# How many 1/3 cups do you need to make 1/2 cup?

Oct 23, 2016

one and a half $\frac{1}{3}$ cups make $\frac{1}{2}$ cup

#### Explanation:

We need to figure out how much more than $\frac{1}{3}$ cup is $\frac{1}{2}$ cup. That translates to this equation:
$\frac{1}{3} + x = \frac{1}{2}$

if we subtract $\frac{1}{3}$ from both sides we get:
$x = \frac{1}{2} - \frac{1}{3}$

In order to subtract or add fractions we need to make the denominators (the bottom parts) of both fractions equal to each other. In order to do that we find the Least Common Multiple between them. In this case between 2 and 3. It is 6, which is 2 times 3. Now we multiply the bottom and top of each fraction by the number in that multiplication above that is missing to get to 6, like this:

$x = \frac{1 \cdot 3}{2 \cdot 3} - \frac{1 \cdot 2}{3 \cdot 2}$

Notice that we multiply the $\frac{1}{2}$ by 3 in the top and bottom because we need 3 to make 2 time something equal to 6, and that we multiply the $\frac{1}{3}$ by 2 in the top and bottom for the same reason,

Once we make those multiplications we get:
$x = \frac{3}{6} - \frac{2}{6}$

$x = \frac{1}{6}$

We can see from the previous calculations that $\frac{1}{3}$ is equal to $\frac{2}{6}$, and that $\frac{1}{6}$ is half of $\frac{2}{6}$, so, in order to make $\frac{1}{2}$ cup you need a whole $\frac{1}{3}$ cup plus half of it.