Question

When Jess makes cupcakes she requires a ratio of sugar to flour of 2:5 if Jessica uses half a cup of sugar for one of her bathes how much flower does she need

Answer 1

sugare:flour=2:5
if sugar is 1/2 we need to find flour

\[\frac{ sugar }{ flour }=\frac{ 2 }{ 5 }=>\frac{ 1 }{ 2\times flour }=\frac{ 2 }{ 5 }\]flour=5/4

Answer 2

You can think of this as a unit conversion:

\[2 \text{ parts sugar} = 5 \text{ parts flour}\]or\[\frac{2\text{ parts sugar}}{5\text{ parts flour}} =1\]or\[\frac{5\text{ parts flour}}{2\text{ parts sugar}}=1\]

Now you can multiply either an amount of flour or sugar by the appropriate fraction (the one that has flour or sugar in the denominator respectively) to find the appropriate amount to use for the other ingredient.

For example, if she uses 2 cups sugar:

\[2\text{ cups sugar}*\frac{5 \text{ cups flour}}{2\text{ cups sugar}} = 5\text{ cups flour}\]
Or maybe she uses a 10 pound bag of flour, and needs to know how much sugar to use:
\[10 \text{ pounds flour}*\frac{2 \text{ pounds sugar}}{5\text{ pounds flour}} = 4\text{ pounds sugar}\]