Video Transcript
Simplify five thirteenths plus
three-quarters plus one-quarter using the properties of addition.
According to the order of
operations, we’ll usually look to deal with the calculation inside the parentheses
first. That would involve creating a
common denominator and then adding the numerators. Alternatively, we recall that the
associative property for addition says that we can add three or more numbers
together, regardless of how they are grouped. Now, of course, if there were, for
example, exponents or multiplications in this problem, we’d need to be a little bit
more careful. But since we only have addition, we
can do this in any order.
Let’s get rid of the parentheses
first. We now know that we can easily add
three-quarters and one-quarter because their denominators are the same. We just add the numerators. Three-quarters plus one-quarter is
four-quarters. And of course, if we have
four-quarters, we essentially have one whole. So, three-quarters plus one-quarter
is equal to one. And we can now add five thirteenths
and one. Now, we could write this as a mixed
number. It would be one and five
thirteenths. Alternatively, let’s think about
how many thirteenths one whole must contain. One whole must be equal to thirteen
thirteenths. And so, five thirteenths plus one
is the same as five thirteenths plus thirteen thirteenths.
Now that their denominators are
equal, we simply add the numerators. And we get five thirteenths plus
thirteen thirteenths equals eighteen thirteenths. We’ve simplified five thirteenths
plus three-quarters plus one-quarter by using the associative property. And we’ve got eighteen
thirteenths.
