How do you add mixed numbers with different denominators? Adding mixed numbers with different denominators can be a bit tricky, but with the right approach, it can be broken down into manageable steps. Mixed numbers consist of a whole number and a fraction, and when the denominators of the fractions are different, you need to find a common denominator before you can add them together. In this article, we will explore the process of adding mixed numbers with different denominators and provide you with a clear, step-by-step guide to make the process easier to understand.
In the first step, identify the mixed numbers you need to add. For example, let’s say we have the following mixed numbers:
3 1/4 + 2 3/8
To add these mixed numbers, you must first convert the whole numbers into fractions with the same denominator as the fractions. In this case, the denominator is 8, since 3 1/4 and 2 3/8 both have fractions with a denominator of 4 and 8, respectively. To convert the whole numbers, multiply them by the denominator of the fractions and add the numerator:
3 1/4 = 3 8/8 + 1/4 = 24/8 + 1/4
2 3/8 = 2 8/8 + 3/8 = 16/8 + 3/8
Now that both mixed numbers have the same denominator, you can add the whole numbers and the fractions separately:
(24/8 + 1/4) + (16/8 + 3/8) = (24 + 1 + 16 + 3) / 8 = 44/8
Next, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 44 and 8 is 4:
44/8 = (44 ÷ 4) / (8 ÷ 4) = 11/2
Finally, convert the improper fraction back into a mixed number. Since the numerator (11) is greater than the denominator (2), you can divide the numerator by the denominator to get the whole number and the remainder as the numerator of the fraction:
11/2 = 5 1/2
So, the sum of the mixed numbers 3 1/4 and 2 3/8 is 5 1/2.
In summary, adding mixed numbers with different denominators involves the following steps:
1. Convert the whole numbers into fractions with the same denominator as the fractions.
2. Add the whole numbers and the fractions separately.
3. Simplify the resulting fraction by dividing both the numerator and the denominator by their GCD.
4. Convert the improper fraction back into a mixed number.
By following these steps, you can successfully add mixed numbers with different denominators and improve your understanding of fraction addition.
