Adding Mixed Numbers with Different Denominators
In this article, we will learn how to add mixed numbers with different denominators, specifically 2 1/6 + 1/4 as a fraction.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 2 1/6 is a mixed number where 2 is the whole number part and 1/6 is the fraction part.
Adding Mixed Numbers with Different Denominators
When adding mixed numbers with different denominators, we need to follow certain steps to ensure that we get the correct result.
Step 1: Convert the mixed numbers to improper fractions
To add mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
For 2 1/6, we can convert it to an improper fraction by multiplying the whole number part by the denominator and then adding the numerator:
2 × 6 = 12 12 + 1 = 13
So, 2 1/6 = 13/6
For 1/4, it is already a fraction, so we don't need to convert it.
Step 2: Find the Least Common Multiple (LCM) of the denominators
The next step is to find the LCM of the denominators, which are 6 and 4. The LCM of 6 and 4 is 12.
Step 3: Convert the fractions to have the LCM as the denominator
Now, we need to convert the fractions to have the LCM as the denominator.
For 13/6, we can convert it to:
(13 × 2) / (6 × 2) = 26/12
For 1/4, we can convert it to:
(1 × 3) / (4 × 3) = 3/12
Step 4: Add the fractions
Now that we have the fractions with the same denominator, we can add them:
26/12 + 3/12 = 29/12
Step 5: Simplify the fraction
Finally, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 29 and 12 is 1, so the simplified fraction is:
29/12
Therefore, 2 1/6 + 1/4 as a fraction is equal to 29/12.
