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# Word Problems/Units Cancellation

Question
QUESTION: Hello:

How is the following expressed mathematically?

An investor owns 30 shares of stock for 3 years. During this time he receives quarterly dividends of \$0.60 per share.

Do all of the units cancel except the dollar units?

Is the following correct?

30 shares/quarter X \$0.60/share X 3 years X 4 quarters/year = \$216.00

ANSWER: I would take that as (30 shares)((\$0.60/quarter)/shares))(3 years)(4 quarters/year).

Now (\$0.60/quarter)/shares is really (\$0.60/quarter)/(shares/1).
It is known that (a/b)/(c/d) is (ad)/(bc), so that becomes \$0.60/(quarters*shares).

Using this, it can be seen that we get shares/shares, years/years, and quarters/quarters.
The only thing left is \$, and that is what is being looked for.
Putting the units together gives us 30 * 0.60 * 3 * 4 = 18 * 12 = 216.
Out only unit was \$, so it is \$216.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply.

I am confused by all of the parentheses that you used.

Is there a different way to explain (30 shares)((\$0.60/quarter)/shares))(3 years)(4 quarters/year)?  I know that the / marks indicate a fraction
but (  )((   ) is confusing to me.

I thank you for your clarification.

Perhaps it would be better to write it as
(30 shares) [(\$0.60/quarter)/shares)] (3 years) (4 quarters/year).

Then note that [(\$0.60/quarter)/shares)] is really [(\$0.60/quarter)/(shares/1)].
On fractions, the one in the divisor is inverted and multiplied, so this is really
\$0.60/(quarter*shares).

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the clarification!

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