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Evaluate and simplify three-eighths times nine sixteenths plus five sixteenths times one-half plus three-eighths times one-eighth plus five sixteenths times negative one-eighth using the distributive property.

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The first thing we do is copy down this expression, and then we think about the distributive property.

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In order to use the distributive property, you’ll need to find a common factor in your terms.

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As we scan the terms, we see that three-eighths occurs twice.

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We also see a one-eighth and a negative one-eighth.

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As well, we see two terms that have five sixteenths as a factor.

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But there aren’t any factors that are shared by all four terms.

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And that means we might have to use the distributive property more than once.

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So let’s use three-eighths and five sixteenths to see if this can help us.

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Before we use the distributive property here, though, we want to regroup these terms.

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We want to group the terms that have the three-eighths together and the terms that have the five sixteenths together.

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At this stage, all we’ve done is rearrange the terms.

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So we’ve switched the position of the second and third terms.

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And now, we’re ready to use the distributive property.

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Our first two terms had a factor of three-eighths.

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If we undistribute that three-eighths, we’ll be left with nine sixteenths plus one-eighth.

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Following that same procedure, we now want to undistribute five sixteenths from the third and fourth term.

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That will give us five sixteenths times one-half plus negative one-eighth.

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Make sure you have that negative with your one-eighth.

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At this stage, we can add or subtract what’s in the parentheses.

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We have nine sixteenths plus one-eighth.

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In order to add nine sixteenths and one-eighth, we need to rewrite one-eighth as two sixteenths.

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And in order to add one-half to negative one-eighth, we’ll rewrite one-half as four-eighths.

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And instead of adding a negative one-eighth, we can just write this as subtract one-eighth.

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This gives us three-eighths times eleven sixteenths plus five sixteenths times three-eighths.

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Four-eighths minus one-eighth is three-eighths.

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At this point, we can actually use the distributive property a third time.

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Three-eighths is still a factor of both of our terms.

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And if we undistribute this three-eighths, we’ll have three-eighths times eleven sixteenths plus five sixteenths.

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Eleven sixteenths plus five sixteenths is sixteen sixteenths, which is one.

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And three-eighths times one is three-eighths.

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This means that the expression we started with after it’s been simplified completely and evaluated is three-eighths.