# Video: Using Array Models to Compare the Results of Multiplying Three Numbers in Different Orders

Compare the expressions. Pick the symbol that is missing. 2 × 3 × 6 ? 6 × 3 × 2 [A] > [B] < [C] =

03:44

### Video Transcript

Compare the expressions. Pick the symbol that is missing. Two times three times six what six times three times two? Is the missing symbol greater than, less than, or equal to.

We’re given two expressions, or two multiplication sentences. Two times three times six and six times three times two. We have to compare these two expressions and pick the missing symbol. Is two times three times six greater than six times three times two? Is two times three times six less than six times three times two? Or are the two expressions equal? Do we need the symbol greater than, less than, or equal to?

Did you notice that each expression uses the same three numbers in a different order? We have a two. They both contain a three. And both expressions contain a six, so the same numbers, just in a different order. Does this give us the same total? Let’s find out.

Here, we have two pictures, which we could call two arrays, or two groups. Each of the arrays contains three rows and six columns. To calculate how many squares there are altogether, first we would have to multiply three by six to find out how many squares there are in one rectangle, and then double it. Two lots of three times six.

What is three times six? Let’s count in threes to find out, three, six, nine, 12, 15, 18. The first model shows two groups of 18. Two lots of 18, or double 18, is 36. So, the first expression two times three times six equals 36.

The second expression has six lots of three times two. First, we need to work out what one lot of three times two is and then multiply it by six. Three times two is six. What is six times six. Let’s count in sixes, six, 12, 18, 24, 30, 36. Six times six is 36. Two times three times six equals 36. And six times three times two also equals 36. The missing symbol is equal to. Two times three times six is equal to six times three times two.