Adding Fractions: 6/10 + 2/3
When it comes to adding fractions, we need to follow certain rules to get the correct result. In this article, we will learn how to add the fractions 6/10 and 2/3.
Step 1: Find the Least Common Multiple (LCM)
To add fractions, we need to find the least common multiple (LCM) of the denominators. The denominators of our fractions are 10 and 3. To find the LCM, we need to list the multiples of each number:
Multiples of 10: 10, 20, 30, 40, 50, ... Multiples of 3: 3, 6, 9, 12, 15, ...
The first number that appears in both lists is 30. Therefore, the LCM of 10 and 3 is 30.
Step 2: Convert the Fractions
Now that we have the LCM, we can convert both fractions to have a denominator of 30:
6/10 = (6 × 3)/(10 × 3) = 18/30 2/3 = (2 × 10)/(3 × 10) = 20/30
Step 3: Add the Fractions
Now that both fractions have the same denominator, we can add them:
18/30 + 20/30 = (18 + 20)/30 = 38/30
Step 4: Simplify the Result
We can simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 38 and 30 is 2, so we can simplify the fraction as follows:
38/30 = (38 ÷ 2)/(30 ÷ 2) = 19/15
The Final Answer
Therefore, the result of adding the fractions 6/10 and 2/3 is 19/15.
