Fraction of a fraction word problem

A problem about fraction of a fraction...

The sixth-graders have a fundraieser. They raise enough money to reach 7/8 of their goal. Nikki raises 3/4 of this money. What fraction of the goal does Nikki raise?

The picture below shows first of all 7/8. Nikki raises 3/4 of this goal. We need to find 3/4 of 7/8.

It's not easy to directly see what is 3/4 of 7/8. So to do that, I divide each 1/8 piece into four pieces, and then color three of the four. That way I color 3/4 of each of the seven eighths.

Of course, those tiny pieces are now 1/32 parts. I have colored 3 x 7 = 21 of them. So, the colored part represents the fraction 21/32.

This problem is also simple to solve without a picture, if you understand what is asked. To find 3/4 of 7/8, you simply multiply those two fractions. The word "of" translates into MULTIPLICATION in fraction math!

 3       7      21
---  x  --- =  ----
 4       8      32


Unknown said…
You can get clear solution for the most complex problems by utilizing algebra help.
Tracy said…
I like the graphical way you teach fractions!
Denise said…
That seems like the hard way to do it. I would rather use the "pan of brownies" model with a large rectangle representing one whole unit (pan).

Cut eighths vertically and remove one slice (or color 7 slices). Then cut fourths horizontally, to find out what 3/4 of those slices would be.

Because of the rectangular structure of the diagram, it's easy to see where the rule for multiplying fractions comes from: The total number of pieces in the whole pan is 4x8, and the section we are interested in has 3x7 of those pieces.
Brian Atice said…
They can really help those who don't really understand the concept of finding a fraction of a fraction. That's how I was taught when I was younger and it seems to be a big help in teaching others. Great post.
Mr hesham said…
thank you for the picture
great post
Mr. Insanium said…
Very innovative way for teaching fractions, thankyou for this.
Anonymous said…
It is quite easy to see and understand what is happening here, as well as guiding a student to see what is happening as well. But what happens when a student is given problems and they can't remember the steps, or they don't fully understand the the meaning behind these steps? What is the best way to explain to a struggling student that this is like taking 7/8x3/4?

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