3.03 Multiplication as a comparison
Are you ready?
Do you remember how multiplication can be thought of as repeated addition?
Write this addition as a multiplication.
$2+2+2+2+2+2$2+2+2+2+2+2
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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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Question 1
Look at the collection of counters.
Fill in the box with the missing number:
$8$8 is $\editable{}$ times as many as $4$4.
Fill in the box with the missing number:
$8$8 is $\editable{}$ times as many as $2$2.
Write this as a multiplication number sentence.
$\editable{}\times\editable{}=\editable{}$×=
We can write comparisons in two ways:
$15$15 is $5$5 times as many as $3$3, and also $15$15 is $3$3 times as many as $5$5.