adding and subtracting fractions with unlike denominators
Simply start writing all the multiples of both denominators, beginning with the numbers themselves. For example: Multiples of 4 are 4, 8, 12, 16, and so on (because 1 × 4=4, 2 × 4=8, 3 × 4=12, 4 × 4=16, etc.). The multiples of 6 are 6, 12, …-- wait, stop! That's the number we're looking for, 12, because it's the first one that appears in both lists of multiples. It's the least common multiple, which we'll use as our least common denominator.
Now that we have our least common denominator, we can make equal like fractions by multiplying the numerator and denominator of each fraction by the factor needed. We multiply 3/4 by 3/3, since 3 times 4 is 12, and we multiply 1/6 by 2/2, since 2 times 6 is 12. This gives the equal like fractions 9/12 and 2/12. Now we can add the numerators, 9 + 2, to find the answer, 11/12. 11/12 is its simplest form, because we cannot divide it by 2 evenly and 11 is a prime number.
Adding and subtracting fractions with unlike denominators involves the following steps:
Step 1: Find a common denominator.
To add or subtract fractions, the denominators must be the same. Find the least common multiple (LCM) of the denominators. This will give you a common denominator.
Step 2: Convert fractions to the common denominator.
To convert each fraction to the common denominator, you need to scale both the numerator and denominator by the same factor. Multiply the numerator and denominator of each fraction by the necessary factors to obtain the common denominator.
Step 3: Perform the addition or subtraction operation.
Once you have the fractions with the common denominator, you can add or subtract the numerators while keeping the denominator the same.
Step 4: Simplify (if needed).
If the resulting fraction can be simplified, divide the numerator and denominator by their greatest common divisor to simplify it.
Let's look at an example to illustrate the steps:
Example: Add 1/4 and 3/8.
Step 1: Find a common denominator.
The least common multiple (LCM) of 4 and 8 is 8. So, the common denominator is 8.
Step 2: Convert fractions to the common denominator.
To convert 1/4 to the common denominator of 8, multiply both the numerator and denominator by 2:
1/4 * (2/2) = 2/8
To convert 3/8 to the common denominator of 8, no conversion is necessary.
Step 3: Perform the addition operation.
Add the numerators while keeping the denominator the same:
2/8 + 3/8 = 5/8
Step 4: Simplify.
In this case, the resulting fraction 5/8 is already in its simplest form.
Therefore, 1/4 + 3/8 = 5/8.