times 69 is equal to 5106, which can be found by adding all four of the numbers inside of the entire box, so 4200 plus 240 plus 630 plus 36. It gives us a total of 5106. So the partial products help us break it down into something smaller that might be easier to work with. But once again, our final answers will be 𝑥 equals 4200 and 𝑦 equals 240.