What Is The Sum Of 2 5 And 2 4

Addingfractions like 2/5 and 2/4 requires finding a common denominator and combining the numerators. Let's break down this process step-by-step to understand the sum thoroughly.

Introduction When faced with adding fractions such as 2/5 and 2/4, many people feel uncertain. The key lies in understanding the fundamental principles of fraction addition. This article will guide you through the complete process, ensuring you grasp not only the solution but also the underlying concepts. The sum of 2/5 and 2/4 is 9/10, but let's explore why this is the case and how to arrive at it methodically.

Steps to Add 2/5 and 2/4

1. Identify the Denominators: The denominators are 5 and 4. These are the numbers below the fraction bars.
2. Find the Least Common Multiple (LCM): To add fractions, the denominators must be the same. The LCM of 5 and 4 is 20, as 20 is the smallest number divisible by both 5 and 4.
3. Convert Each Fraction: Rewrite both fractions with the common denominator of 20.
   • For 2/5: Multiply both the numerator and denominator by 4 (since 5 × 4 = 20). This gives (2 × 4) / (5 × 4) = 8/20.
   • For 2/4: Multiply both the numerator and denominator by 5 (since 4 × 5 = 20). This gives (2 × 5) / (4 × 5) = 10/20.
4. Add the Numerators: Now that both fractions have the same denominator (20), add the numerators: 8 + 10 = 18. The new fraction is 18/20.
5. Simplify the Result: The fraction 18/20 can be simplified. Both 18 and 20 are divisible by 2. Dividing both by 2 gives (18 ÷ 2) / (20 ÷ 2) = 9/10.

Therefore, the sum of 2/5 and 2/4 is 9/10.

Scientific Explanation Fractions represent parts of a whole. Adding fractions is essentially combining these parts, but only when they refer to the same whole. The denominator indicates the size of each part (e.g., fifths or fourths), while the numerator indicates how many of those parts are being considered. To combine parts of different sizes (different denominators), we need a common size (common denominator). This is achieved by finding the LCM of the denominators, which allows us to express each fraction in terms of the same smaller parts. Adding the numerators then tells us the total number of these smaller parts. Finally, simplifying the resulting fraction ensures it's expressed in its most basic, understandable form.

FAQ

• Q: Can I add fractions with different denominators directly?
  A: No. You cannot add fractions like 2/5 and 2/4 directly because the parts they represent are different sizes. The denominators must be the same.
• Q: Why do we find the Least Common Multiple (LCM)?
  A: The LCM provides the smallest common denominator that allows both fractions to be expressed with the same sized parts, making addition possible.
• Q: What if the fractions are already simplified?
  A: Simplification doesn't prevent you from adding them. You still need a common denominator to combine them. The simplification happens after the addition.
• Q: Can I use any common denominator, not just the LCM?
  A: Yes, you can use any common multiple of the denominators (like 40, 60, etc.), but the LCM results in the simplest intermediate fraction (18/20 in this case), which makes the final simplification step easier.
• Q: How do I know if a fraction is simplified?
  A: A fraction is simplified when the numerator and denominator have no common factors other than 1. For example, 9 and 10 share no common factors, so 9/10 is simplified.

Conclusion Understanding how to add fractions like 2/5 and 2/4 is a fundamental mathematical skill. By finding a common denominator (the LCM), converting each fraction, adding the numerators, and simplifying the result, you arrive at the correct sum of 9/10. This process ensures accuracy and builds a strong foundation for tackling more complex fraction operations in the future. Remember, the key is recognizing the need for a common base before combining the parts.