Adding Mixed Numbers with Unlike Denominators
When adding mixed numbers with unlike denominators, we need to follow a step-by-step process to get the correct answer. Let's take the example of 1 2/3 + 2 1/4.
Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert both mixed numbers to improper fractions.
1 2/3 = (3 + 2)/3 = 5/3
2 1/4 = (8 + 1)/4 = 9/4
Step 2: Find the Least Common Multiple (LCM)
To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 3 and 4.
The multiples of 3 are: 3, 6, 9, 12, ... The multiples of 4 are: 4, 8, 12, ...
The least common multiple is 12.
Step 3: Convert to Equivalent Fractions
Now, we need to convert both fractions to equivalent fractions with the LCM as the denominator.
5/3 = (5 × 4)/(3 × 4) = 20/12
9/4 = (9 × 3)/(4 × 3) = 27/12
Step 4: Add the Fractions
Finally, we can add the fractions:
20/12 + 27/12 = 47/12
Step 5: Simplify the Fraction (Optional)
If possible, we can simplify the fraction:
47/12 = 3 11/12
And that's the answer! 1 2/3 + 2 1/4 = 3 11/12.
