Find the sum. Write your answer in simplest form.
$12+8 \frac{1}{7}$
The problem asks for the sum of the integer \(12\) and the mixed number \(8 \frac{1}{7}\). To solve this, we need to add the integer part of the mixed number to the integer \(12\), and then combine it with the fractional part. A mixed number like \(8 \frac{1}{7}\) can be represented as the sum of its integer part and fractional part, which is \(8 + \frac{1}{7}\).
We want to calculate the sum:
\[12 + 8 \frac{1}{7}\]
Using the definition of a mixed number, we can rewrite this as:
\[12 + \left( 8 + \frac{1}{7} \right)\]
By the associative property of addition, we can group the integer parts together:
\[(12 + 8) + \frac{1}{7}\]
Calculating the sum of the integers:
\[20 + \frac{1}{7}\]
This expression simplifies directly to the mixed number \(20 \frac{1}{7}\). Alternatively, this can be written as an improper fraction by multiplying the integer by the denominator and adding the numerator:
\[\frac{20 \times 7 + 1}{7} = \frac{140 + 1}{7} = \frac{141}{7}\]
However, \(20 \frac{1}{7}\) is generally considered the simplest form for a sum involving mixed numbers.
The sum of \(12\) and \(8 \frac{1}{7}\) is \(20 \frac{1}{7}\). This is our final result in simplest form.
\[\boxed{20 \frac{1}{7}}\]
Imagine you are baking cookies and have already prepared 12 batches of dough. Then, you decide to make an additional \(8 \frac{1}{7}\) batches using a different recipe. To find out the total number of batches, you would add the two quantities together. This skill of adding mixed numbers is essential for scaling recipes, managing inventory, or even in construction when measuring lengths that include whole units and fractions. Mastering simple arithmetic with mixed numbers ensures you can handle real-world measurements with ease.