There are problems in which you need to add mixed numbers. For example, to find the value of the expression . To solve this example, **you need to add the whole and fractional parts separately**.

First, let's write down the mixed numbers in expanded form:

Apply the combinative law of addition. Group the whole and fractional parts separately:

Let's calculate the integers: 2 + 3 = 5. In the main expression, replace the expression in parentheses (2 + 3) with the resulting five:

Now let's calculate the fractional parts. This is the addition of fractions with different denominators. We already know how to add such fractions:

We got . Now in the main expression replace the fractional parts with the resulting fraction .

Now let's collapse the resulting mixed number:

Thus, the value of the expression is . Let's try to represent this solution in the form of a picture. If you add three whole pizzas and an eighth to two whole pizzas and a half, you get five whole pizzas and five eighths of pizzas:

Examples like this need to be solved quickly, without stopping for details. If we were in school, we would have to write down the solution to this example as follows:

If you see such a short solution in the future, don't be frightened. You already understand where it came from.

**Example 2.** Find the value of the expression

Let's write the mixed numbers in expanded form:

Let's group the integers and fractions separately:

Let's calculate the integers: 5 + 3 = 8. In the main expression, replace the expression in parentheses (5 + 3) with the resulting number 8

Now let's calculate the fractional parts:

We obtained a mixed number of . Now replace the expression in parentheses in the main expression with the resulting mixed number

We got the expression . In this case, the number 8 must be added to the integer part of the mixed number . To do this, the mixed number can be temporarily expanded to make it clearer what to add to what:

Let's add the whole parts. We get 9

We wrap up the finished answer:

Thus, the value of the expression is .

The complete solution of this example is as follows:

There is a universal rule for solving such examples. It looks like this:

**To add up mixed numbers, you have to:**

**reduce the fractional parts of these numbers to a common denominator;****perform addition of integers and fractions separately.**

**If adding fractions results in an improper fraction, isolate the integer part of the fraction and add it to the resulting whole.**

The use of ready-made rules is acceptable if the essence of the topic is fully understood. A formulaic solution, looking at other similar examples, leads to errors that take extra time to find. Therefore, it is more reasonable to understand the topic first, and then use a ready-made rule.

**Example 3.** Find the value of the expression

Let's use a ready-made rule. Let's reduce the fractional parts to a common denominator, then add the whole and fractional parts separately:

2. If you find an error or inaccuracy, please describe it.

3. Positive feedback is welcome.