Video Transcript
Associative Property of
Multiplication
In this video, we’re going to learn
how to identify and apply the associative property of multiplication to multiply
three one-digit numbers. The associative property of
multiplication is a maths rule that tells us the way in which factors are grouped in
a multiplication doesn’t affect the product. For example, we could group these
two factors together and find two times four. We know that two times four is
eight. So we need to multiply eight by our
remaining factor, which is five. And we know that eight times five
is 40, so the product of two times four times five is 40.
But what if we were to group these
two factors together and multiplied them first? We know that four times five is
20. So now we just need to multiply 20
by our remaining factor, which is two. And we know that two times 20
equals 40. It doesn’t matter how we group the
factors; the product doesn’t change. Two times four is eight, and eight
times five is 40. And if we multiply four times five
first, we get 20. And if we multiply 20 by two, we
also get 40. Let’s practice now multiplying
three one-digit numbers using the associative property of multiplication.
When we multiply three numbers, we
can choose which calculation to do first. Do the highlighted calculations to
find the missing numbers. Six times five times two equals six
times what. Six times five times two equals
what times two. What is six times five times
two?
In this question, we’re being asked
to multiply three one-digit numbers together: six, five, and two. The question tells us that we can
choose which calculation to do first. We have to do the highlighted
calculations to find the missing number. In the first calculation, we have
to multiply five times two first. We know that five times two is 10,
so six times five times two is equal to six times 10. So the missing number in the first
calculation is 10.
The second calculation is the same
as the first. We’re still finding six times five
times two, but this time we have to multiply six by five first. Six times five is 30. Now all we have to do is multiply
30 by two. The missing number in the first
calculation is 10, and the missing number in the second calculation is 30. So to find six times five times
two, if we multiply five by two first, we get 10. And then we multiply six by 10. So the product of six times five
times two is 60.
Let’s check if we get the same
answer in our second calculation. Six times five is 30, and 30 times
two is also 60. It doesn’t matter how we group the
factors; the product doesn’t change. This question is all about the
associative property of multiplication. It doesn’t matter how we group the
factors; the product stays the same. Six times five times two equals
60.
Let’s recap what we’ve learned
about the associative property or the associative rule of multiplication. When we’re multiplying three
one-digit numbers like three times two times four, it doesn’t matter how we group
the factors; the product stays the same. We could find three times two
first. And we can see from the array that
three times two equals six. Then all we have to do is multiply
our six by four. Six times four is 24. Three times two times four equals
24.
We could also find three times two
times four by changing the order of the factors. Three times two times four is equal
to two times four times three. And we know we can group the
factors in any order. So let’s start by finding two times
four. This array shows two rows of
four. Two times four is eight. Now we just need to multiply eight
by three. And eight times three is 24. So we’ve learned that when we’re
multiplying three one-digit numbers, we can use the associative property and the
commutative property. It doesn’t matter which order we
multiply the numbers or how we group the factors; the product stays the same. Let’s practice what we’ve learned
by answering another question now.
Compare the expressions. Pick the symbol that is
missing. Two times three times six is
greater than six times three times two or two times three times six is equal to six
times three times two or two times three times six is less than six times three
times two.
In this question, we’re given two
expressions. And we have to choose the correct
symbol to compare them: greater than, equal to, or less than. Our two expressions have been
modeled using arrays. Our first array shows two groups of
three times six. Three times six is 18. And double 18 is 36. Two times three times six equals
36. Our next model shows six lots of
three times two. We know that three times two is six
and six times six is 36. So six times three times two is
also 36. Both of our expressions contain the
same three factors of 36: two, three, and six. It doesn’t matter which order we
multiply the numbers or how we group them; the product stays the same.
So the missing symbol is equal
to. Two times three times six is equal
to six times three times two. The missing symbol is equal to.
Fill in the blank with the missing
factor: Two times what times three equals 18.
In this question, we have to find
the missing factor. This part of our expression is
inside a pair of brackets. This tells us that we need to
multiply these two factors together first. So something multiplied by three
and then multiplied by two equals 18. Two multiplied by what equals
18. We know that two times nine is
18. So what do we need to multiply by
three to give us nine? Three times three is nine. So two times three times three
equals 18. Three times three is nine; two
times nine is 18. The missing factor is three.
Another way we could’ve found the
missing factor is to start with the numbers we already had. Two times three times what equals
18. First, we can multiply two by
three, which is six. Then all we need to think about is
what do we time six by to give us a product of 18. And we know that six times three is
18. It doesn’t matter how we group the
factors or the order in which we multiply them; the product doesn’t change. Two times three times three equals
18. Two times three times three equals
18. And three times three times two
equals 18. The missing factor is three.
What have we learned in this
video? We’ve learned that when we multiply
three one-digit numbers, we can multiply the numbers in any order and group the
factors in any order and the product stays the same.
