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## Properties of numbers and order of operations

# Commutative law of multiplication

## Video transcript

Use the commutative law of
multiplication to write 2 times 34 in a different way. Simplify both expressions
to show that they have identical results. So once again, this commutative
law just means that order doesn't matter. It sounds very fancy. Commutative law of
multiplication. But all that says is that it
doesn't matter whether we do 2 times 34 or whether
we do 34 times 2. The order does not matter. We can commute the two terms.
Both of these are going to get you the same exact answer. So let's try it out. What is 2 times 34? And we could write it like
this, literally. You'll almost never see it
written like this, but it is literally 2 times 34. Almost always people write the
larger digit on top, or the digit with more digits,
or the number with more digits on top. But let's do it this way. 4 times 2 is 8, and then
we'll put a 0. 3 times 2 is 6, or you can view
it as 30 times 2 is 60. Add them together. 8 plus 0 is 8. 6, bring it down. It's not being added
to anything. You get 68. So 2 times 34 is 68. Now, if you do 34 times 2, 2
times 4 is 8, 2 times 3 is 6. That's why it's always nicer to
write the number with more digits on top. It also is equal to 68. So it doesn't matter whether you
have two groups of 34 or thirty-four groups of 2,
in either case, you're going to have 68.