# Tori has 1/2 pound of sugar in her cabinet. Her cake recipe calls for 2/10 of a pound of sugar. How many cakes can she make?

Mar 8, 2018

#### Answer:

Exactly $2.5$ cakes (or $2$ whole cakes if you need to round)

#### Explanation:

So Tori has $\frac{1}{2}$ pound of sugar and one cake calls for $\frac{2}{10}$ of sugar. All we have to do is divide the fractions to see how many cakes she can make.

How do you divide fractions? It's actually pretty easy. Here are our two fractions:
$\frac{1}{2} \div \frac{2}{10}$

Now all you have to do is flip the second fraction upside down to be the reciprocal and change the $\div$ sign to a $\times$ sign.
$\frac{1}{2} \textcolor{\mathmr{and} a n \ge}{\div} \frac{\textcolor{red}{2}}{\textcolor{b l u e}{10}}$ becomes

$\frac{1}{2} \textcolor{\mathmr{and} a n \ge}{\times} \frac{\textcolor{b l u e}{10}}{\textcolor{red}{2}}$

Now all you have to do is multiply the two top numbers (numerators) together and multiply the two bottom numbers (denominators) together. I changed the problem a little to make it more clear:
(1 xx 10)/(2 xx 2) = ?

$\frac{10}{4} = 2.5$

Tori can make exactly $2.5$ cakes, or $2$ whole cakes.

Mar 8, 2018

#### Answer:

She can make $\frac{5}{2} = 2.5$ cakes if she can make a half-recipe cake, or $2$ whole cakes with some sugar left over.

#### Explanation:

CountryGal answered first, and did a very nice job. I just wanted to share another method as an alternative.

Tori has $\frac{1}{2}$ pounds of sugar, but needs $\frac{2}{10}$ for each cake. We can convert $\frac{1}{2}$ into tenths: $\frac{5}{10}$.

Then we divide $\frac{5}{10}$ by $\frac{2}{10}$. We'll invert and multiply, as CountryGal did:

$\frac{5}{10} \times \frac{10}{2} = \frac{5}{\cancel{10}} \times \frac{\cancel{10}}{2} = \frac{5}{2} = 2.5$