Video Transcript
Which equation shows the
commutative property of multiplication? Is it (A) two-thirds times one
equals two-thirds? Is it (B) 0.5 times three is equal
to 0.5 plus 0.5 plus 0.5? Is it (C) 3.5 times two is equal to
two times 3.5? Is it (D) a half times four minus a
quarter times four is equal to a half minus a quarter times four? Or, is it (E) a half times a
quarter times two-thirds is equal to a half times a quarter times two-thirds?
Let’s recall what we mean by the
commutative property of multiplication. The commutative property says that
when two numbers are multiplied together, the result will be the same no matter the
order of the numbers. For example, two times three is the
same as three times two. And actually, this is a really
useful property. For example, if you know you feel
unconfident with a certain times tables, knowing that three times seven is the same
as seven times three means you can think about the times table that you do know by
heart. So, which of these examples shows
this property? Well, it’s not (A). In fact, (A) is the multiplicative
identity property. This says if you multiply a number
by one, you get the original number.
Is it (B) 0.5 times three is 0.5
plus 0.5 plus 0.5? Well no, this just shows us that we
can think about multiplication as repeated addition. So, what about (C) 3.5 times two is
equal to two times 3.5? Well, yes we’ve shown that the
result is the same even if we change the order in which we perform the
multiplication. So, it’s (C). Let’s look at (D) and (E) next. (D) says that a half times four
minus a quarter times four is equal to the difference between a half and a quarter
times four. This is called the distributive
property of multiplication.
And finally, (E) does look like
it’s going to be correct, but in fact, this is all to do with grouping. This is called the associative
property. And it says that when three or more
numbers are multiplied together, the product is the same regardless of how those
numbers are grouped. Notice that we use the parentheses
to show the grouping here. And so the answer to this question
is (C). The commutative property of
multiplication is demonstrated by the equation 3.5 times two equals two times
3.5.
