Adding Fractions: A Comprehensive Guide to Solving 2 3/7 3/4
Welcome to our guide on adding fractions, where we will walk you through the process of solving the problem 2 3/7 3/4. This comprehensive guide will break down the steps required to find the sum of these two fractions, providing a detailed explanation and example to ensure you understand the concept fully.
Understanding Fractions and the Problem
Fractions are a fundamental part of mathematics, representing a portion of a whole. They consist of two numbers: the numerator (the top number) and the denominator (the bottom number). The problem at hand, 2 3/7 3/4, is a mixed fraction added to a simple fraction. Mixed fractions contain a whole number and a fraction, and this problem requires us to convert and find a common denominator to solve it accurately.
Step 1: Identifying the Common Denominator
The first step in solving 2 3/7 3/4 is to find a common denominator for the fractions. The common denominator is the smallest number that both denominators can divide into evenly. In this case, the denominators are 7 and 4. The least common multiple (LCM) of 7 and 4 is 28. This means we need to convert both fractions to have a denominator of 28.
Step 2: Converting Fractions to Common Denominators
Next, we convert the fractions 3/7 and 3/4 to fractions with a denominator of 28.
Contacting 3/7 to a Common Denominator
2 3/7 can be written as 2 12/28 because 3/7 is equivalent to 12/28 when converted to a fraction with a denominator of 28. Here's how we calculate it:3 × 4 12 (numerator) and 7 × 4 28 (denominator).
Contacting 3/4 to a Common Denominator
3/4 can be written as 21/28 because 3/4 is equivalent to 21/28 when converted to a fraction with a denominator of 28. Here's how we calculate it:3 × 7 21 (numerator) and 4 × 7 28 (denominator).
Now we have the fractions 12/28 and 21/28, both with the same denominator of 28.
Step 3: Adding the Fractions
With the fractions now having a common denominator, we can add them together.
The Equation
2 3/7 3/4 2 12/28 21/28
Performing the Addition
2 12/28 21/28 2 33/28
Since 33/28 is an improper fraction, we can convert it to a mixed number. 33/28 can be written as 1 5/28 (because 33 ÷ 28 1, remainder 5).
The Final Result
Therefore, 2 3/7 3/4 3 5/28.
The Final Answer
The sum of 2 3/7 and 3/4 is 3 5/28. This comprehensive guide has demonstrated the step-by-step process of solving similar problems, ensuring that you have a clear understanding of the concepts involved in adding fractions with different denominators.
Conclusion and Further Learning
Understanding how to add fractions is crucial for many areas of mathematics, from algebra to higher-level calculations. We hope you found this guide useful and that it helped you in solving similar problems. For further learning, consider exploring more examples and exercises, and if you have any more questions, feel free to ask! Happy learning!