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!
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
Comments
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.
great post