Solving the Fraction Problem: 2/3 + 3/4
In this article, we will tackle the problem of adding two fractions: 2/3 and 3/4. Fractions can be intimidating, but with the right steps and a clear understanding of the concept, we can easily solve this problem.
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 in this case are 3 and 4. To find the LCM, we need to list the multiples of each number:
Multiples of 3: 3, 6, 9, 12, ... Multiples of 4: 4, 8, 12, 16, ...
The first number that appears in both lists is 12, so the LCM is 12.
Step 2: Convert the Fractions to Have the LCM as the Denominator
Now that we have the LCM, we need to convert both fractions to have 12 as the denominator.
2/3 = ?/12
To convert 2/3 to have a denominator of 12, we need to multiply both the numerator and the denominator by 4:
2/3 = (2 × 4)/(3 × 4) = 8/12
3/4 = ?/12
To convert 3/4 to have a denominator of 12, we need to multiply both the numerator and the denominator by 3:
3/4 = (3 × 3)/(4 × 3) = 9/12
Step 3: Add the Fractions
Now that we have both fractions with the same denominator, we can add them:
8/12 + 9/12 = (8 + 9)/12 = 17/12
The Final Answer
Therefore, the solution to the problem 2/3 + 3/4 is 17/12.
By following these steps, you should be able to add any two fractions with confidence. Remember to always find the least common multiple, convert the fractions to have the same denominator, and then add them together.
