Question

Find the sum. $$3 \frac{2}{7}+4 \frac{1}{2}$$

Short answer

The sum is \(7\frac{11}{14}\).

Step-by-step solution

Separate the Whole Numbers and Fractions

Firstly, let's divide this problem into smaller parts. Separate the whole numbers and the fractions so we add them separately. So, we'll have \(3 + 4\) for the whole numbers and \(\frac{2}{7} + \frac{1}{2}\) for the fractions.

Add the Whole Numbers

Add the whole numbers \(3 + 4 = 7\). So, the whole number part for the result is 7.

Finding Common Denominator

Before adding the fractions, make sure they both have the same denominator. For our case, find a common multiple of 7 and 2. The smallest common multiple is 14.

Convert to Like Fractions

Now we will convert \(\frac{2}{7}\) and \(\frac{1}{2}\) to fractions with 14 as the denominator. \(\frac{2}{7}\) is equivalent to \(\frac{4}{14}\) and \(\frac{1}{2}\) equates to \(\frac{7}{14}\). So, our equivalent fractions are \(\frac{4}{14} + \frac{7}{14}\).

Add the Fractions

We can now add the fractions \(\frac{4}{14} + \frac{7}{14} = \frac{11}{14}\). So, the fractional part of the result is \(\frac{11}{14}\).

Combine the Result

After that, combine or add the whole number sum and the fractional sum to get the final result. So, \(7 + \frac{11}{14} = 7\frac{11}{14}\).

Simplify

Lastly, we need to check if the fraction part can be simplified. However, in this case, \(\frac{11}{14}\) is already in the simplest form. So the final result remains \(7\frac{11}{14}\).