Finding Common Ground: Adding Fractions

In math, the denominator (the bottom number) tells us the 'size' or 'name' of the fraction pieces. If you try to add $\frac{1}{2}$ and $\frac{1}{4}$, it's like trying to add 1 apple and 1 orange—you can't just say you have 2 'apples.' To add or subtract fractions, the pieces must be the same size. This means the denominators must be identical. When they aren't, we have to find a Common Denominator.

To make the denominators the same, we find the Least Common Multiple (LCM). This is the smallest number that both denominators can divide into perfectly. For example, if your denominators are $3$ and $4$, you list their multiples: - Multiples of $3$: $3, 6, 9, 12, 15...$ - Multiples of $4$: $4, 8, 12, 16...$ The first number they both share is $12$. That is your new Common Denominator!

Once you have the LCM, you must change your fractions to match it. But there is a Golden Rule: Whatever you do to the bottom, you must do to the top. If you multiply the denominator by $3$ to get to your LCM, you must also multiply the numerator by $3$. This keeps the fraction's value the same, even though it looks different. These are called Equivalent Fractions.

Now that the denominators match, you are ready for the final step! Simply add or subtract the numerators (the top numbers) and keep the denominator exactly the same. Never add the denominators together! If you have $8$ twelfths and add $3$ twelfths, you simply have $11$ twelfths.