Simplifying 2/5 + 3/8 In Simplest Form

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Adding fractions can be a bit tricky, but with the right steps, you can simplify them easily. Let's dive into simplifying 2/5 + 3/8.

Understanding the Problem

When adding fractions, we need to have the same denominator. The denominator is the number below the line in a fraction. In this case, we have 5 as the denominator for the first fraction (2/5) and 8 as the denominator for the second fraction (3/8).

Step 1: Finding the Least Common Multiple (LCM)

To add these fractions, we need to find the least common multiple (LCM) of 5 and 8. The LCM is the smallest number that both 5 and 8 can divide into evenly. To find the LCM, we can list the multiples of each number:

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40 Multiples of 8: 8, 16, 24, 32, 40

As we can see, the first number that appears in both lists is 40. Therefore, the LCM of 5 and 8 is 40.

Step 2: Converting Fractions to Have the Same Denominator

Now that we have the LCM, we can convert both fractions to have a denominator of 40.

For the first fraction (2/5), we need to multiply the numerator (2) and the denominator (5) by 8 to get a denominator of 40:

2/5 = (2 × 8) / (5 × 8) = 16/40

For the second fraction (3/8), we need to multiply the numerator (3) and the denominator (8) by 5 to get a denominator of 40:

3/8 = (3 × 5) / (8 × 5) = 15/40

Step 3: Adding the Fractions

Now that both fractions have the same denominator (40), we can add them:

16/40 + 15/40 = (16 + 15) / 40 = 31/40

Simplifying the Result

The result, 31/40, is already in its simplest form. However, we can express it as a mixed number or a decimal:

31/40 = 0.775 (as a decimal) 31/40 = 3/4 + 7/40 (as a mixed number, but not simplified)

In this case, the simplest form is the improper fraction 31/40.

Final Answer

The simplified form of 2/5 + 3/8 is 31/40.

We hope this explanation helps you understand how to simplify fractions when adding them. If you have any more questions or need further clarification, feel free to ask in the comments below!