Simplify 4 1/2 + 1 3/5 In Easy Steps

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Adding fractions with different denominators can seem daunting, but with a step-by-step approach, it's quite manageable. Let's simplify 4 1/2 + 1 3/5 in easy steps.

Step 1: Convert Mixed Numbers to Improper Fractions

To add these mixed numbers, we first need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.

4 1/2 can be converted to an improper fraction as follows: 4 × 2 + 1 = 9 So, 4 1/2 = 9/2

1 3/5 can be converted to an improper fraction as follows: 1 × 5 + 3 = 8 So, 1 3/5 = 8/5

Step 2: Find the Least Common Denominator (LCD)

To add these fractions, we need to find a common denominator. The least common denominator (LCD) is the smallest number that both denominators can divide into evenly.

The denominators are 2 and 5. The multiples of 2 are 2, 4, 6, 8, 10, and so on. The multiples of 5 are 5, 10, 15, 20, and so on. Therefore, the least common denominator is 10.

Step 3: Convert Fractions to Have the LCD

Now, we convert both fractions to have the denominator of 10.

9/2 = (9 × 5) / (2 × 5) = 45/10 8/5 = (8 × 2) / (5 × 2) = 16/10

Step 4: Add the Fractions

Now that both fractions have the same denominator, we can add them.

45/10 + 16/10 = (45 + 16) / 10 = 61/10

Step 5: Simplify the Result (Optional)

If the result is an improper fraction, we might want to simplify it by converting it back to a mixed number.

61/10 = 6 1/10

Final Answer

The simplified result of 4 1/2 + 1 3/5 is 6 1/10.

Takeaway

Adding fractions with different denominators requires converting them to have the same denominator, the least common denominator. By following these easy steps, you can simplify such additions with confidence.

What's your favorite way to simplify fraction additions? Share your thoughts or questions in the comments below!