 antennense

2022-07-07

Subtracting or Multiplying Fractions $\frac{3}{4}-\frac{1}{2}$
This is the given scenario to help visualize the problem at hand. A bird feeder is filled with $\frac{3}{4}$ of a full bag of seeds. The birds ate $\frac{1}{2}$ of what was in the bird feeder. What fraction of a full bag of bird seed is left in the bird feeder?
The previous scenario involved the same numbers but it asked what fraction of a full bag of bird seed were eaten. I was able to concluded that $\frac{3}{8}$ of the full bag of seeds was eaten. You are not able to use the formula: $\frac{3}{4}-\frac{1}{2}$ on this scenario because you are taking fractions of each other, not just the whole bag of seeds.
Does that justification sound correct? With that justification, how could I solve the question that is asking for the fraction of a full bag of bird seed left in the feeder? Could I use $\frac{3}{4}-\frac{1}{2}$ to answer that? I know that $\frac{3}{4}-\frac{1}{2}=\frac{1}{4}$ but that is not seeming like a correct answer to the scenario. Please help me, I don't completely understand this. SweallySnicles3

Expert

Well the important thing, when dealing with fractions of stuff, is not just the fraction itself but what the fraction is of. $\frac{1}{2}$ of the distance to your closest library is far less than $\frac{1}{2}$ of the distance to the moon (I hope).
In this assignment, you've got $\frac{3}{4}$ of a bag of seeds on the feeder, and half of that is eaten. That means the birds eat $\frac{1}{2}$ (a half $=0.5=50$%) of what's in the feeder, not $\frac{1}{2}$ of the whole bag, hence $\frac{3}{4}×\frac{1}{2}=\frac{3}{8}$. Simple subtraction won't give the correct result because the two fractions are of different things: $\frac{1}{2}$ is a fraction of the seeds on the feeder while $\frac{3}{4}$ is a fraction of the entire bag of seeds.

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