What does this mean fraction

[Ronnieb]

Hi
My homework shows this question

8/3 of 27. 8/3 is a fraction

Does this mean 8/3 is divided.
Confused?

 

[Deleted member 4993]

Hi
My homework shows this question

8/3 of 27. 8/3 is a fraction

Does this mean 8/3 is divided.
Confused?

If you replace "of" with "multiplied by" - does it make better sense?

 

[JeffM]

Hi
My homework shows this question

8/3 of 27. 8/3 is a fraction

Does this mean 8/3 is divided.
Confused?

I'd like to supplement Subhotosh's excellent answer. An issue here involves English usage.

If we say what is "one fifth of 30," we understand that what is meant is

\(\displaystyle \dfrac{1}{5} * 30 = \dfrac{1}{5} * \dfrac{30}{1} = \dfrac{30}{5} = 6.\)

In other words, "of" means multiplication when dealing with fractions.

But we do not say what is "seven of 30" when we mean \(\displaystyle 7 * 30.\)

It is just one of the confusing peculiarities of natural languages.

What makes it even more odd is that the order of terms makes a difference.

We say what are 30 sevens and what are 30 one-fifths to mean multiplication.

 

[mmm4444bot]

8/3 of 27

Does this mean 8/3 is divided?

Yes, but you do not need to do that division.

Write the whole number 27 in rational form: 27/1.

\(\displaystyle \dfrac{8}{3} \times \dfrac{27}{1}\)

Do you see the cancellation to do, before multiplying these two fractions together? :cool: