To add and subtract fractions that have different bottom numbers (denominators), you can follow these simple steps:

Step 1: Find a Common Denominator

A common denominator is a number that both bottom numbers can divide into evenly. The least common multiple (LCM) is the smallest common denominator.

Example:
Let’s look at the fractions 2/3 and 1/4:

1. The denominators are 3 and 4.
2. The multiples of 3 are: 3, 6, 9, 12, 15...
3. The multiples of 4 are: 4, 8, 12, 16...
4. The smallest number that appears in both lists is 12.

Now we have our common denominator, which is 12.

Step 2: Change the Fractions

Next, we need to change the original fractions so they both have a denominator of 12.

For 2/3:

• To convert it, we multiply the top and bottom by 4 (because 3 x 4 = 12).
• Now it looks like this: (2 x 4)/(3 x 4) = 8/12.

For 1/4:

• Here, we multiply the top and bottom by 3 (because 4 x 3 = 12).
• Now it looks like this: (1 x 3)/(4 x 3) = 3/12.

Step 3: Add or Subtract the Fractions

Now that both fractions have the same bottom number, we can add or subtract them easily.

For example, to add 8/12 and 3/12:

• Just add the top numbers: 8 + 3 = 11.
• So, 2/3 + 1/4 = 11/12.

Step 4: Simplify if Needed

If the top number and bottom number can both be divided by the same number, you can simplify. But in this case, 11/12 is already in its simplest form.

And that’s it! Now you know how to add and subtract fractions with different denominators!