Question

A meatloaf recipe calls for `7/8` cup of breadcrumbs for the loaf and the topping. If `3/4` is used for the loaf, what fraction of a cup used for the topping?

Answer 1

`\frac{1}{8}` of a cup of breadcrumbs will be used for the topping.

Explanation:

To find what fraction is used for the topping, we need to subtract the fraction used for the loaf from the total amount of breadcrumbs:

`color(red)(\text{Total breadcrumbs})-color(blue)(\text{part used for loaf})=color(green)(\text{part used for topping})`

We know two of those values, which we can plug in:

`color(red)(\frac{7}{8})-color(blue)(\frac{3}{4})=color(green)(\text{part used for topping})`

In order to subtract fractions, we need a common denomator. Here, we can multiply the blue fraction by `\frac{2}{2}` to get a common denominator of `8`:

`color(red)(\frac{7}{8})-color(blue)(\frac{3\times 2}{4\times 2})\quad\rightarrow\quad color(red)(\frac{7}{8})-color(blue)(\frac{6}{8})`

Now we can subtract the fractions:

`color(green)(\frac{1}{8})=color(green)(\text{part used for topping})`