3.03 Multiplication as a comparison

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Do you remember how multiplication can be thought of as repeated addition?

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Since multiplication can be thought of as repeated addition, we can also think of it as a comparison.

For example, from $3+3+3+3+3=15$3+3+3+3+3=15 we can say that $15$15 is $5$5 groups of $3$3, or that $15$15 is $5$5 times as many as $3$3. We write this as the multiplication $15=5\times3$15=5×3.

With the commutative property of multiplication we can also write this as $15=3\times5$15=3×5, and so we can say that $15$15 is also $3$3 groups of $5$5, or that $15$15 is $3$3 times as many as $5$5.

 

Groupings like this appear in all sorts of places. For example, on a farm there are $20$20 apple trees arranged in a grid:

We can see that there are $5$5 trees in each row, and $4$4 rows in total, so we can say that $20$20 is $4$4 times as many as $5$5.

We can also see that there are $4$4 trees in each column, and $5$5 columns in total, so we can say that $20$20 is $5$5 times as many as $4$4.

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