Chloe ordered two boxes of candies from the candy shop for her daughter’s birthday party. Each box has 850 candies. How many candies does she order?
First important piece of information we’re given in this problem is that Chloe ordered two boxes of candies. We’re then told that each box contains 850 candies. So, to find the number of candies that Chloe orders, we need to find two lots of 850. In other words, we need to find the answer to two times 850. Or if we look at it the other way, 850 multiplied by two.
One way we can model how to do this is by splitting the number 850 into eight 100, five 10s, and zero ones. Let’s use this rectangle to represent our first digit. That’s our hundreds digit. And it has a value of 800. And we’re multiplying by two. We can draw another rectangle then to represent our second digit. This is our tens digit. We have five 10s. And this has a value of 50. Our final digit is zero. Because two multiplied by zero equals zero, it might be worth not drawing a rectangle to end with. If we drew a rectangle like this and labelled it zero, it wouldn’t really make sense.
So, we split 850 in to eight 100s and five 10s. Now, we can multiply each of these parts by two. We know that eight multiplied by two equals 16. So, eight 100s multiplied by two must be 16 100s, or 1600. We can see now why this is called the area model of multiplication. If this rectangle had a length of 800 and a width of two, we’d find the area by multiplying the two together. And the answer would be 16 100s, or 1600.
Next, we need to multiply 50 by two, or, in other words, find the area of the orange rectangle. 50 doubled is 100. And as we’ve said already, we don’t need to worry about multiplying zero ones by two. When we worked out the two parts to our multiplication, we found that 800 multiplied by two equals 1600. And five 10s multiplied by two, or 50 multiplied by two, equals 100. So, to find the overall answer, we just need to add our two parts back together. And we can see that the answer is 1700.
We used the area model of multiplication to find the answer here. We wanted to multiply 850 by two. And so, by using this model, we were able to split up 850 into 800 and 50. We multiplied each part separately and then combined our two answers together to find the overall total. If Chloe ordered two boxes of candies, and each box has 850 candies, we can say that the total number of candies that Chloe orders is 1700.